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A meta-interaction model for designing cellular self-organizing systems
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A meta-interaction model for designing cellular self-organizing systems
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A META-INTERACTION MODEL FOR DESIGNING CELLULAR SELF-ORGANIZING SYSTEMS by Winston Wen Chiang A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) August 2012 Copyright 2012 Winston Wen Chiang ii Acknowledgements First and foremost, I am deeply grateful to my research advisor and mentor, Yan Jin, who has supported me throughout my thesis. I sincerely appreciate all of the patience and knowledge he has given me. Without his support, this thesis would not have been completed. I am indebted to him not only for his research guidance, but also for helping me grow as a person. I express my gratitude to the USC Department of Mechanical engineering, but in specific the advisors Samantha Graves, Marrietta Penoliar, April Mundy, Silvana Martinez-Vargas, and also Lizsl DeLeon (CS dept.) who were always willing to lend a helping hand. I especially thank Professors Henryk Flashner and Firdaus Udwadia. They have always had an open door to give me further advice along the way. The coursework I completed under them also greatly impacted the development of this thesis. The time I spent with them aided the development of my personal philosophy. Additionally, I must thank the professors who served on my committees, Henryk Flashner, Eva Kanso, Satwindar Sadhal, Ari Requicha, and Yong Chen, who helped criticize and reinforce my thesis. I am also grateful to the financial support from the Viterbi Fellowship provided by the Viterbi School of Engineering. Thank you to the instructors I worked with as a TA, Yen-Lin Han, Jerry Chen, and Charles Radovich. Along the way, I was blessed with great research colleagues, who have worked and played with me in the office during these past years. To Chang Chen who started and finished in parallel with me, as our research journey shared similar paths, yet he always seemed to lead the way; To Jon Sauder with whom stimulating scientific and iii philosophical discussions were prolific and a welcomed procrastination tool; To the preceding lab mates George Zouein and Majid Yahyaei who initially guided us and led the group's research; and to younger lab mates Cherry Liu, Newsha Khani, James Human, and Robert Fletcher who will continue the great work of the group; thank you for putting up with me through the years. I will always remember sharing the rollercoaster of PhD life with you and especially the chase for free food. I also thank all of the friends, students and fellow researchers, of whom there are too many to name, that have both directly and indirectly supported me through the years. All of you have helped shape my experience, and there is no value without the people I had met. The most important thing is not about what you are doing, or where you are, but who you are with. All have you have created the value that makes the journey worth it. And finally my sincerest gratitude to my family: sisters, cousins, aunts and uncles, but especially my parents Dalen and Ru-Fang Chiang. Obviously, without them, nothing I can do is possible. Every achievement I may accomplish is attributed to them. I am an especially difficult son that they have always supported and continually loved. Thank you for your faith and unlimited love. To you, this thesis is dedicated. iv Table of Contents ACKNOWLEDGEMENTS ........................................................................................ i LIST OF FIGURES ................................................................................................. vi ABBREVIATIONS .................................................................................................. ix ABSTRACT .............................................................................................................. x CHAPTER ONE: INTRODUCTION ....................................................................... 1 1.1 BACKGROUND AND MOTIVATIONS ............................................................................. 1 1.1.1 Advantages ................................................................................................................................... 5 1.1.2 Applications ................................................................................................................................. 7 1.2 RESEARCH STATEMENT.............................................................................................. 8 1.2.1 Research Issues .......................................................................................................................... 10 1.2.2 Research Objectives ................................................................................................................... 11 1.3 THESIS OVERVIEW ................................................................................................... 13 CHAPTER TWO: RELATED WORK ................................................................... 15 2.1 INTRODUCTION......................................................................................................... 15 2.2 DESIGN METHODOLOGY .......................................................................................... 16 2.2.1 Systematic Design ...................................................................................................................... 16 2.2.2 Axiomatic Design ....................................................................................................................... 19 2.2.3 General Design .......................................................................................................................... 21 2.2.4 Conventional Design Limitations............................................................................................... 22 2.3 MULTI-AGENT ROBOTICS ........................................................................................ 22 2.3.1 Hardware Systems ..................................................................................................................... 23 2.3.2 Distributed Control Approaches ................................................................................................ 27 2.4 COMPLEXITY THEORY .............................................................................................. 30 2.4.1 Dynamical Systems, Self-Organization, and Emergent Behavior .............................................. 30 2.4.2 Global to Local Challenge ......................................................................................................... 32 2.4.3 Natural Systems ......................................................................................................................... 34 2.5 NEED FOR A NEW APPROACH ................................................................................... 38 CHAPTER THREE: A META-BEHAVIORAL MODEL APPROACH ................ 39 3.1 INTRODUCTION......................................................................................................... 39 3.1.1 Limitations of Classical Design Theory ..................................................................................... 40 3.1.2 Towards Complex Systems ......................................................................................................... 43 3.2 DESIGNING CELLULAR SELF-ORGANIZING SYSTEMS ............................................... 46 3.2.1 Gap in Design Knowledge ......................................................................................................... 47 3.2.2 The Demand-Supply Relationship of Complexity....................................................................... 51 3.2.3 Design Spectrum ........................................................................................................................ 54 3.2.4 Fundamental Change in Design Philosophy.............................................................................. 57 3.3 THE META-BEHAVIORAL MODEL APPROACH .......................................................... 58 3.3.1 Behavioral Based Design ........................................................................................................... 59 v 3.3.2 Interactive Behavioral Based Design ........................................................................................ 62 3.3.3 The Meta-Behavioral Model ...................................................................................................... 66 3.3.4 The Three Levels of Abstraction with Meta-Behavioral Design ................................................ 69 3.5 CONCLUDING REMARKS ........................................................................................... 73 CHAPTER FOUR: META-INTERACTION MODEL EVALUATION USING MULTI-AGENT SYSTEM SIMULATION ............................................... 76 4.1 INTRODUCTION......................................................................................................... 76 4.2 SYSTEM MODEL ....................................................................................................... 78 4.2.1 Individual Cell Model ................................................................................................................ 78 4.2.2 COARM Interactive Behavioral Model ...................................................................................... 80 4.2.3 COARM Meta-Interaction Model .............................................................................................. 83 4.3 SIMULATION ENVIRONMENT .................................................................................... 85 4.4 META-INTERACTION MODEL ANALYSIS .................................................................. 86 4.4.1 Flocking .................................................................................................................................. 107 4.4.2 Stability of Flocking Behavior ................................................................................................ 117 4.4.3 Searching ................................................................................................................................ 119 4.5 COARM BEHAVIORAL MODEL RELATIONSHIP FINDINGS ..................................... 123 4.6 CONCLUDING REMARKS OF MAJOR FINDINGS ....................................................... 125 CHAPTER FIVE: EXAMPLE APPLICATIONS USING THE COARM META-INTERACTION MODEL ......................................................... 128 5.1 INTRODUCTION....................................................................................................... 128 5.2 SEARCH-AND-SURROUND ....................................................................................... 129 5.2.1 Foraging: Search-and-Surround Extended............................................................................. 134 5.3 MISSILE GROUPING ................................................................................................ 138 5.4 MATERIAL FILL ...................................................................................................... 142 5.5 IMPLICATIONS AND CONCLUDING REMARKS.......................................................... 146 CHAPTER SIX: CONTRIBUTIONS AND FUTURE DIRECTION .................... 149 6.1 CONTRIBUTIONS ..................................................................................................... 149 6.2 FUTURE DIRECTIONS .............................................................................................. 153 BIBLIOGRAPHY ................................................................................................. 156 vi List of Figures FIGURE 1: POINTS OF DEPARTURE .................................................................................................................. 15 FIGURE 2: SYSTEMATIC DESIGN PROCESS ...................................................................................................... 17 FIGURE 3: FOUR DOMAINS OF AXIOMATIC DESIGN ........................................................................................ 20 FIGURE 4: EXAMPLE MULTI-AGENT ROBOTIC IMPLEMENTATIONS ................................................................ 26 FIGURE 5: NAGPAL'S ORIGAMI SHAPE LANGUAGE ......................................................................................... 32 FIGURE 6: CHEMICAL PATTERN SHAPE FORMATION ...................................................................................... 34 FIGURE 7: CRAIG REYNOLD'S BOIDS SIMULATION ......................................................................................... 35 FIGURE 8: DESIGN METHODOLOGY COMPARISON .......................................................................................... 45 FIGURE 9: CERTAINTY-DESIGN MATRIX ........................................................................................................ 48 FIGURE 10: EXTENDING THE ENVELOPE OF DESIGN PROCESSES .................................................................... 50 FIGURE 11: PROBLEM DEMAND CURVE ......................................................................................................... 52 FIGURE 12: SOLUTION SUPPLY CURVE ........................................................................................................... 53 FIGURE 13: CSO DEMAND SUPPLY ................................................................................................................ 54 FIGURE 14: DESIGN SPECTRUM: AUTOMATION .............................................................................................. 55 FIGURE 15: DESIGN SPECTRUM: DESIGN ENGINEERING ................................................................................. 55 FIGURE 16: DESIGN SPECTRUM: NATURAL PROCESS ..................................................................................... 56 FIGURE 17: DESIGN SPECTRUM: NATURE MIMICKING ................................................................................... 57 FIGURE 18: TARGETED CONFIGURATION FLOW ............................................................................................. 60 FIGURE 19: EMERGENT SYSTEM FROM COLLECTIVE BEHAVIOR .................................................................... 62 FIGURE 20: BEHAVIORS: INDEPENDENT AND INTERACTIVE ........................................................................... 64 FIGURE 21: PARAMETERIZATION OF INTERACTIVE BEHAVIORS ...................................................................... 65 FIGURE 22: EXAMPLE PARAMETRIC PROFILE VISUALIZATION ....................................................................... 68 FIGURE 23: META-INTERACTION MODEL PROCESS ........................................................................................ 70 FIGURE 24: THREE LAYERS OF ABSTRACTION TO THE META-INTERACTION MODEL ..................................... 73 FIGURE 25: DESIGN SPECTRUM: CSO ............................................................................................................ 75 vii FIGURE 26: LOCAL NEIGHBORHOOD OF A CELL .............................................................................................. 80 FIGURE 27: COARM PROFILE VISUALIZATION.............................................................................................. 84 FIGURE 28: RANDOMLY SELECTED INITIAL POSITIONS ................................................................................... 87 FIGURE 29: PURE COHESION .......................................................................................................................... 88 FIGURE 30: PURE AVOIDANCE ....................................................................................................................... 89 FIGURE 31: PURE RANDOMNESS .................................................................................................................... 90 FIGURE 32: DISORDER ENTROPY OF PURE INTERACTIVE BEHAVIORS .............................................................. 91 FIGURE 33: COHESION AND AVOIDANCE COMBINATION ................................................................................ 92 FIGURE 34: COMPARISON OF COHESION AND AVOIDANCE ............................................................................. 93 FIGURE 35: PURE COHESION PHASE PLANE PLOT OF 2 CELLS ......................................................................... 94 FIGURE 36: PURE AVOIDANCE PHASE PLANE PLOT OF 2 CELLS ....................................................................... 95 FIGURE 37: COHESION-AVOIDANCE COMBINATION PHASE PLANE PLOT OF 2 CELLS ....................................... 96 FIGURE 38: COHESION-AVOIDANCE COMBINATION SEPARATION DISTANCE COMPARISON ............................. 97 FIGURE 39: COHESION-ALIGNMENT COMBINATION ....................................................................................... 98 FIGURE 40: COHESION AND COHESION-ALIGNMENT COMBINATION RESULT COMPARISON ............................ 99 FIGURE 41: COHESION AND RANDOMNESS COMBINATION ........................................................................... 100 FIGURE 42: DISORDER ENTROPY FROM COHESION COMBINATIONS OF INTERACTIVE BEHAVIORS ................ 101 FIGURE 43: COHESION-AVOIDANCE AND ALIGNMENT COMBINATION RESULT COMPARISON ....................... 102 FIGURE 44: DISORDER ENTROPY OF COHESION AVOIDANCE AND ALIGNMENT ............................................ 103 FIGURE 45: COHESION-AVOIDANCE-ALIGNMENT COMBINATION WITH INCREASED ALIGNMENT ................. 104 FIGURE 46: COHESION-AVOIDANCE-ALIGNMENT-MOMENTUM COMBINATION ........................................... 105 FIGURE 47: DISORDER ENTROPY OF FLOCKING ............................................................................................ 106 FIGURE 48: STANDARD DEVIATION OF DIRECTION OVER 300 STEPS ............................................................. 108 FIGURE 49: COMPARISON OF PROFILES BASED ON MINIMUM STANDARD DEVIATION .................................... 109 FIGURE 50: PROFILES AT THE EDGE OF SYNCHRONIZED MOTION .................................................................. 113 FIGURE 51: TIME PERFORMANCE COMPARISON ............................................................................................ 114 FIGURE 52: PROFILES USED FOR PERFORMANCE COMPARISON ..................................................................... 115 viii FIGURE 53: FORAGING: TWO CONTRASTING LOCATIONS FOR A PASSIVE OBJECT .......................................... 120 FIGURE 54: SEARCH COMPARISON................................................................................................................ 122 FIGURE 55: SEARCH AND SURROUND CSO DESIGN PROCESS ...................................................................... 131 FIGURE 56: REPRESENTATIVE PROFILE FOR PHASES OF SEARCH-AND-SURROUND ........................................ 131 FIGURE 57: SEARCH-AND-SURROUND EXAMPLE .......................................................................................... 132 FIGURE 58: INITIAL SYSTEM STATE WITH EIGHT CIRCULAR CELLS, OBSTACLES, AND A PASSIVE OBJECT ...... 135 FIGURE 59: PURELY RANDOM SYSTEM WITHOUT COHESION, ALIGNMENT, OR AVOIDANCE ........................ 136 FIGURE 60: EIGHT CELLS MOVING A PASSIVE OBJECT ................................................................................... 137 FIGURE 61: PLANNING WITH UNCERTAINTY FOR MISSILE GROUPING .......................................................... 139 FIGURE 62: REPRESENTATIVE PROFILE FOR PHASES OF SEARCH-AND-SURROUND ........................................ 140 FIGURE 63: EXAMPLE FLIGHT OF 10 SELF-ORGANIZING MISSILES ................................................................. 141 FIGURE 64: PLANNING WITH UNCERTAINTY FOR MATERIAL FILL ................................................................ 143 FIGURE 65: 10-BY-10 GRID FOR MATERIAL FILL ........................................................................................... 144 FIGURE 66: REPRESENTATIVE PROFILE FOR PHASES OF SEARCH-AND-SURROUND ........................................ 144 FIGURE 67: PERCENTAGE OF VOIDS FILLED COMPARISON ............................................................................ 145 FIGURE 68: EXTENDING THE DESIGN ENVELOPE TOWARDS ARTIFICIAL NATURE ....................................... 153 ix Abbreviations A Alignment, a component of COARM BM Behavioral Model BBD Behavioral Based Design C Cohesion, component of COARM CM Cell Model COARM Cohesion-Avoidance-Alignment-Random-Momentum Behavioral Model CSO Cellular Self-Organizing FBD Form Based Design IBD Interactive Behavioral Based Design IBM Interactive Behavioral Model M Momentum, a component of COARM MAS Multi-Agent System MBM Meta-Behavioral Model MIM Meta Interaction Model O Avoidance, a component of COARM R Randomness, a component of COARM W Weight, the parametric variables in the Meta-Behavioral Model x Abstract The Cellular Self-Organizing (CSO) system takes the nature inspired biological processes of self-organization and emergence towards complex, multi-agent systems. Self-organization can be observed in many natural systems, and researchers hope to harness the biological advantages of simple individuals, versatile collective functionality, and robustness. The point in being cellular is to emphasize the simple nature of each agent and the idea of a large system population. A single simple cell may not be successful on its own, but a collective system of cells can be extremely adaptable and functional. Technological development is facing increased challenges as design engineers begin to tackle problem domains with greater uncertainty. Future engineered systems must be able to function in unpredictable environments such as deep ocean, rough terrain, and outer space while performing uncertain tasks like hazardous waste cleanup and search-and-rescue missions. CSO systems can provide the adaptability in order to manage uncertainties that traditional systems cannot. As the uncertainty of the problem domain increases, engineering design methods must be advanced in order to properly address the changing needs and constraints. This thesis details a new CSO approach inspired by natural phenomena in order to extend the design envelope towards an artificial nature. While natural systems had the luxury of evolution over millions of years, achieving bottom-up adaptability by design represents a major challenge to the systems engineering and design research community. Two fundamental issues must be addressed: one is the analysis problem of predicting the xi global emergence from local interactions; and the second is the design problem of compiling local rules based on a desired global function. The presented approach broadens the traditional design and re-design methods by utilizing the self-organization process exhibited in natural systems. The goal is to design systems that excel in unpredictable environments where it is impossible for the designer to conceptualize every possible contingency. The key is to focus on the behaviors of the system. This work suggests a meta-behavioral model based on cellular self-organization that can be used as a design approach towards CSO systems. Specifically, interactive behaviors are keyed in on as interaction is the intrinsic property of complexity, and thus adaptability. In this CSO framework, a system is composed of multiple mechanical (e.g., robotic) cells, which self-organize themselves through individual actions and mutual interactions. To deepen our understanding and provide design methods for the development of CSO, we focus on the relationship between local agent interactions and emergent collective system behavior. More specifically, a parametric approach centered upon interactive behaviors will be used to develop a Meta-Interaction Model (MIM) of the behavioral model of agent interactions. Using the parametric approach provides tunable dynamical variables towards managing collective behavior, leading to various desired global functions. Furthermore, parameterizing local behaviors provides an opportunity to analyze the relationship between different types of local interactions in addition to the relationship between the local interaction and the collective functionality. xii The MIM approach is used to design for applications with uncertainty by designing with uncertainty. Instead of designing single specific capabilities, the MIM method designs for emergent functional capacities. This is a fundamental change in design theory. By doing so, designers are trading deterministic functionality for self- organizing and emergent adaptability. The MIM technique can be used to manage adaptability by specifying interaction patterns of agents in a multi-agent system thus guiding the emergence of functional capacities. A simulation based study of the Cohesion-Avoidance-Alignment-Random- Momentum (COARM) Behavioral Model is completed in order to analyze the COARM meta-model. The study shows the increased complexity with the increased behavioral set. It also proves Alignment as the stabilizing simple behavior for collective synchronized motion, although not the only attractor for such collective behavior. Random behavior demonstrates the ability to handle task application uncertainty. Ultimately, the approach introduces a new design space based on behaviors. The space is created through the parameter variables that can be tuned to control system behavior. The simulation study specifically analyzes interactive behaviors. The resulting system's multi-functionality is demonstrated through different mechanical applications. The MIM approach provides a design framework for developing CSO systems. It gives top-down control over functional bottom-up organization. Moreover, in the future, it can easily lend itself as an outlet for other artificial intelligent means such as learning, evolutionary algorithms, and control feedback. 1 Chapter One: Introduction 1.1 Background and Motivations Designing complex, multi-agent systems has become a major challenge and research topic for engineering applications. Multi-robotic systems have gained increased interest in various fields and extensive research has been carried out on autonomous mobile robots. Much of the research on autonomous mobile robots is based on a single robot interacting with its environment but has been shifting towards many cooperative agents in the field. Furthermore, top-down explicit approaches have been dominant but bottom-up self-organizing approaches have been gaining recognition. Many artificial intelligence solutions to problems such as path planning and obstacle Avoidance have been proposed and tested. The main approach to autonomous robots involves an intelligent agent to construct a local representation of the environment through sensors, and then from the representation and perceived obstacles, generate an optimal collision-free path satisfying given constraints and conditions. Problems often encountered in autonomous navigation models are delay in the feedback information, sensor and actuator errors, and limited sensor range (Feng & Krogh, 1989). Due to the large amount of computation required to process the sensor data and solve the path finding algorithms, a delay is expected in obtaining the local map in addition to deciding on a strategy. Moreover, limited sensor range and correctness may cause uncertainties in the path planning and obstacle Avoidance result. These limitations are only amplified in multi-robotic systems. 2 There has been an increased interest in teams of multiple autonomous mobile robot systems due to their applicability in various applications in unknown and hazardous environments. Large populations of mobile robots have many advantages, especially when high reliability is required. Cellular multi-agent adaptive systems are envisioned to be dynamic, massively distributed, and deeply embedded networks of interacting components, or cells, which can provide robustness, adaptability, and versatility. These cells may be homogeneous, meaning all cells are equivalent, or heterogeneous. Just to clarify, the definition of an agent used here is an entity or computational process that senses the environment and acts on it. This work first addresses physical mobile entities, although many of the concepts may be used for non-physical entities or computational processes. In many engineering tasks and mission situations, a designer often cannot predict all possible function requirements and operation situations encountered by the system being designed. Examples of such application domains include mine sweeping, natural disaster search & rescue, planetary & ocean exploration, and missile flocking. The common theme within these applications is the uncertainty from unforeseen circumstances in either the operation environment or in the required functionality. Environment exploration is a major application of interest because unknown environments such as space planetary surface and the deep ocean are beyond the reach of direct human exploration. Another major difficulty from a design perspective is the increased complexity with the growing size of the system. As the system size increases, the dependencies 3 within the system multiply, which adds to the uncertainty in the system operation. Engineers may simply add components onto a system expecting for dependencies to only exist where designed, but may unplanned interdependencies often arise. Designers have to manage this extra uncertainty in addition to the uncertainty in task environment and functional demands. Traditionally, designers strip the complexity and attempt to simplify the system, but this ignores the inherent complexity from interdependencies that cannot be removed. Furthermore, complexity can be the source of the system's adaptability. Various multi-agent system approaches have been proposed, taking advantages of the flexibility and robustness of many interacting agents. Modular multi-agent systems actively alter their overall structure and inter-relationships, translating into great versatility. However, self-reconfiguration introduces a difficult planning problem as the number of modules (and degrees of freedom) in the system increases. Problems such as coordination of multiple manipulators, motion planning, and coordination of multi-robot systems are generally approached with a centralized controller that is often hierarchical. Until recently, most of the multi-robot systems have been fixed systems without autonomously moving elements Common solutions have employed central commands that process a network of sensors, utilize explicit cooperation algorithms, and then provide the signals for actuation of each component in the system; however, the constant exchange of data with the control center from the sensor nodes and back to the actuator nodes would constrain the performance and capabilities of the system. Moreover, as systems scale larger in population size, it is unrealistic to control each element individually through a central 4 controller. Complex coordination algorithms also can become unmanageable with scale. This method decreases the robustness due to redundancy because the system as a whole will critically fail if the single central command entity fails. Another approach to implementing multi-agent systems builds upon natural complex systems theory utilizing self-organization and emergence. These concepts are inspired by nature as engineers strive to take advantage of the robustness and adaptability exhibited in natural systems such as cellular processes, fish schooling, and locust swarms. The self-organization method would have a distributed system where cells only interact with their neighbors and individually decide their own actions. Self-organization research studies emergent structures from a global macro perspective, especially system properties that may not have been perceived from only the local micro view. Self-organization is the idea that individuals will organize based only on local rules and local communication. Emergence is the principle that unintuitive or unexpected global patterns will observably materialize from the interactions in the system. Self-organization and emergence are often coupled although technically, one can occur without the other. Both play a role in cellular, self-organizing systems, which can reconfigure their relationships, and thus their functionality, as either the external (environmental perturbations) or internal state (individual behavior) changes. This provides much inherent adaptability. Utilizing complex systems in the creation of artificial systems is inspired by the perseverance of natural systems. This work finds much inspiration in biological systems that are able to operate with minimal directed communication. The critical advantage of 5 collectively intelligent Cellular Self-Organizing (CSO) systems is their adaptability, i.e., the ability to persist through external and internal changes. The natural world exhibits many examples of adaptive systems that robustly adapt to both the external environment and to internal changes. In schools of fish, many fish are capable of moving as a single entity while they disperse to avoid predators and obstacles but quickly gather to reform the school. This collective behavior results from each fish applying a few simple behavior rules of separation and movement. At a deeper micro-level, cells with identical DNA combine to form complex structures. In the human immune system, white blood cells continuously patrol and protect the body in a principally distributed way. By relying on vast numbers of resource limited and unreliable cells, cellular systems achieve reliability even in cell death, varying scale, and uncompromising environments. 1.1.1 Advantages In some cases, the preprogrammed, deterministic organization will be the best design choice. But in many situations, the designer will prefer the adaptability advantages of CSO systems. Flexibility & Versatility – One of the key advantages is the ability to reconfigure and achieve multi-functionality. This allows the system to dynamically respond to multiple environments and changing tasks, especially unforeseen circumstances. Specialized robots will likely always be better at their one specific action, but for tasks that require flexibility, the specialized robots will not be able to complete the mission. 6 Reliability – The large number of similar agents provides redundancy such that the failure of a single cell does not destroy the effectiveness of the system since it is easily substituted by a working cell. In addition, with distributed control, there is no central commander that the system relies on. The failure of any single unit will not cause critical failure for the system. Another means by which complex systems maintain reliability has been termed degeneracy, which can be defined as multiple processes with identical consequences (Edelman & Gally, 2001). Basically, the ability to do the same thing with multiple processes for achieving the same function makes it unlikely that a single type of disruption can disable the whole system and all these different processes. Evolvability – The combination of versatility and reliability gives the system great adaptability to external (environment) and internal changes. Further adaptability can be achieved when the system can actually develop and grow new structures and behaviors, therefore functions. When the system is given the empowerment to create new functionality, it will become truly adaptable to unperceived circumstances as the system will actually grow and increase its functional space after deployment. Inexpensive Manufacturing – Due to the simple architecture of each individual cell, the cost of manufacturing is kept to a minimum. A self-organizing system can accomplish complex tasks with simple individual behaviors and components, requiring simple programming and simple communications. In addition, since each cell does not perform extensive processing or analysis, so complex software is not required. Since agents only 7 rely on a local neighborhood of communication, high power and high bandwidth communication hardware does not need to be integrated. Scaling – Complex adaptive systems are ideally scalability as a consequence that most processes are performed locally, at a lower cost. Because these systems are designed around the concept of massive population and distribution, they are theoretically scalable from medium teams to very large teams; however, realistically, there will be a lower and upper limitation to the resolution (population size) of the system. 1.1.2 Applications Autonomous systems are widely used, especially manufacturing robots used for wielding, riveting, painting, etc. These systems are “simple” since the environments and desired functions and component relationships are wholly understood and predictable. The task and task environment are easily deterministic, but what happens when the environment is continuously changing or unpredictable? What would happen if the designer cannot specifically define the exact function and interactions to be performed and the design space is difficult to identify? CSO system’s adaptability provides many advantages to traditional robotics in unknown environments because they can better respond to unforeseen circumstances. This advantage lends CSO systems to many different applications from a wide range including embedded wireless sensor networks to micro-cellular robotics. Further example application domains include mine sweeping, natural disaster search & rescue, planetary & ocean exploration, and missile flocking. The common theme within these applications 8 is the uncertainty from unforeseen circumstances in either the operation environment or in the required functionality. Environment exploration is a major application of interest because unknown environments such as space planetary surface missions and the deep ocean are beyond the reach of simple human exploration. In addition, robots can be utilized to more safely navigate hazardous environments such as mine sweeping and waste management. In a general sense, CSO systems are useful for search-type missions such as seeking information, search and rescue, or even search and destroy. Another general application is in mass entity movements where many objects must synchronously move like in bird flocking and fish schooling. Furthermore, emerging technologies are making it possible to produce large-scale multi-agent systems by bulk manufacturing tiny computing and sensing components. These components may act as individual cells in a collective swarm or as embedded agents in material items and the environment. This can lead to programmable materials that provide a multitude of functions from a generic form-factor. 1.2 Research Statement In order to achieve the full potential of CSO systems, the difficult challenge of intelligently managing the massive collection of independent cells must be addressed. Traditionally, robotic motion focuses on path planning of finding collision-free paths through the environment, but this quickly becomes too complex for existing algorithms when manipulating a multitude of independent units. As the number of cells increases, the difficulty of the planning problem increases. 9 It is difficult to characterize local rules and even simple compositions can have un-intuitive behavior. Many approaches have been developed to understand how global phenomena emerges from local interactions, but most follow an empirical approach where local rules are designed and the resulting systems are simulated in order to observe the emergent global dynamics. This trial-and-error approach is difficult to use as an engineering tool. Many researchers have focused on the re-configuration problem, which has two main parts: what are the functional configurations? And how does the system transition from one configuration to another? While it is possible to allow for a human operator to physically rearrange the cells, for physically remote or hazardous applications, such as space exploration, the system needs to have automatic reconfiguration. In addition, it is possible to initially design the system for only a set of different functional configurations, but this constrains the system's ability to truly adapt to unforeseen needs. How can the system determine sufficient, or even optimal, configurations to satisfy a task criterion and how can it achieve such configurations? The CSO approach does not focus on specific configurations, but allows configurations to emerge from self-organization. To guide this emergence, this thesis attacks the problem by focusing on the local interaction of the cells. To combine design with self-organizing systems, the goal is to understand both the forward and reverse problem of global-to-local compilation. The forward problem is how can the system take user specified goals for the collective system and automatically derive strategies at the 10 local agent level? The reverse problem is how to understand what emergent patterns arise from a set of simple rules bounding local interaction. 1.2.1 Research Issues This ambition can be broken down into several key research challenges: Research Issue 1: How do we design collectively intelligence multi-agents systems with adaptability? How does the design process change to design with complexity, the characteristic that provides adaptability? The main goal of this research is to develop design techniques for cellular and self-organizing systems. The critical advantage of CSO systems is their adaptability. The properties that grant the system adaptability need to be taken into consideration when proceeding through the design process. When completed, designers will have a better tool to identify and utilize the key properties required for developing CSO systems with adaptability. Research Issue 2: How do interactions of individuals affect collective behavior of the group? Can top-down functionality be achieved with bottom-up self- organization? How does one translate desired global functions into local interactions of the individuals? What are design variables that can characterize pattern dynamics, the rules governing cell behavior, in order to achieve collective functionality? To develop design tools, we must first gain insight into the global-to-local relationship in collectively intelligence systems. Specifically, this work is looking at the global-to-local behavior and how local rules of interactions will affect the 11 global behavior. Furthermore, characterizing and parameterizing local behavior will provide an opportunity to analyze the relationship between different types of local interaction in addition to the relationship between the local interaction and the collective functionality. Research Issue 3: How can a CSO system be implemented while maintaining simple agents and rules. How little can each individual know about the group, the global goal, the environment, and the other agents while still achieving collective functionality? A core motivation for this research is simplicity of the individuals. The intention is to maximize the simplicity of the individual agents and their functions. This means to minimize resource usage, computation, and persistent memory. Is it possible to achieve collective functionality without individuals modeling other agents or even being aware of what is the global goal? In a functional system, can each agent essentially be oblivious to individual desires, including their own, and collective desires? 1.2.2 Research Objectives The overall purpose of this research is to understand the relationship between local interactions of independent individuals and the collective functionality of the system in order to develop a new design approach to harness the effectiveness and reliability exhibited in self-organizing, biological systems. How can we design and synthesize artificial systems inspired by natural systems? The core objective of this research is to explore design techniques for complex systems with an emphasis on 12 adaptability. The result of this research is a method for the design of a cellular self- organizing system. Furthermore, the framework serves as a conceptual basis for the complex system design process. A system is also developed that implements the novel approach to distributed multi-agent design and control. To address the research issues as described, the work focuses upon the following objectives: Research Objective 1: To develop a parametric approach to model behaviors of individuals in CSO systems. Research Objective 2: To develop tools that can be applied to analyze the relationships between local self-organizing behaviors and global emergent effects of select CSO systems. Research Objective 3: To gain insights into how complex global patterns can arise from simple, self-organizing agents. Research Objective 4: To present a multi-functional artificial CSO system that utilizes identically programmed cells with a small neighborhood of locality for limited communication and no centralized information or global awareness. 13 1.3 Thesis Overview While natural systems had the luxury of over millions of years of bottom-up evolution, in our engineering world, achieving bottom-up adaptability by design represents a major challenge to the systems engineering and design research community. Two fundamental issues must be addressed: one is the analysis problem of predicting the global emergence from local interactions; and the second is the design problem of compiling local rules based on a desired global function. This research proposes a CSO approach to developing complex adaptive systems. In the CSO framework, a system is composed of multiple simple mechanical cells, which self-organize themselves through individual actions and mutual interactions. The CSO approach is inspired by natural processes and biology such as locust swarms, cellular processes, and collective animal behavior. It utilizes simple cells with simple rules but embraces system complexity. To deepen our understanding and provide design methods for the development of CSO systems, we introduce the Meta-Interaction Model (MIM) approach focusing on the relationship between local agent interactions and emergent collective system behavior. More specifically, a parametric approach centered upon Behavioral Based Design (BBD) will be used to develop a meta-model of the Behavioral Model (BM) of cell interaction. The approach can be used to manage adaptability by specifying interaction patterns of agents in a multi-agent system. Furthermore, parameterizing local behaviors provides an opportunity to analyze the relationship between different types of local interactions in addition to the relationship between the local interaction and the collective functionality. 14 In the proposed CSO system, each simple mechanical cell or agent usually cannot accomplish much by itself, but many cells organized properly can collectively achieve specified tasks. Global patterns will emerge from only local interactions between the individuals. Properly designed local rules of self-organization will result in useful emergent collective behaviors and functions and that by utilizing a behavioral approach focusing on interaction between cells, a CSO system of many agents can be designed with collective functionalities. Using the parametric approach provides tunable dynamical variables towards managing collective behavior, leading to various desired global functions. Before giving the details of the approach, first a literature review will be presented covering design methodologies, multi-agent robotics, and complexity science. Next, the challenges of the classical engineering approach towards complex systems are detailed, and then steps towards a new approach are discussed that will better harness the inherent advantages of complex systems. After that, the model for a self-organizing system is developed exhibiting the new design concepts. The Meta-Behavioral Model approach is presented and discussed, followed by a detailed description and discussion of simulation based case studies. Local rules for interaction are cultivated in order to provide collective functionality. To demonstrate the proposed strategy, simulation results are examined for various collective behaviors. Toy examples are used to analyze the collective behavior. Multifunctional application examples are then explored. Finally, the contributions are discussed along with future research directions. 15 Chapter Two: Related Work 2.1 Introduction This research utilizes self-organization for nature inspired systems in multi-agent robotic applications. The approach integrates theory from different research areas. This research departs from three major fields of research: Design Methodology, Multi-Agent Robotic systems, and Complexity. Figure 1: Points of Departure Within the design field, there are several classical engineering approaches that have become standard design practice. Much work has been undertaken in multi-agent Design Methodology Complexity & Self-Organization Multi-Agent Robotics 16 robotics, a subfield of multi-agent systems, especially in the hardware prototypes for modular reconfigurable robots. A major issue for multi-agent robotics is in distributed control approaches that scale well with the size of the entire system. While complexity science is not a new topic, it has recently gained Momentum as human engineered systems take inspiration from natural systems in order to harness the inherent robustness, reliability, and versatility exhibited by nature. Self-organization and emergence are major topics in complexity science and are not yet well-understood. 2.2 Design Methodology Engineering design theory and methodology is a process that all engineering disciplines must exercise in system development. Methodologies in Design Theory have a different focus than traditional science theory, which analytically observes nature in order to discover and describe the natural behaviors (Suh, 1990). Design Theory centers on processes humans can use to produce functional systems. Design methodology is a course of action for the design of technical systems. It includes strategies, rules, and principles to achieve various goals when designing a solution for a task. There are many different design theories but a few methodologies outline the classical paradigm: Systematic Design (Pahl & Beitz, 1996), Axiomatic Design (Suh, 2001), and General Design Theory (Tomiyama, Yoshikawa, 1987; Yoshikawa, 1981). 2.2.1 Systematic Design Systematic Design (Pahl & Beitz, 1996) was developed through years of observing the natural engineering design practice where design is approached from a systematic and practical point of view. It looks not only at the defined problem but also at the surrounding environment. The design process can be divided into four main steps: the planning and clarifying the task phase, the conceptual design phase, the embodiment design phase, and the detail design phase. distribution of a single solution. The following figure exhibits the Systematic Design process. Systematic design practical point of view. It is based on the observation of problems through many years of engineering practice. roughly classified into four stages Step 1: Planning and Clarifying the Task Clarification of the task requires the constraints that will act on the solut Planning and Clarifying • Environment Definition • Market/User Demands • Solution Constraints • Performance Specifications • Narrowing Functional Requirements Conceptual Design • Abstract Essential Problem • Generalized Solution • Characterize Concept • Working Principle solution and function structures al point of view. It looks not only at the defined problem but also at the surrounding environment. The design process can be divided into four main steps: the planning and clarifying the task phase, the conceptual design phase, the embodiment , and the detail design phase. This is all followed by the exact tribution of a single solution. The following figure exhibits the Systematic Design design (Pahl & Beitz, 1996) is to describe design process from a t is based on the observation of solution process from real problems through many years of engineering practice. The activities of designers can be roughly classified into four stages. Figure 2: Systematic Design Process Planning and Clarifying the Task Clarification of the task requires exactly defining all of the functional requirements and the constraints that will act on the solution in the problem environment. Conceptual Design Abstract Essential Problem Generalized Solution Characterize Concept Working Principle solution and function structures Embodiment Design • Conceive Realistic System • Identify Sub- Components • Justify Working Design with Technical Data (Mathematic and Physical Analysis) Detail Design • Detail component inter-operation • Test Prelimnray Design • Finalize Prototype (dimensions, material, specificatino, etc.) 17 al point of view. It looks not only at the defined problem but also at the surrounding environment. The design process can be divided into four main steps: the planning and clarifying the task phase, the conceptual design phase, the embodiment exact replication and tribution of a single solution. The following figure exhibits the Systematic Design design process from a process from real design he activities of designers can be the functional requirements and Production • Replication of a single solution 18 Step 2: Conceptual Design This phase is the part of the design process where the principal solution is characterized by concepts. This is a general type of solution that will be pursued in later phases. The principal solution is found by identifying the essential problem through abstraction, establishing function structures, searching for compatible working principles, and then combining these into the working structure. A complex overall function is decomposed into sub-functions with less complexity. Step 3: Embodiment Design This phase takes the abstract conceptual path from the conceptual phase and produces a system that can realistically be produced, often completed by piece-by-piece design. In this phase, real technical criteria (mathematical and physical analysis) will be used to justify the working design and available sub-components will be incorporated. The result is the preliminary design for the solution. Step 4: Detail Design This phase allows for testing of the preliminary design so that adjustments can be made from the results. More detail about how each component will operate and function together are clarified. The prototype schematics and parts are finalized such that all specifications are completely defined. The result of this phase is the specifications for production. 19 Systematic Design offers a very strong methodology for many mechanical systems but is very limited when applied to CSO systems. Firstly, it is difficult to fully specify all of the functional requirements and environmental constraints within the Planning and Clarifying Task. CSO systems excel in uncertain conditions and unknown environments. Systematic Design is often implemented with piece-by-piece design, which ignores the macro-level emergence inherent to CSO processes. Furthermore, CSO systems are envisioned to grow and evolve after deployment, directly countering the production method associated with Systematic Design. The design methodology and its phases are based around selecting a single solution for production. 2.2.2 Axiomatic Design Nam P. Suh (1990, 1998, 2001) developed axiomatic design to systematically analyze the transformation of a product or system from the customer needs. The customer needs are systematically transformed into functional requirements, design parameters, and process variables. Suh illustrates the process as a relationship between the four key domains of the customer domain, the functional domain, the physical domain, and the process domain. Customer needs result in functional requirements. Design parameters satisfy those functional requirements, and finally process variables associate the design parameters into a manufacturing process. The design is executed along a zigzag process through the mapping between the four domains. 20 Figure 3: Four Domains of Axiomatic Design To assist designers to make proper decisions when facing multiple alternatives available during decompositions or mapping, two design axioms are introduced as a basis for evaluation of proposed solution candidates: the Independence Axiom and the Information Axiom. The independence axiom states that one should “maintain the independence of functional requirements.” This maintains a decoupled relationship in the design such that changing a single design parameter will only affect a single function. The information axiom states that one should “minimize the information content of a design.” This axiom suggests that the simplest design is probably the optimal design. Axiomatic Design addresses several fundamental issues and proposes useful ideas towards design. However, it can only serve limited use in designing CSO systems. The two axioms directly counter the main characteristics of CSO systems. The Independence Axiom opposes the complex interaction and reactions inherent to CSO systems, which 21 also provide the inherent adaptability. Secondly, the Information Axiom advocates simplicity, not complexity. 2.2.3 General Design General Design Theory (Yoshikawa, 1981; Tomiyama, Yoshikawa, 1987; Tomiyama, 1995; Reich, 1995) is a design theory based on mathematical foundations as it attempts to map design specification to design solution by set theory. The process has three basic elements: entities, attributes values, and functions. An entity is a real object that existed in the past, presently exists, or will exist in the future. The set of these objects is the entity set. An attribute is an observed or measured property (physical, mechanical, chemical, etc.). Entities have values for their attributes. A function is a special behavior exhibited under specific circumstances. General Design Theory believes that a desired functionality can be achieved by the nature of objects. There is a one-to-one correspondence between the entity set and its representation as described by its attributes. The theory assumes that a designer can know all of the mappings between function and entity set without ambiguity by abstract concepts, which can clearly separate an entity from other entities. This theoretical method for engineering design, in which functions and entities are mapped by attribute association, has found most use as a model to offer some guideline for building CAD systems. However, General Design Theory is difficult for designers to directly apply as its assumptions are too restrictive. Although useful for CAD systems, the methodology is impractical to use for complex systems where the mapping between entities, attributes, 22 and functions is poorly understood. When designing complex systems, it is impossible to meet General Design Theory's assumptions. 2.2.4 Conventional Design Limitations These traditional design methodologies have worked great for many of the engineering innovations that have already occurred, and they will continue to work for many problems that society still faces. However, is the traditional approach best for all applications? Does it even always work? The growing field of multi-agent robotics will test the limits of these design paradigms. The similarity in these conventional engineering processes is that the environment must be well-defined and the functional requirements completely identified. These requirements may be impossible when the task environment is unknown or unpredictable. In addition, the designer may not be able to foresee all possible circumstances that the system will encounter nor predict the functions needed to operate in those circumstances. Furthermore, the traditional design practices aim for a single target solution although engineers admit multiple possible solutions. This solution must operate exactly as expected thus there is no room for self-innovation, evolution, or growth to compel increased adaptation. Research in the design field have recognized the need to develop design methodologies to address design of complex systems (Minai, Braha, Bar-Yam, 2006), but few approaches have been fully outlined. 2.3 Multi-Agent Robotics Much of the work in multi-agent robotic system has been in the realization of structures that implement modular reconfigurable robotics. Modular reconfigurable 23 robotics is a popular subclass of multi-agent systems. The key characteristic of modular reconfigurable robots is their ability to change configuration automatically, enabling them to adapt their shape to suit multiple, changing tasks. Self-reconfigurable robotics is a relatively new field that is still growing, but initial research has concentrated on prototyping systems capable of reconfiguration, implementing multiple configurations in the single system, and the reconfiguration problem itself. The underlying design philosophy is to build complicated systems through a varying number of basic units, or modules. Many of the early reconfiguration algorithms relied on centralized planners often using heuristic-based methods. As the systems advanced, more distributed approaches were realized. 2.3.1 Hardware Systems Early on, Fukuda and Nakagawa of the University of Tokyo introduced the methods and technologies required for the realization of reconfigurable systems (Fukuda & Nakagawa, 1988a). Their initial attempt at autonomous modular robotic systems was the Dynamically Reconfigurable Robotic System (DRRS) (Fukuda & Nakagawa, 1988b) and later Fukuda and Kawauchi developed the CEBOT (Fukuda & Kawaguchi, 1990). However, these preliminary designs required explicit definitions of the final configuration in addition to access of global positioning. Pamecha and Chirikjian developed a system that forms structures by modules rolling over each other in a plane (Pamecha & Chirikjian, 1996). Chirikjian, Pamecha, and Chiang suggested breaking the reconfiguration problem into suboptimal sequences that would lead from the initial configuration to the final configuration (Chirikjian, 24 Pamecha, & Ebert-Uphoff 1996; Pamecha, Ebert-Uphoff, & Chirikjian, 1997; Chiang & Chirikjian, 2001). The suboptimal sequences can be optimized through local searches. I-Cubes focused on a simplistic system of active links and passive cubes (Unsal, Kiliccote, & Khosla, 1999, 2001). The active links were capable of attaching to and detaching from the passive cubes. This group proposed a high-level hierarchical planner that could abstract away low-level controllers for more intuitive planning (Unsal et al., 2001; Prevas, Unsal, Efe, & Khosla, 2002). Based on high-level plans, the lower level then produces the detailed sequence of actions. Rus’s group at MIT has developed several different modular robotic systems. The Crystalline Robot strays from the convention of moving individual units across the surface of the structure (Rus & Vona, 1999, 2000, 2001). The “crystalline” modules are cubic structures that are capable of expanding and contracting their size by moving the cube’s faces. Reconfiguration occurs through this internal contraction and expansion transformation of the individual unit’s body. Another prototype, the Molecule, utilized two different types of modules, each with two degree-of-freedom (Kotay & Rus, 1998; Kotay, Rus, Vona, & McGray, 1998). The Molecule was inspired by chemical principals where simple molecules are the building blocks of complicated structures. Using planning algorithms, the units could rearrange into desired three-dimensional structures. Another approach was to use an intermediate configuration that all re-configurations could transition through (Rus & Vona, 1999). By picking an intermediate configuration that is simple to configure to and from, the reconfiguration problem can be simplified. 25 Murata, Tomita, and Yoshida (1998, 1999) developed Fracta, which could form three-dimensional shapes by having modules rotating about each other. The concept was further developed where modules could climb over one another. Yim have introduced various self-reconfigurable systems and algorithms, including Telecubes, whose cubic modules can move in three dimensions (and through the structure) to form desired shapes (Vassilvitskii, Yim, & Suh, 2002; Yim, Zhang, & Duff, 2002). Yet none of the systems discussed so far exhibited multiple mobile configurations. Yim developed PolyBot which demonstrated multiple distinct modes of locomotion (Yim, 1993, 1994; Casal and Yim, 1999; Yim, Duff, & Roufas, 2000; Yim, Zhang, & Duff, 2002). PolyBot uses chain reconfiguration, which is characterized by modules moving in groups or chains, which can improve their reachability. This contrasts to other modular reconfigurable systems where single modules can move on their own and thus reconfiguration happens as a series of individual module motions. While this was a significant advancement, the PolyBot required manual reconfiguration. The SuperBot from Shen’s group at the University of Southern California also utilizes chain structures similar to Yim’s PolyBot (Shen, Krivokon, Chiu, Everist, Rubenstien, & Venkatesh, 2006). SuperBot is a progression from the group’s previous generations of reconfigurable systems M-TRAN, CONRO, ATRON (Castano & Will, 2000; Castano, Shen, & Will, 2000; Shen, Salemi, & Will, 2002). SuperBot is composed of homogeneous modules. These modules contain three degrees of freedom (joints) and three points of connection. The authors were able to establish six modes of locomotion including rolling, walking and climbing. Furthermore, SuperBot demonstrated the ability for modules to wirelessly communicate with each other in order to autonomously reconfigure between configurati Molecule SuperBot S-bot Figure for modules to wirelessly communicate with each other in order to autonomously reconfigure between configurations. Polybot I Crystalline J Figure 4: Example Multi-Agent Robotic Implementations 26 for modules to wirelessly communicate with each other in order to autonomously I-Cubes Jasmine 27 The presented work provides the technological prototyping to prove that such systems are possible and capable of multiple configurations demonstrating different abilities, such as various types of movement. The research focused on physical system aspects such as interfaces and configurations, thus centering no form based design. Many of these systems relied on centralized control and heuristic planning, which has been acknowledged as inadequate control methods for many applications, especially in the case of system size scaling. Not only do the approaches still rely on complicated algorithmic control, but they also tend to be specific to singular problem domains. The next section discusses additional systems and methods that move towards distributed approaches. 2.3.2 Distributed Control Approaches Many of the discussed systems still rely on centralized control; however, one of the main goals in this research is to diverge from the restrictions of a central controller and take advantage of the benefits from distributed control. In addition, planning-based top-down approaches have been criticized for scaling poorly with the complexity of the system, such as the system size (Brooks, 1991a, 1991b). Beni (1988) recognized the importance of having a robotic system that, regardless of being heterogeneous or homogenous, had decentralized control. Beni outlines what he calls a Cellular Robotic System (CRS). The CRS is a completely conceptual model of a robotic system relying on the fundamental definition of a robot system as something that can “process both information as well as matter.” 28 Coordination is a common approach to synchronize individual functions towards a global goal. Usually the global behavior is related back to the component behavior through global coordination variables where agents can coordinate their decision making processes through globally shared information. The global set of information relates the individual actions directly to the global functionality. Thus components can seek to achieve desirable coordination states as specified by the shared information. This is approach is commonly used in multi-agent systems (Weiss, 1999; Wooldridge, 2002), collective robotics (Kube & Zhang, 1992), and swarm systems (Bonabeu, Dorigo, & Therauluaz, 1999). Stoy and Nagpal (2004a, 2004b) introduced a distributed approach where information is communicated in the form of directional gradients. A user provides a CAD represented desired shape that is divided into a scaffold grid of target locations for elements, thus the shape is scale dependent on the number of available modules. The system is able to automatically reconfigure into the desired shape using the information gradients. The approach is for modules to move over other established modules in the scaffold. The directed gradients provide the information to direct module movement into locations that require additional modules. However, this method constrains the system to preconceived structures dependent upon human understanding and creativity. A distributed method for task execution is the bio-inspired Digital Hormone Model (Shen et al., 2002). With DHM, each cell of a system can communicate via hormones and execute local actions via receptors. These actions are based not only on the received hormone, but also on the cell’s local topology, current internal state, and 29 sensored environment. Each cell may react to the same hormone differently although all cells have the same decision-making protocol. Turing’s (1952) reaction-diffusion model used differential equations to model the periodic pattern formation in a ring of discrete cells that interact with each other through a set of chemicals he called “morphogens.” DHM is different because it extends Turing’s reaction-diffusion model by considering the network topological structure around each individual and the local sensory and actuator state in addition to the interplay between reactions and diffusions (Shen et al., 2002). Like real hormones, DHM messages do not have destination addresses but propagate through the system (Shen et al., 2002). DHM is interesting because the information propagated through the system can alter during diffusion as cells can modify the hormone before passing it along. Lack of destination combined with altering hormones results in no guarantee that every robot in the network will receive the same copy of the original message. However, constantly propagating messages, which is dependent upon diffusion and dissipation rates, may cause communication energy concerns. Many of these developed systems have created the individual modules by focusing on specific individual functions. They later achieve reconfiguration through planned results and arbitrary manipulation. Essentially, the system is designed by focusing on individual mechanisms thus the underlying methods are often specific to the single system rather than providing general design principles. The later methods are more distributed bringing the control and communication to the local level, for example, all interaction in Shen’s DHM only occurs within a local radius of communication through hormones. As research moves into this distributed direction, with many interacting 30 agents, the system development will rely on many concepts from the next section, Complexity Theory. 2.4 Complexity Theory What is a complex system? Systems are complex because they are composed of a large number of inter-relating elements and inter-element interactions. While elements can be locally simple, the global system may produce collective results that are difficult to predict. The system behavior is determined not only by the individual behavior of the elements, but also by the interactions between the elements. 2.4.1 Dynamical Systems, Self-Organization, and Emergent Behavior Any group of interacting agents over time is a dynamical system. Complex theory and dynamical systems deals with the non-linear coupling of the many-agent system. Two major interesting concepts from this field are self-organization and emergence. Self-organization and emergent behavior have been popular research topics in the complex systems field (Bojinov, Casal, & Hogg, 2000; Butler, Kota, Rus, & Tomita, 2001; Fukuda & Kawauchi, 1990; Neumann, 1966; Weisbuch, 1991; Wolfram, 2002; Zouein, 2009). Self-organization is large scale organization through the limited local interactions of the constituent components. Emergence represents the concept that patterns are observably exhibited in the large scale organization, often unpredictably. The main idea is that each simple unit cannot accomplish much by itself, but many units organized properly can collectively achieve complex tasks. Essentially, global patterns will be determined by the local interactions between the individuals, and these 31 global patterns are intended to be system behaviors or functions. The hope in studying complexity theory is that the local rules of self-organization will result in useful emergent collective functions and behaviors. Cellular Automaton is a self-organizing, dynamical system that is discrete in both time and space. Each cell in the grid decides its next action based on information, whether directly or indirectly, gathered from its neighbors. A famous example for cellular automaton is Conway’s Game of Life (Gardner, 1970). In the system, cells are part of a rectangular grid and each cell is given rules on whether to live or die based on its surrounding neighborhood. The Game of Life’s evolution is based only on its initial state. From just the simple rules of interaction emerged unpredictable but clearly recognizable patterns. Inspired by Conway’s discovery, many more cellular automaton based fractals have been explored (Wolfram, 2002). These developments in the pure complexity theory was a major advancement, but still relied on fixed local rules and observation based mergence processes thus not allowing for dynamical adaption to changing functional needs. Relating back to modular reconfigurable robotics, Butler’s team developed a generic decentralized locomotion algorithm for self-reconfigurable robots based upon the notion of cellular automata using geometric rules to control module actions (Butler, Kotay, Rus, & Tomita, 2001, 2002). 32 2.4.2 Global to Local Challenge One of the difficulties with self-organizing and cellular automaton systems is that most research has only been able to observe emergent patterns. This leaves the challenge of actually taking a global goal and then generating the local rules of interaction. Radhika Nagpal (2001) had developed a language for instructing a sheet of identically-programmed agents to assemble themselves into a predetermined global shape using only local interactions. The global shape corresponds to a process of construction, which are sequenced, triggered, and communicated through the cells of the sheet by means of a gradient message. In Nagpal’s model, cells only interact with nearby cells in the sheet or cells that come into direct contact as a result of changes in the shape of the sheet. There is no global coordinate system, no global clock, or centralized control. Cells are randomly but densely distributed in the amorphous sheet. Cells are able to query and broadcast information in their local neighborhood by means of the gradient message. Figure 5: Nagpal's Origami Shape Language Although the approach is successful in reaching a global structure from only local interactions, there are several limitations to the approach. Nagpal focused on the 33 construction process itself for instructing the origami sheet to assemble themselves into a predetermined global shape (2001). Not only is the global shape predetermined, but it also does not have any translation to functionality. Additionally, the initial state is known as a square sheet, and edge and corner cells do have a global sense of position therefore diminishing the concept of zero global awareness in self-organizing systems. Unlike the DHM model where an agent’s neighbors may be constantly changing, the gradient system does not expect major turn over for defined neighbors. Both DHM and Nagpal’s approach are based on reactive responses such that implemented strategies are a collection of preprogrammed condition-action pairs. Despite these limitations, Nagpal's system does step towards a more general global-to-local compilation as it takes a desired global structure and constructs the local rules of interaction. However, the local rules are defined around specific individual reactions from a communication trigger as oppose to purely interaction and reaction between local neighbors. Much of the research in self-organizing and emergent systems simply observes the emergent behavior after specifying the local rules of interaction. While there have been some attempts, this field is still lacking a framework that provides understanding on how to construct local rules to obtain a desired emergent global dynamic. Furthermore, many of the reactive bottom-up approaches require the implemented strategies to be a collection of preprogrammed condition-action pairs. But this requires the designer to perceive all the significant conditions that the cells may encounter. Self-organizing systems actually exist all around us in different natural systems and researchers have been looking to these systems for inspiration in developing artificial 34 self-organizing systems. The effort to build self-organizing systems is an attempt to create artificial systems analogous to natural systems, with all their strengths and weaknesses. 2.4.3 Natural Systems Self-organization is a commonly studied in cybernetics, the study of structure and regulatory systems such as controlling societal behavior by rules or restrictions. Cellular automaton has been used to study natural systems such as chemical pattern formation, traffic jams, termites, and ant social behavior (Deneubourg, Gross, Franks, Sendova- Franks, Detrain, & Chretien, 1990; Resnick, 1994; Turing, 1952; Werfel, 2006). Figure 6: Chemical Pattern Shape Formation. Populations of the molecule in image A self-organize into the structure in image B. Artificial systems such as mobile robots are often developed by application of ant- like behaviors such as stigmergy (Deneubourg et al., 1990; Werfel, 2006). In contrast to traditional AI, which addresses intelligence in the individual, this work hinges on the 35 belief that intelligent behavior of a multi-agent system is tied to agent interaction and cannot be understood in isolated individual circumstance (Mataric, 1994). The advantage that natural systems display is their adaptability because of the collective behaviors from the local interaction of the individuals. The collective group can exhibit abilities and actions that are very different than the individual. The local interactions in self-organizing systems are similar to a societal set of rules. The social set of rules is shared by each individual in the society and significantly affects individual behavior (Gould, 1982; McFarland, 1987). While collective groups, or societies as Gould describes it, can be different from one another, such as in the abilities and actions of the individuals or in size and complexity, they all share a common property: a maintained shared culture, where social rules are continually refined (Gould, 1982). Figure 7: Craig Reynold's Boids Simulation One of the earliest works in modeling life science for artificial systems was Boids. Reynolds (1987) developed Boids as a computer simulation of flock-like motion. Each 36 bird followed three simple rules of interaction based on separation: avoid crowding by avoiding collisions with nearby flock mates; velocity matching with nearby flock mates; and flock centering to stay close to nearby flock mates. Boids is an example of emergent behavior in swarms as the collective complexity results from the local interaction of individual agents. The work shows emergent behavior such as splitting and reuniting flocks. Boids was a significant advancement in simulation and is often used in computer graphics to provide representations of flocks, schools, or herds of animals; however, more complex rules must be added to produce obstacle Avoidance and goal seeking for true system functionality (Reynolds, 1987). Couzin’s group uses a method extended from the Boids framework in order to study movements in real collective animal systems (Eriksson, Jacobi, Nystrom, & Tunstrom, 2010). By using a parametric matching approach, they try to find the true characterization of collective motion in animal groups. While the knowledge gained from these works are very important, they still leave the design questions of mechanical implication and how to utilize the knowledge. Werfel (2006) developed an ant-inspired system for automatic construction. Through extended stygmergy, or communication through environmental modification, the robotic system collectively, and automatically, constructs two-dimensional structures. This work provided an automatic method for bringing a user specified global goal into local interactions but provides no behavioral or group analysis. Stigmergic interaction is an analogical approach where the functionality of existing natural complex systems such as insect colonies is used to infer desirable agent behaviors (Dorigo, Caro, & Gambardella, 1999). 37 Mataric (1994) studied intelligent behavior as it was situated within a society stating that “intelligence is a social phenomenon.” She recognized that social interactions can spawn or vanish in a single generation providing a faster alternative for adaptation than evolution. Essentially, social rules can be directly transferred to current or future generations, thus a single individual’s discovery can be immediately adopted by the entire population. Mataric developed learning in group environments by using a set of basic behaviors abstracted from the Boids framework (1994). The basic behaviors served as building blocks for synthesizing and analyzing more complex group behaviors. Specifying the system goals as higher level primitives makes design more intuitive for the user, however, the work needs to delve deeper into the relationship of the basic behaviors in order to provide a framework of designing systems around the model. Learning methods were Mataric’s goal in utilizing the basic behavior, but learning algorithms mostly require agents to maintain and create models and predictions for the environment and other agents. This inherently increases the amount of information and processing performed by each agent. But how simple can we keep the agent and individual processing while still achieving emergent functional behaviors? While all of these techniques and systems have been important to advancing multi-agent systems, they have all centered on specific system developments without specifically addressing the general complex system's engineering design challenge. Most methods still reside at the extremes of top-down, central controller planning-based methods or bottom-up observation. Few methods have been able to fully harness the advantages of CSO as they often still rely on preconceived structures and single, non- 38 evolvable solutions. This thesis aims to progress our design understanding of CSO systems to better achieve adaptability. 2.5 Need for a New Approach Complexity rises from the multitude of interactions and reactions that exist in a many entity system. The traditional engineering design process has not been well- adjusted to design these CSO systems. While designers realize we must take a different approach towards complexity, so far, design has mostly addressed complicated systems. In order to deepen our understanding and provide design methods for the development of CSO systems this thesis introduces a design approach focusing on the relationship between local agent interactions and emergent collective system behavior. In the CSO framework, we consider a system composed of multiple mechanical cells, which self- organize themselves through individual actions and mutual interactions. The objective is to extend the envelope of design processes towards complexity. Before diving into the details of the approach, the next chapter will first discuss the critical concepts that build the foundation for designing CSO systems. 39 Chapter Three: A Meta-Behavioral Model Approach 3.1 Introduction The classical engineering process has produced many of the current technological advances including lunar rovers and microprocessors. While these systems have “complexity” challenges, they have only been designed as “complicated” systems. As Braha and Sumpter point out, ‘complicated’ does not equal ‘complex’ (Minai, Braha, Bar-Yam, 2006; Sumpter, 2010). Scientific complexity arises from the numerous actions and reactions that happen in the inter-relationships of the components. As an example, space shuttles are both a complicated and complex system, but the design process in creating the space shuttle only considered the system as a complicated system. A space shuttle that has the requirements of making a round-trip voyage from earth to mars is very difficult; however, we can exactly specify the functional need and the environment of operation. The challenge holding designers from reaching mars is not the complexity of the system or the environmental uncertainties but the lack of resources like technology. In essence, we know how to do it, but the technology is not yet there. Complexity and emergence gives rise to a pooled result that is much more than simply the additive sum of the component parts. The traditional approaches attempt to indirectly consider complexity by simplifying the system and stripping the complex nature of the problem. By stripping the inherent complexity of the system, the system loses the advantages gained through the complexity. Instead of trying to simplify the system and environment, complexity must be embraced. Engineers can take advantage of 40 the benefits of self-organization employed by natural systems by designing solutions with complexity. 3.1.1 Limitations of Classical Design Theory The first question that might be asked is, “why do complex adaptive systems need a new design approach?” What makes the classical paradigm deficient in designing these systems? Complex systems are defined because of the many acting agents, of which there are many interactions. While examples such as economical markets and insect colonies (Bar-Yam, 1997) are complicated systems, the scientific complexity arises from the numerous actions and reactions that happen in the inter-relationships of the system’s components. Natural systems, which often work on some level of self-organization, can show great robustness to perturbations and to failures of individual elements. However, systems explicitly engineered by humans, such as the microprocessor, can cease to function when a single component fails. Microprocessors are a product of top-down, piece-by-piece design where every component is specifically defined and deliberately placed such that a functioning system is absolutely deterministic. The following points characterize the classical process. Environment specification – there are well defined constraints and tolerances that represent the designer understanding of the circumstances in which the system will need to operate. The task environment is absolutely specified. Form specification – the end solution has a specific target structure. Top-Down approach – The system is broken into hierarchical levels moving from the desired functionality followed by piece-by-piece design. 41 Testing – The system is validated under conditions that mimic the expected reality of operation. Testing intrinsically follows the design phases and precedes final implementation and manufacturing phases. Manufacturing – exact copies are made such that users expect each copy to perform precisely as the original design. The classical design paradigm is a top-down goal-oriented process that seeks one specific solution, usually of a single function, for a well understood environment. But complex systems will function in complex and dynamic environments and may have to grow with the unpredictable circumstances the system will face. Complex system characteristics must reflect this reality. This is not to say that every problem engineers have solved exists in a completely laid out environment, but even in unpredictable environments, the designer solves the problem with the assumption that they can create and specify the details of the environment. This often arises as constraints on the operation environment. The classical design process begins with an exact specification of the requirements of the system. This requires the task environment and the function to be well-defined. The needs are formulated as thoroughly as possible on the assumption that the final intended design will never work outside these needs and constraints. After this design specification, the next step is to perform a hierarchical functional break-down which will be followed by piece-by-piece design (Minai et al., 2006). Most complicated systems today were designed through the functional decomposition method, but this will not work for complex systems. Design methods strive to decrease the level 42 of complexity by attempting functional breakdown in the design process. Of course, there may be some zigzag in the design specification and functional solution as the conceptual design becomes more complete and detailed. However, regardless of the early zigzag evolution, the end-goal is to generate a single solution that will be precisely replicated such that users can expect an exact form. Engineers admit that multiple equally good solutions to a problem may exist, yet the traditional goal is always to produce a single design. Given a problem, the classical approach seeks to discover a single solution that will be reproduced the same way every time. This process leaves the system without the ability to adapt, evolve, or grow after release. The classical engineering process seeks a system whose behavior will be predicted and precisely described. But this paradigm creates a system that lacks adaptability and evolve-ability. Minai, Braha, & Bar-Yam (2006) point out that robustness is designed into the classical system as merely the system’s ability to maintain performance under pre-specified sources of uncertainty rather than actually altering itself to adapt to system faults. On the other hand, complex systems are needed when the task environment cannot be thoroughly predicted. Additionally, it is difficult to create a self-organizing system through purely top- down approaches. Decomposition-based engineering is fundamentally limited in developing highly complex systems, largely in part because in a complex system, individual components cannot be isolated. Designers must focus on the interaction between components. By attempting to impose a top-down approach, the innovative 43 patterns and structures that arise from emergence would be suppressed since only human- conceived global forms and functions would be enforced. The classical approach creates a good design only when the designer can foresee all the unpredictabilities and thus eliminate the unforeseen, the unexpected, and the unintended from the process. This is done because complexity is seen as an obstacle in the search for optimality. The performance on the system will depend on the knowledge, capability, and innovation of the designer since the designer will absolutely determine the system form, behavior, and functionality. Traditional design attempts to control and limit the system complexity rather than embrace it; however, this method will be inadequate within systems that are inherently complex. 3.1.2 Towards Complex Systems Specialized robots will likely be better at their isolated functions, but for tasks that require a variety of functions, the specialized robots will not be able to complete the mission. Complex systems based on self-organization and adaptation will excel in complex, open environments containing unforeseeable contingencies. In these environments, design engineers cannot anticipate all the possible contingencies that the system may encounter and thus will not be able to produce a system that can achieve all task requirements. Complex systems will trade the predictable behavior of classical systems for adaptability that can produce completely unexpected results. Since the problems that complex systems will confront are not entirely predictable, all the possible solutions cannot be determined in advance or optimized. Complex systems must explicitly leave room for unpredictable task environments and 44 unforeseen challenges. Consequently, engineers must actually build systems with a partial ignorance towards the system, or residual irreducibility (Minai et al., 2006). Unlike designers of classical systems, complex system engineers must realize and even appreciate their own inherent knowledge limitations. This ignorance leaves the complex system free to innovate its own solutions, and thus the global consequence will arise through self-organization rather than through explicit design. The complex systems engineer will not focus on every specific detail of the system. Instead, the engineer must concentrate on configuring the context of the local interactions between elements. These local interactions will lead to the system global behavior. Essentially, the designer must design interactions rather than individual functions. This is the primary challenge for complex system engineering. The conventional design approaches attempt to eliminate the self-organization processes in favor of piece by piece design, but using self-organizing rather than explicit design can leave the system free to innovate its own solutions. Furthermore, self- organization shows us that non-trivial and large-scale order can be produced through simple processes on simple agents. While complex systems may initialize as replicates, through time, they will evolve into unique entities. No two ant colonies or bee hives will are exactly alike. Designers and users should not expect two separate complex systems to behave exactly alike. This embraces the multiple-solution concept. In general, the existence of variety enables multiple approaches and progressive improvement in the system. Different environments may offer variable benefits for different unique systems, but the inherent variety achievable by the system allows for adaptation to changing 45 demands. Therefore each individual adaptive system operating in varying complex environments will develop unique structural and behavioral characteristics (Minai et al., 2006). Conventional Design still achieves the advantages of high functionality and is well understood. This leads to direct optimizations of efficiency and cost effectiveness. But their limited adaptability leaves them weak to situation change. As systems grow in size and increase complexity, many unplanned dependencies are unknowingly added. Self-organizing design, on the other hand, has high adaptability from flexibility and evolvability. It is also theoretically scalable and can lead to inexpensive manufacturing. Its nonlinear characteristic does make system behavior difficult to predict which can result in limited performance. The self-organizing process is also thus far not very time efficient. However, CSO systems will leverage the advantages of self-organizing design to solve problems where conventional designs are not suitable. The following table summarizes these arguments. Conventional Design Self-Organizing Design Advantages Highly Functional Well-understood Cost Effective Efficient & Optimized Adaptability Flexibility Evolvability Scalability De-centralized Deficiency Weak to Situation Change Limited Adaptability Increasingly Complex - Unknowingly add man dependencies Nonlinear - difficult to predict Possibly Limited Functional Performance Time Inefficient Figure 8: Design Methodology Comparison 46 3.2 Designing Cellular Self-Organizing Systems Natural systems have evolved over millions of years through bottom-up adaptability. Consequently, one method is to use purely empirical approaches, which implement human conceived understandings of natural systems into a simulation and then observe the emergent responses. However, this strongly relies on trial-and-error and can be difficult as an engineering tool. Applying traditional processes in the design of complex systems runs into difficulties in the first step of planning and clarifying the task. Clarification of the task requires defining the functional requirements and the problem environment. While this process has created systems with complexity, the process was not completed under the nature of complexity. Instead, only complicated systems were created and complexity is not the same as complicated. Complexity is based on the difficulty to understand the relationship and reaction in all the interactions of a many component system. The complexity in a design problem sources from the designer's inability to understand the relationships in the environment, target functionality, and system form. The complexity in the solution arises from the inability to comprehend the entire space of global emergence from local interactions. Using self-organizing rather than explicit design can leave the system free to innovate its own solutions. The problems that complex systems will confront are not entirely predictable so all the possible solutions cannot be determined or optimized in advance. Complex systems must explicitly leave room for unpredictable task environments and unforeseen challenges. 47 Traditional design relies on a complete knowledge of the problem statement, but complex systems are advantageous in applications where this knowledge is incomplete. Moreover, especially because the problem domain cannot be completely specified, the functional domain is also uncertain. Traditional design methodologies rely on deterministic information; therefore there is a gap in the design process between the problem domain and finding a solution in the solution domain. 3.2.1 Gap in Design Knowledge If the problem could be one-hundred percent perfectly specified and the solution can be achieved from completely understood technologies, then designers could simply apply an automatic process to define and optimize the solution. Engineers are constantly pushing this knowledge envelope as more and more processes become automatic. Designers are needed once there is at least a small amount of uncertainty and knowledge such that a choice must be intuitively selected from several possible solutions based on a functional objective. Nature works in the complete opposite way. There are vast amounts of simple building blocks that react to local environments and interactions to form emergent structures. Besides survival, there is no specific function or structure enforced by a functional break-down and hierarchy. As humans study and observe nature, the exact behaviors, motivations, and processes of the different natural systems are difficult to specifically identify and replicate. Even after exactly mimicking some systems, there is question in how perfect the knowledge is about the system. So far, we can only observe and copy natural systems. Design of CSO systems human automation and natural behaviors. inspired approaches to develop challenge of the inherent massive issues and extend the envelope of design methodologies deeper towards natural methods. In the early phases of design, designers there is uncertainty in their knowledge, whether it requirements, functional specification, available technologies, etc. In general, there are 4 main zones as exhibited in figu 1. Certain You Know This is the information that the space in which designers try to work functional requirements, environmental constraints, and systems will be somewhere in between the two extremes of human automation and natural behaviors. Complex design engineers will use nature develop artificial systems but must overcome the solvability herent massive dependencies. The CSO approach will address these issues and extend the envelope of design methodologies deeper towards natural methods. Figure 9: Certainty-Design Matrix In the early phases of design, designers often realize they lack some knowledge or there is uncertainty in their knowledge, whether it is in the task environment, customer requirements, functional specification, available technologies, etc. In general, there are 4 exhibited in figure 9. Certain You Know This is the information that designers are absolutely certain they d the space in which designers try to work, exactly specifying details such as functional requirements, environmental constraints, and desired solution form. 48 somewhere in between the two extremes of will use nature- the solvability will address these issues and extend the envelope of design methodologies deeper towards natural methods. realize they lack some knowledge or in the task environment, customer requirements, functional specification, available technologies, etc. In general, there are 4 do know. This is , exactly specifying details such as solution form. 49 2. Certain You Don't Know This is information that designers are absolutely certain they do not know about. Designers often put this case as a fifty-fifty chance and tend to avoid this space. 3. Uncertain You Don't Know This is the realm of nature and the abyss of unknown. Current scientific knowledge does not even know the vastness of the world and the information out there. Design engineers and scientists cannot be certain how much they do not know about a problem or solution. Natural systems fall into this space and are completely different than our artificial systems. Human knowledge is repeatedly discovering new things about nature that was not known before. A prime example is the quantum mechanics breakthrough after Newtonian mechanics. 4. Uncertain You Know This space is really the space of things the designer knows but they may have not even realized. The argument is that this space is related to intuition, creativity, and experience. Intuition is basically not knowing what we do know. Creatively new and practical solutions are unproven ideas we knew but had not previously realized. It may work more on sudden instinct rather than rigorous processing. 50 Figure 10: Extending the Envelope of Design Processes The above figure displays the four design envelopes. Conventional design strives to stay near Certain Knowledge, the smallest envelope, although just outside of automation. Computer Scientists will attempt to optimize specific system implementations without pushing the envelope further. On the other side of the spectrum, ecologists and evolutionary biologists study natural systems with the objective to understand the exact behaviors and processes. Nature and the study of nature fall into the largest design envelope that contains all of knowledge that designers are uncertain about the lack of knowledge. Intuition and creativity can play a role in any of the categories where designers lack knowledge. The next step is to reach further into the medium envelope conceding that there is uncertain knowledge in the system implementation and design. The CSO design approach will push the envelope of design techniques further into the spectrum and closer towards natural processes. The designer will realize that the possible solution form may be unknown and plans to take advantage of the natural process of self-organization in order to allow solutions to emerge. 51 Regardless of how much the designer admits to know or not know, in the end, with the traditional design process, the designer must make executive decisions specifying an assumption of certain knowledge. Stated another way, as designers solidify the final design solution, they must make final decisions on the assumption that they are certain about what they know. In order to stay within the smallest, most certain envelope, they will exactly specify the task environment, the functional requirements, the solution form, and the functional behavior. If the system fails outside the specified bounds, it is not the designs fault. 3.2.2 The Demand-Supply Relationship of Complexity In the design process, the demand is the design problem and the supply is the design solution. CSO approaches will develop complex solutions using uncertain emergent functions and thus should be used for problems with uncertainty. As Ashby points out with the Law of Requisite Variety, "variety absorbs variety, defines the minimum number of states necessary for a controller to control a system of a given number of states" (Ashby, 1956). CSO systems are better suited for applications with uncertain and changing demands that conventional systems are weak towards. 52 Figure 11: Problem Demand Curve The above figure displays two example problem demands curves. The solid curve represents a demand that is peaked at one point in the problem space. It represents the sharp, top-down attack of conventional design. There is absolute certainty about the needs of the problem and it is at one known point. The designer knows exactly the requirements within the problem space, and the problem type can be specified with absolute certainty. The dotted line more closely exhibits the human understanding of natural problems. We have a guess at what are the problem specifications but we really do not know everything about it. The design demand represented by the dotted line curve shows an uncertainty in what exactly defines the problem. 53 Figure 12: Solution Supply Curve A similar and parallel figure can represent the supply side. With traditional design, designers endeavor to create a product that performs a single solution at a very high certainty. On the other hand, the dotted line represents a system that might have many forms and perform many functions. It represents the bottom-up self-organizing natural approach towards an emergence function. Designers or scientists may not even have a strong certainty of what might be that function. Note that the y-axis does not represent effectiveness of the solution, although there may be some correlation with efficacy and the certainty in the design solution, which can be explored in future research. 54 Figure 13: CSO Demand Supply Ideally, designers could create systems with both a wide and tall supply curve where the solution could achieve many solution instances with a high certainty. However, design research can only take small steps in reaching this ideal. The CSO processes takes this step with objective solutions lying somewhere in between the thin solid curve and the dotted line, represented by the thick solid line in the above figure. Essentially, to deal with uncertain applications, CSO offers solutions with managed complexity. This results in a system that has a wider capacity of functions. The CSO approach lies somewhere in the middle of the two extreme supply curves and fulfills similar demand curves. The first step is to trade some determinism and certainty for variety of functionality. 3.2.3 Design Spectrum Matching solutions to problems, or supply to demand, is the role of the design process. If the designer absolutely knows the information about the problem, the functional objective, the performance specifications, and the task environment as well as CSO Approach 55 having perfect knowledge regarding the necessary technology and resources, then the designer can do a pure automation for the solution. The automatic process will take as input the functional requirement information and output a single optimized solution. Figure 14: Design Spectrum: Automation Once the designer lacks a little bit of information, then experience and intuition are needed. The design process is a framework that designers employ in order to identify a usable solution. But the designer may not totally be sure about which component technology is better, or what should be the main performance metric. Maybe there are many possible good solutions that are pareto optimal, but based on the lack of certainty around the knowledge base, the designer must make a choice decision. Sometimes different solutions are considered to be better in different environments. The designer will use their experience, intuition, and creativity to develop and choose the best solution. Figure 15: Design Spectrum: Design Engineering 56 Human knowledge does not yet perfectly understand nature's methodology and process. Scientists guess at what might be the desired function. Natural processes occur, and some solution emerges, which scientists study and hope to understand. Scientists believe that in the majority of natural systems there is an overall objective of species survival, but the translation of how that breaks down to functional objectives is unknown. Scientists are striving to understand and predict the emergent solutions that occur from different natural processes. Figure 16: Design Spectrum: Natural Process Engineers use the scientific understanding in order to copy nature and create artificial systems. The engineers identify functional desires and parallel them to natural systems. Then a simulated system is created to perform trial-and-error analysis to develop observed solutions. 57 Figure 17: Design Spectrum: Nature Mimicking This trial-and-error process is not a good design process for developing new systems. Also, it relies on having parallels in nature. However, nature-inspired engineering solutions do not need to exactly mimic nature, only be inspired by it. The inspiration already arises from realizing the benefits of the natural processes of self- organizing and complexity. Designers must use these tools to approach the problem of designing complex systems and focus on the source of complexity: interactions. 3.2.4 Fundamental Change in Design Philosophy In order to achieve solutions with managed complexity, this approach relies on the unique processes of self-organization and emergence. Relying on emergence is a fundamental change in design approach. Emergence is not deterministic, unlike the currently trusted design methods. Allowing a function to emerge from the system through local interactions leaves a large question in the certainty of the function. With emergence, initially, we know nothing about the final result and consequence. In order to manage this uncertainty, CSO design will impose some top-down guidance, although not to the extent of traditional design. This combined top-down guidance with bottom-up self-organization will result in the emergence of a functional capacity. We will prepare an emergence capacity as oppose to one specific function 58 capability. The function capacity emerges from the self-organization of the system, and will have a high coverage in the functional space with many run-time possibilities, although a lower ceiling of certainty. This is the essence of designing with uncertainty, and it should be used for applications with uncertain and changing demands. Instead of designing a solution with a specific problem in mind and providing a specific solution for it, CSO will provide guided function capacities for problems with expected but uncertain requirements. Essentially, the approach prepares a capacity to at least deal with what might happen, although the problem cannot yet be perfectly defined. This thesis develops the concepts and processes to engage the guided emergence approach. 3.3 The Meta-Behavioral Model Approach The CSO design approach recognizes that to design for uncertainty in the problem, there must be uncertainty in the solution. CSO explicitly designs for unpredictable task environments and unforeseen challenges. The uncertainty in the guided emergent solution consequences in the adaptability carried by CSO systems. The Meta-Behavioral Model (MBM) will be used to manage the uncertainty and guide the system's emergent capacity. The gain of adaptability is a direct trade-off with the loss of determinism. The designer must initially accept that not all possible solutions will be humanly determined and even appreciate the inherent knowledge limitations. The system will be engineered with partial ignorance. 59 The challenge in the CSO approach is to guide specific system capacity rather than simply allowing and observing any global behavior to emerge. In form based approaches, a single system function is defined by the overall final configuration of the cells where the designer constructs a target configuration given some functional requirement. Then a transformation algorithm provides the step process to obtain the target configuration. However, in the Meta-Behavioral Model approach (MBM), only the end system behavior is significant, not the specific target configuration. There are no predetermined structures as long as the collective system can achieve the desired function. In actuality, it is more likely that the system will not maintain a consistent specific structure. From a design perspective, how can the CSO system be modeled such that the local-to-global link can be realized. Furthermore, how will the approach provide global control through self-organization? The next section takes the first step and presents Interactive Behavioral Based Design (IBD) where the collective behavior will translate into the end system functionality. 3.3.1 Behavioral Based Design In many of the past approaches, Form Based Design (FBD) is practiced. The system function is defined by the overall final configuration of the cells. As exhibited in the figure below, the concept is for a human designer to construct a target configuration given some functional requirement set. A transformation algorithm provides the process steps or rules to the system in order to obtain the target configuration. 60 Figure 18: Targeted Configuration Flow FBD is advantageous in many ways, especially with traditional design approaches. It is simple to understand system functionality based on the system's form. It also provides deterministic operation and functionality, which allows for an easily optimized system with high efficiency. However, it also relies on pre-conceived fixed structures, thus not facilitating self-organizing emergence. This makes it weakly adaptable to changing demands. For example, consider a simple system of two gears and a belt that has been designed with the specific configuration to achieve the function objective of horizontally displacing an object. If suddenly the functional object was to vertically displace an object or carry it over an obstacle, the system would have to be at least reconfigured if not completely redesigned. To expand the analogy, imagine a reconfigurable robot that has three pre-conceived configurations that can crawl, roll, and walk. After it is deployed, it encounters a gap, but it knows no configuration that can cross gaps, even though it may be physically capable. Relying only on pre-conceived structures consequences in limited run-time adaptability. Furthermore, most re- configuration processes are not self-organized but optimized sequences. These limitations are not favorable for self-organizing and emergent approaches. 61 Behavioral Based Design (BBD) can answer those deficiencies. In BBD, only the end system behavior is significant, not the specific target configuration. There are no predetermined structures as long as the collective system can achieve the desired function. BBD decouples system function from a required specific structure. In actuality, it is more likely that the system will rarely maintain a consistent single structure. With BBD, the collective behavior will translate into the end system functionality. The behavior of any agent gives the action of the agent based on the observed environment and the current state. The behavior of the collective system is a result of the aggregated combination of the behavior of all the cells and results in the function of the system. Equation 1: ( ) ( ) ( ) { } ( ) [ ] i i i i a Action a State a Env a Beh ⇒ = , Equation 2: ) ( ) ( } ) ( { system Func system Beh i a Beh i ⇒ = ∀ As long as certain behaviors are maintained, while the system may be constantly changing configurations, a system function can be retained. The self-organizing BBD approach is concerned with the emergent collective behavior as oppose to predicting the precise behavior of individual components. This approach explores designing rules of local interaction based on a high-level desire. As mentioned previously, distributing work among cells by a central controller has many disadvantages, so this approach designs the behavior of individual cells such that collective intelligence emerges from the cell cooperation. 62 Figure 19: Emergent System from Collective Behavior My approach takes functional requirements and composes the system capacity through the behaviors of individually acting agents. The effective result is the emergent functional capacity from the collective system. As shown in figure 19, the designer identifies the functional capacity that the system might need to achieve based on the functional requirements and the problem uncertainties. This is the target capacity for the system. Behaviors are use to provide the self-organizing rules for the cells of the system. The collective behavior of the system will emerge from the pooled effect of all the reactions and actions occurring through the local interactions and this collective behavior will translate into the end system functionality, not the overall configuration. Since starting and target configurations are not significant, the emerged system itself can serve as the starting point towards another desired function. 3.3.2 Interactive Behavioral Based Design The major challenge of BBD is connecting the behaviors to system functionality. In order to make this connection, a model and representation of the behaviors must be established. The actions that each cell takes, and thus the system, depend on the 63 behavioral set, which defines the Behavioral Model (BM). The designer breaks down and isolates the simple component behaviors. These behaviors result in the behavioral set. Many different behaviors exist such as attraction, repulsion, gravitational, random, cooperative, following, or dissenting. The possible behavioral set is a function of the individual Cell Model (CM). Equation 3: { } { } ( ) CM f B B B B BM m = = = ,..., , 2 1 Inherently there is an inverse relationship between the BM and CM, thus the CM can also be developed after the BM is found. The action that each cell will take is a result of the BM. Equation 4: ( ) ) (a action BM f ⇒ Behaviors can be decomposed into two different types of behaviors: independent and interactive. Independent behaviors are behaviors where the cell does not consider the influence of others. The cell only considers its own behaviors to produce its next action. Interactive behaviors are behaviors that are influenced by the behaviors of neighboring cells. In a sense these behaviors are more social. The cell will observe and consider the behaviors of the neighboring cells when determining to its own action. Chen has already explored cellular systems where the added function arises from the pooled effect of many independent behaviors (Chen, 2012). Such method emphasizes 64 the 'cellular' in Cellular Self-Organizing systems. The approach taken here is to focus on the interactive behaviors between the cells because interaction is key element providing complexity. In Interactive Behavioral Based Design (IBD) the local behaviors of each cell will be based, not only on the perceived environment external to the full system, but also on the interaction with other cells within the system. This will emphasize the 'self- organization' of CSO systems. Figure 20: Behaviors: Independent and Interactive In order to translate the local interaction between cells to the collective function, the BM can be parameterized by weighting and aggregating the different simple behaviors. Equation 5: ) ( ) ( 2 2 1 1 i m m a action B B B BM f ⇒ + + + = μ μ μ Λ 65 As shown in the above equation, variable parameters μ k are introduced to the linearized BM. Linearization may not be the only possible technique, but linearization is an intuitive model for engineers and it will be shown later that it works. Figure 21: Parameterization of interactive behaviors introduces a tunable mapping between local interactions and global result The parameters μ k are dynamical variables that can be manipulated to change the collective behavior in order to achieve different global functions. This creates a tunable connection and bridges the gap between the local interactions and the global emergence. Furthermore, these parameters provide an opportunity to analyze the relationship between different interactive behaviors in addition to the relationship with the collective behavior. This tunable mapping between the local interactive behaviors and the collective behavior provides the basis for this Meta-Behavioral Model (MBM) design approach, which is further discussed in the next section. Utilizing behaviors can hide low-level details of control and allow for higher- level primitives in specifying robot tasks, which are more intuitive for the user. Changes in an individual cell’s behavior can influence the overall behavior of the system as the 66 other cells will respond to the changed behavior. With this characteristic, a cell that discovers some predefined entity, such as a mine, can modify their own behavior, and then other cells that are within the neighborhood will respond. In addition, this also gives operators the capability to affect the whole system just by changing a single cell’s behavior or by introducing a new cell to the system. 3.3.3 The Meta-Behavioral Model After the abstraction layers of the individual cell model (CM) and the behavioral model (BM), the Meta-Behavioral Model (MBM) can be defined. The MBM is abstracted on top of the BM through the variable parameters. It links local interaction to collective functionality. Using the MBM integrates top-down design with bottom-up self- organization. Top-down design is achieved by guiding system emergence from self- organization through the accessible and tunable parameters. This provides a method to direct and manipulate the system multi-functionality and adaptability. The cell action at each time step can be represented as a dynamical system where each action will depend upon a weighted profile of the identified component behaviors as shown in the following equation. Equation 6: ) ( 2 2 1 1 i m m a action B B B ⇒ + + + μ μ μ Λ With each time step, cells can change the behavior of their actions by altering the weighted profiles. The information guiding these changes is found through the MBM. The MBM provides the connection between the behavioral set and the emergent behavior 67 thus revealing the information on how the actions should change in order to change the global function. The pooled behavior of all the individual cells results in the system's capacity. The MBM represents the transformation from the BM to the emergent functional capacity. One way to represent this information is an n x m matrix where n is the number of global function capacities and m is the number of component behaviors. In many systems, the size of n may be unknown since idealistically the system may grow and evolve to discover new functions. This relationship is exemplified by the equation below. Equation 7: ⇐ m nm n n m m m n B B B FC FC FC FC Μ Λ Μ Ο Μ Μ Λ Λ Λ Μ 2 1 2 1 3 32 31 2 22 21 1 12 11 3 2 1 μ μ μ μ μ μ μ μ μ μ μ μ or Equation 8: MB FC ⇐ The elements of M are the different parameter profiles where each row represents one profile. The profiles are made of parameter variables that come from the weights assigned to each interactive behavior. The figure below is an example visual representation of a single profile of a BM consisting of six behaviors where each weight varies from one another. 68 Figure 22: Example Parametric Profile Visualization The general goal of the Meta-Behavioral Model is to provide a design tool linking the local interactive behaviors and the global function. Essentially, the approach creates a tunable connection between the local and global behaviors. The BM is an abstracted layer above the individual cell functions. The MBM is an abstracted layer above the BM. Through the MBM parametric approach, designers can control the parameter adjustment in order to manage the system's multi-functionality. Given a profile, no matter what environment, the function capacity is likely to happen. The MBM approach supplies accessible and tunable variables to guide the overall system behavior. This is a direct method to manipulate the system multi-functionality, and thus adaptability. The MBM is the tool to guide emergent functional capacities. A major implication of the Meta-Behavioral Model is a new design space based on behaviors. The design space involves adjusting parameters to guide emergence of function capacities. These parameters make up the M matrix that connects behaviors with function capacity. Emergent capacities from self-organization can be designed by tuning the Meta-Model matrix. The MBM provides a design technique for oriented function capacity, the group of possibilities that the system can achieve. With this approach, we 69 take a step from previously having minimal knowledge of emergent possibilities towards guiding the emergence of expected capabilities to having a guided expectation. The self- organizing system will remain dynamical, thus changing with time, and is not constrained to static states i.e. force-balance design. Furthermore, utilizing the tunable variables, the behavioral relationships can be investigated. The MBM can be used to provide information on the indication and prediction relationships between the global function and the local interactions. With the parametric approach, profiles can be built based on the relative contributions of the different types of interaction. By changing the profiles of the parameters controlling individual cells interactive behavior, the collective behavior will consequently change. Since the collective behavior will result in different global functions, the parameter profile can be used to manage the system function. Once the space for a selected model can be built, it will provide a guide to understand the possible global function based on the current system profiles, and also a heuristic on how to change the profile based on a desired global function. This method is also easily extensible to combine with other artificial intelligence techniques Now that the theory behind the model has been developed, what behaviors can be used? The next section discusses the different layers of abstractions. One point in the MBM design space will be selected and explored, which is detailed in Chapter Four. 3.3.4 The Three Levels of Abstraction with Meta-Behavioral Design The first step is still to plan and clarify the task. The difference is that the CSO - MBM process does not fully specify the environment and task requirements. Unknowns 70 are also accepted into the planning phase. Designers are still far from achieving comprehensively multi-functional and adaptive systems, but the MBM approach only calls for general task environment type. The designer would know of some expected function requirements and thus would identify certain functional capacities that might be desirable. Figure 23: Meta-Interaction Model Process After the planning and clarifying task, there are three levels of abstraction to develop. Either the Cell Model or the Behavioral Model can first be developed, depending on what is the design problem. Some zigzag can also happen. If the designer can identify the necessary behaviors, then the cell model can be developed accordingly. On the other hand, if the system itself and its cells have already been defined, then the scope of possible component behaviors will already be constrained. 71 The first level of abstraction is to model the individual cells and define their capabilities. This level of abstraction is still compatible with traditional design. This level defines the individual cells that will be used in the CSO system. Admittedly changing cell functions can greatly affect not only the emergent properties, but also change the entire space of possible collective behaviors. With increased functionality of the individual cells, the collective system has more degrees of freedom likely resulting in greater possible global behaviors and functions. However, the current purpose is not to study how individual capacity changes collective emergence. Maintaining simple cells allows the research to focus on the design method based on behaviors and interaction, so the individual cells will be constrained to a very simple mechanical cell that will be described in greater detail later. This also aligns with the premise that useful emergent properties can occur from self-organization from simple cells. The next level of abstraction is the Behavioral Model, breaking down the component interactive behaviors. This involves identifying the possible ways that cells can interact with each other, meaning choosing their actions based on their relationship with the neighboring cells. For a simple mobile with limited memory and communications, the resulting possible interactions will consist of physical relationships. For every system, there are many BM's that may exist. The designer may pick behavioral models from previous experiences or develop new interaction sets. The designer has already accepted that the specific end behavior of the global solution will not be exactly defined, but using experience and knowledge can identify a set of local behaviors. Simple behaviors provide a mechanism to structure the simple rules, thus granting a basis of 72 structuring and analyzing the collective behavior. Simple behaviors are the building blocks for the cellular control. This thesis specifically focuses on interactive behaviors. And coming from a mechanical background, based off the simple mechanical cell, spatial behaviors of interactions can be used characterizing how cells move among each other. Craig Reynold's Boids model is a good example. And lastly, the Meta-Behavioral level assesses the relationship trends in the simple interactive behaviors. These trends provide a heuristic for the designer to tune the system to perform functions. Secondly, they act as a guide for learning and evolutionary methods that can be implemented to facilitate the growth of the system. Using the insights from the MBM, the designer can identify interaction behaviors for different function capacities. Essentially, by controlling parametric variables, the system’s mechanical implications can be manipulated. If the BM is centered on interactive behaviors, then we specifically have a Meta-Interaction Model (MIM), which is a sub- space of the MBM design space. Based on behaviors of spatial movement, the Meta- Interaction Model will provide spatial guidance. The figure below shows the three abstraction layers and provides examples for each. Here we can see the selection of a simple mechanical cell that will have behaviors of spatial movement, and thus the MIM will outline spatial guidance. The meta- interaction model is abstracted on top of the Interactive Behavioral Model, which depends on the Cell Model. 73 Figure 24: Three Layers of Abstraction to the Meta-Interaction Model 3.5 Concluding Remarks In this chapter we discussed the proposal for a MBM design process. Our aim is to formulate this conceptual but practical model and validate it by observation of simulation. The goal is to introduce a new paradigm in design theory towards complex systems and to harness the benefits provided by CSO. To make the design theory more universal requires bringing together as many domains as possible. We discussed shifting the paradigm in design in order to extend the envelope of the design process towards complexity, a more "natural" way. We have presented the conceptual framework for the MBM design process. With the results, we want to achieve a theory of design that is applicable in practice. The design process will become less 74 dependent upon the single interpretation and capability of a designer but actually heed determinism for the sake of adaptability. The space of the MBM parameter profiles provides design variables that can be tuned to explore the system's functional capacity. This new design space is based on behaviors. The behavioral approach allows the designer to focus on the interaction between cells, thus designing with complexity as oppose to stripping the complexity. Using this design space, the system can function dynamically as oppose to optimized static states. The MBM connects function to the behavioral interaction of simple cells. The MBM design process is based on the self-organization process. In order to do so, it takes an Interactive Behavioral Based Design approach focusing on the key aspect of behavioral interaction, the fundamental property of complex systems. Using the Meta- Behavioral Model, it aims to explore the space of collective behaviors that may achieve mechanical functionality. It is a step to extend the envelope of design and shift, not just towards artificial intelligence, but artificial nature. The MBM design process may not be the one and only approach to extend the envelope, but it is a working one. The MBM is a BBD approach with no reliance on preconceived configurations. It links local behavioral interaction to collective functionality. By doing so, it can integrate top-down design with bottom-up self-organization. The MBM provides design information for the prediction of collective functionality from local interactions and for the indication of local interactions based on desired functionality. The collective behavior of the system will emerge from all the reactions and actions occurring through the local interactions, and this collective behavior will translate into the end system functionality. 75 Figure 25: Design Spectrum: CSO The CSO-MBM approach pushes further into the design spectrum towards nature. The input for the design process has been relieved of the absolute deterministic constraint only requiring general definitions and classes. The output is not a single solution form but an amorphous system that can perform many functions. With further development, these systems will be able to grow and evolve to produce completely new structures and optimally specialize for certain tasks and environments. It is important to note that CSO Design does not eliminate the design engineer. This is not an automatic process that can work in the general case. It does not exclude the conventional approaches but still relies on the same basis of traditional design techniques and theory. It works in conjunction with established design approaches because it is a hybrid process combining principles from design theory with those from self- organization theory. This approach still relies on designer capabilities and intuition but not completely as it allows room for further natural developments. However, it does not reach a fully natural process as that is also not design. Natural processes are fully reactionary while design approaches have specific functional objectives. 76 Chapter Four: Meta-Interaction Model Evaluation using Multi-Agent System Simulation 4.1 Introduction While the goal of the general research in this field is to design for any type of complex adaptive system, the current state-of-the-art is still primitive. Thus key constraints are imposed on the experimental domain in order to structure the exploration of the interactive behaviors. Agents are physically homogeneous. In the model that will be presented, all of the agents of interest have the same physical attributes. This means they have the same sensing, communication, actuator, and effector capabilities. Said differently, the agents are similar such that their individual dynamics and behavior sets are all the same. An important note is that homogeneity also has the implication of providing robustness through redundancy as agents are interchangeable and can substitute for one another. In extension of the homogeneity, there is no hierarchy of control power as each agent has a similar understanding of themselves and the world. This means that initially, there are no explicit leaders, followers, or hierarchical organization structure known a prior. This furthers robustness because there is no primary agent whose failure could cause critical catastrophe to the system. However, it may be possible that implicit leaders may rise and fall during system operation, 77 such as a cell that seeds a behavioral change after discovering some new information. Agents do not perform explicit modeling or form expectations. This work currently focuses on the simplest interactions between the simplest agents. The concept is to achieve complex collective behaviors from simple basic individual behaviors. Agents do not produce or maintain models of each other or their surroundings. Of course, it is impossible to avoid implicit modeling since the behavioral algorithms are designed around agent interaction in a collective system, thus they assume the presence of other agents performing similar behaviors. Agents recognize other agents. Although agents do not explicitly model each other, they must recognize each other. We assume that agents can recognize other agents and sense certain attributes about those agents, including the relative location of the other agent. Agents are able to differentiate between other agents and other possible entities such as wall-obstacles and passive objects. No directed communication or explicit cooperation. Agents are unaware of global information such as positioning, thus they may not be aware of how many other agents are present. Agents only have a locality of communication. They do not perform directed communication, which means a specific message with a targeted address (choosing who gets the message). Moreover, since an agent does not maintain global coordinates or models of other agents, it would not have any information in order to select another specific individual for communication. 78 4.2 System Model MIM design works as an approach to developing CSO systems, but in order to further the discussion on design using MIM, an example system will be developed. This section will outline the system details and the three levels of abstraction: the Cell Model, the Interactive Behavioral Model, and the Meta-Interaction Model. 4.2.1 Individual Cell Model There are many possible cell models available and currently already in use. Some examples are software agents, sensor nodes, or even biological organisms. Taking a mechanical perspective and emphasizing simple cells, as a starting step, a simple mechanical cell will first be considered. The system will be homogeneous consisting of mobile, circular mechanical cells. Each cell only has 2-D movement such that the decision process is simply to consider in which direction to move. Cells maintain no long-term memory of the environment and have a limited communication and sensing range. Specifics regarding how information is obtained through sensors are beyond the scope of this work. The approach assumes that each cell can communicate wirelessly over a finite spatial locality of communication in addition to perceiving relative positions and velocities of other individuals. Also, the cells can identify like-cells from other environment entities. No cell has knowledge over the global state of the system beyond its local neighborhood. Therefore a cell can be characterized in the simulation by its x-y- coordinate position, its velocity, its physical diameter, and its neighborhood of locality. The size of the neighborhood of locality can have major implications of the system. As 79 the size increases infinitely, the system is moving towards full global awareness. As the size decreases to zero, the complexity from interaction becomes minimized. Additionally, other research groups such as Couzin's (Eriksson, Jacobi, Nystrom, & Tunstrom, 2010) have committed to focus studies of the differences between different neighborhood definitions. Although the neighborhood is definitely a factor in the resultant emergent capacity of the system, it is outside the scope of this work. But there will definitely be some lower limit and upper limit to the size of the neighborhood, in addition to the changes of the different ways of defining the neighborhood, as explored by other researchers. Each simple mechanical cell maintains only a small amount of information. In the simulated system, the following state parameters represent the cells: Location (x) – <vector> – the current location of the cell. Velocity (v) – <vector> – the current velocity of the cell estimated using the current location, last location, and time step. Diameter (d) – [scalar] Neighborhood (η) – [scalar] – This model assumes a circular neighborhood defined by a radius. In the following figure, the center cell has a neighborhood of radius 'r' and thus is aware of 3 neighbors. 80 Figure 26: Local neighborhood of a cell Weights (W) – [scalar] – each cell has parameter weights used in its decision algorithm, which will be discussed in the next section. 4.2.2 COARM Interactive Behavioral Model The next level of abstraction is modeling the interactive behaviors between cells. An infinite amount of interactive behaviors probably exist between cells. Many different interactive behaviors have been demonstrated such as physical interfaces, communication & information protocols, shared knowledge bases, or even environmental modification. Focusing on mechanical implications of the simple cell, interactive behaviors that fall under the class of spatial movement will be studied. This thesis uses a behavioral model extended from the Boids model, which consisted of the three interactive behaviors: centering, maintaining a separation distance, and Alignment. As the cells have no global coordinate system, they can only perceive the relative positions of the other cells. 81 Centering, or here-in called Cohesion, is implemented by each cell moving towards the average position of all the other cells in its neighborhood. With Cohesion, x i is the relative position of cell i iterated over all other cells within the neighborhood. Equation 9: ∑ ∈ = η i i x N C 1 Each cell maintains separation distance by generating a unidirectional repulsive virtual spring from other cells and perceived obstacles. This means that the closer a cell is to an obstacle, the greater the cell wants to move in the opposite direction. The Avoidance vector is given by Equation 10: ∑ ∈ − = η i i i i x x x N O 1 where x i is the relative position of component i and ( η ∈ i ) denotes iterating over all other elements within the neighborhood. N is the number of other elements that have been perceived, or stated differently, the number of elements inside neighborhood η besides the cell itself. An important consequence to notice is that the interactive repelling force between two neighboring cells is effectively doubled since both cells are repelling from each other. In addition, the vector is undefined when the denominator equals zero; however, this never occurs because two elements will not exist at the exact same location. 82 Velocity matching, or Alignment, is achieved by each cell moving in the average direction of all the other cells in its neighborhood. Equation 11: ∑ ∈ = η i i v N A 1 Alignment is the velocity parallel to Cohesion. Alignment is a vector pointing in the average direction of the other cells’ movements. Inspired by Sean Luke's Flockers (Luke, S., 2004) each cell also takes into account its own Momentum (M), maintaining some of its previous velocity as inertia rejects change. The simulation estimates velocity by Equation 12: 1 − − = t t x x v where t is the current time step and (t-1) was the previous step. Cells can also exhibit a small amount of Random (R) variation in the selected direction. The cells have parameter weights, which correspond to each of the presented vectors. This 'COARM' BIM has the weights of Avoidance (W O ), Cohesion (W C ), Alignment (W A ), Randomness (W R ), and Momentum (W M ). Each cell takes the above factors into account and generates its decided movement. The change in position, Δx, for a single time step is given by Equation 13: M W R W A W O W C W x M R A O C + + + + = Δ 83 Substituting in each derived term gives the equation Equation 14: M W R W v N W x x x N W x N W x M R i i A i i i i O i i C + + + − + = Δ ∑ ∑ ∑ ∈ ∈ ∈ η η η 1 1 1 The positional difference for a cell in a time step is given by Δx = x t+1 - x t . It would be more thorough to incorporate the time step notation into equation 6, which gives Equation 15: ( ) 1 1 1 1 1 − ∈ ∈ ∈ + − + + + − + = − ∑ ∑ ∑ t t t M t R t i t i t t A t i t i t i t i t t O t i t i t t C t t x x W R W v N W x x x N W x N W x x η η η 4.2.3 COARM Meta-Interaction Model The MBM is abstracted on top of the BM. If the BM had been based on the behavioral class of negotiation, then the MBM might provide the structure of that negotiation. If the BM was built on learning interactive behaviors, then the MBM might define what facilitates the learning. The COARM BM is a spatial movement class, so the COARM MBM outlines the spatial control based on position, and velocity, which is speed and direction. Furthermore, this BM is concentrated on interaction. Interactive behavioral models are a subset of all behavioral models. Thus the MBM s Meta-Interaction Model (MIM), which is just one point in the design space introduced by the MBM approach. The COARM MIM is just one point in the MIM design space. IBM's would result in a different MIM space, thus diverse capacities. Just to reiterate, 'COARM' represents Randomness, and Momentum, respectively. interactive behaviors, which corresponds to each of the presented These weights associate with Randomness (W R ), and Momentum visualization where the weights The weights of the COARM profile fit into the would give a single row in the COARM MIM matrix shown below. capacity of the system is an emergent result of which profile is applied to the behavioral models are a subset of all behavioral models. Thus the MBM s Interaction Model (MIM), which is just one point in the design space introduced by the MBM approach. The COARM MIM is just one point in the MIM design space. IBM's would result in a different MIM space, thus diverse capacities. 'COARM' represents Cohesion, Avoidance, Alignment, omentum, respectively. Weights have been assigned to each interactive behaviors, which corresponds to each of the presented COARM te with Cohesion (W C ), Avoidance (W O ), Alignment Momentum (W M ). The following figure provides an example ization where the weights of the COARM profile are uniform. Figure 27: COARM Profile Visualization The weights of the COARM profile fit into the MIM matrix. Each COARM profile e row in the COARM MIM matrix shown below. The functional capacity of the system is an emergent result of which profile is applied to the 84 behavioral models are a subset of all behavioral models. Thus the MBM studied here is a Interaction Model (MIM), which is just one point in the design space introduced by the MBM approach. The COARM MIM is just one point in the MIM design space. Other lignment, Weights have been assigned to each type of COARM vectors. Alignment (W A ), The following figure provides an example Each COARM profile The functional capacity of the system is an emergent result of which profile is applied to the system. 85 Equation 16: ⇐ M R A O C n W n W n W n W n W W W W W W W W W W W FC FC FC M R A O C M R A O C M R A O C n 2 2 2 2 2 1 1 1 1 1 2 1 Μ Ideally, the elements of M could be solved automatically by the system, but currently the solution relies on a simulation based study. 4.3 Simulation Environment The currently available mathematical tools cannot solve systems at this much complexity. Highly complex systems are difficult to analyze purely through current mathematical theory, thus this work uses computational methods to evaluate the approach. The simulation environment is built on Luke’s MASON framework leveraging the Flockers simulation (Luke, S., 2004). MASON is a discrete-event multi-agent simulation library built in JAVA. The simulation study is done with 2-dimensional space, but the conclusions can easily be extended to a 3-D space. The environment field is toirodal, which means that exiting the screen on the right will bring cells to the left and vice versa (the same with top and bottom). The simulation occurs in discrete time meaning that at each time step, agents will be able to go through one decision process: sense the environment, make decision, and perform action. Although real robotic multi-agent systems would likely act in parallel, 86 the simulated agents do not run on parallel threads. However, the approach is not designed around sequential agent actions, and the system does not know which agent will act first. The model maintains no central time so there is no restraint requiring sequential or synchronized actions. This would also be true for parallel processing agents that do not maintain a centralized or synchronized time reference. Furthermore, the agents lack a large memory database, nor do they make expectations for the future. The agents do not explicitly maintain a sense of time, so they do not consider the order or synchronization of actions with others. In the simulated results, the change in position is normalized when the desired step size is greater than the maximum step size. Equation 17: ) ( ~ stepsize x x x Δ Δ = Δ This limits the distance a single cell can take in any given step just like real hardware would speed limits. In addition, it makes the study more focused on the directional changes thus constraining the analysis of the system from having to explore cases where cells might take significantly larger steps than other cells. 4.4 Meta-Interaction Model Analysis This section will examine the interactive behaviors of Cohesion, Avoidance, Alignment, Random, and Momentum. It is important to understand the balance between these simple behavioral rules of interaction. To do this, the parameter weights will be 87 toggled between the values of zero through three in order to having no inclusion of a single behavior (W = 0), some inclusion (W = 1), and increased inclusion (W = 2 or 3). The neighborhood size will be unit length 9 with each cell having a diameter of 3 and the system will be instantiated at rest meaning no initial velocities. For the following, randomly selected initial positions for 100 cells compose the full system in an open toroidal environment as can be seen in the figure below. The color of the cells do not represent any significant differences between the cells but aid in differentiating the cells from one another between image captures of time steps. Figure 28: Randomly selected initial positions of 100 cells In order to compare different states of the system, the disorder entropy calculation was used as follows, Equation 18: j i where x x N E N i N j j i d ≠ − = ∑∑ 1 2 1 ln 88 The calculation is the sum of the minimum toroidal distance between each i-j cell coupling divided by the N number of cells in the system. The equation equates decreased disorder with a more tightly packed system. The first simple behavior that will be investigated is Cohesion. With all the other parameters given weights of zero, it would be intuitive to assume, that cells would group towards each other. This can be seen in the following figure. time step 1 time step 5 time step 30 Figure 29: Pure Cohesion in 100 cell system Figure 29 exhibits how the cells group together into cohesive collections. However, they do not cluster into a single group but many different local groups since they do not have an infinite view or knowledge of global positioning. The cells are not even aware of the other groups due to their limited locality of vision. As a result of this, some cells exist by themselves since they are not aware of any other entities and thus have no motivation for movement. It is also possible for a cell to be equally pulled in two opposite directions by separate entities thus having a zero net effect on the cell’s motion. Furthermore, if 89 another entity moves into the neighborhood of the cell that is being equally pulled as the system evolves, then the zero net effect will be disturbed such that the cell will move towards the newly discovered entity. However, this can also have a chain effect of having the original two entities to also move as the position distribution in their neighborhood will also shift. The Cohesion behavior is very simple and exhibits behavior coinciding with what could be intuitively expected. Even in being simple, the local interaction can cause chain reactions that will affect many individuals in the system. Avoidance is the counter-part of Cohesion although the given model does not implement them as pure opposites to each other. The Avoidance contribution is not only used for maintaining minimal separation distance between cells, but also for obstacle Avoidance. Therefore, Avoidance is very important to keep cells from running into each other or the environment. This inspired implementing an Avoidance magnitude that increase as the distance from the cell to the other entity decreases such that cells are more greatly repelled by closer objects. time step 2 time step 5 time step 30 Figure 30: Pure Avoidance in 100 cell system 90 The intuitive expected result is for the cells to move away from other entities until they are outside of the visible range from each other. Of course, due to the density of the whole system, it may not be possible for every cell to be outside the neighborhood of every other cell. The cells separate and distribute themselves in the available space in order to maximize distance between all the cells as exhibited in figure 30. Again the local interaction between two individuals can propagate and affect the rest of the system. If you consider the case where the entire right half of the screen may have reached a local equilibrium while the left half is still expanding, then as the cells push right (and left due to the toroidal field), it’ll eventually force the cells in the right half to redistribute when new cells enter the right side's local neighborhoods thus breaking the equilibrium. Moreover, if the system would suddenly have another cell dropped into it, the entire system would redistribute to accommodate the new density because of the many reactions that would propagate through the system. Another important contribution to the cell’s decision on movement is the Random effect. time step 2 time step 4 time step 8 Figure 31: Pure Randomness in 100 cell system 91 From figure 31, it can be seen the system under pure uniform Randomness does not seem to change significantly between steps. This is as expected because using a uniform distribution for the random directions, over a time average, the cells would not be expected to achieve a large displacement. The cells essentially gyrate in a spot, taking a random direction with each step, but often counteracting previous steps. Figure 32: Disorder entropy of pure interactive behaviors Figure 32 exhibits the disorder entropy of the three previous pure cases of interactive behavior. The figure shows how Cohesion acts to decrease the disorder of the system, Avoidance increases the disorder, and Randomness exhibits no discernible trend. This would seem to make sense since Cohesion tightens the global system together in a Disorder Entropy: Pure Interactive Behavior 7.546 7.547 7.548 7.549 7.550 7.551 7.552 7.553 0 5 10 15 20 25 30 35 40 Time Step Disorder Entropy (nats) Pure Cohesion Pure Avoidance Pure Random 92 more ordered and structured configuration. Avoidance, of course, is the opposite of Cohesion, and Random is as expected, random. Addressing the other interactive behaviors, Alignment and Momentum do not have any effect without some type of initial velocities since they are calculated based on velocities. This means that a system that starts at rest with zero velocities will not change based only on Alignment or Momentum. Only the "static" behaviors that do not rely only on cell movement can produce non-zero effects when the system is at rest. Next, combinations of the local interactive behaviors are observed. Since the concept behind this system is the collective behavior of many individuals, Cohesion is an important factor for the many individuals to actually stay together. If Avoidance was able to dominate by too much, then for any system where the accessible space is very large compared to the number of cells (low density system), eventually, every cell would be on its own and the collective benefits may be nullified. Therefore, the first combination to investigate is the combination of Cohesion and Avoidance. time step 1 time step 5 time step 15 Figure 33: Cohesion and Avoidance combination in 100 cell system 93 In figure 33, the cells initially move in a direction similar to pure Cohesion, yet clearly do not become as cohesively grouped. Additionally, the end result is not nearly as dispersed as pure Avoidance. For comparison the figure below shows the results for the three different systems of pure Cohesion, pure Avoidance, and the combination of the two. Pure Cohesion time step 30 Pure Avoidance time step 30 Cohesion-Avoidance Combination time step 20 Figure 34: Comparison of Cohesion and Avoidance. Red markings show similarities in spacing. With the combination of Cohesion and Avoidance the cells have appeared to strive for some specific separation distance such that cells that are further apart yet within each other’s neighborhood come slightly together while cells that are very close push apart. This separation distance can be solved based on the decision algorithm for Cohesion and Avoidance. Of course, in a many-agent system, the system of equations because large and cumbersome as is the nature with complex systems. 94 Figure 35: Pure Cohesion phase plane plot of 2 cells. x and y represent the locations of the 2 cells. For demonstration purposes, consider the simple analysis of a two-cell system in 1-dimension. Figure 35 shows the phase plane plot for the two-cell system under pure Cohesion. As can be seen in the phase plan plot, there is an equilibrium line such that x and y are equal, where x and y are the positions of the two cells. The equilibrium position for pure Cohesion should have the cells at the exact same position, but this is never actually achieved since in practicality, two physical entities cannot occupy the exact same space. 95 Figure 36: Pure Avoidance phase plane plot of 2 cells. x and y represent the location of the 2 cells Figure 36, which shows the phase plane plot of the two cells in pure Avoidance, the line that represents the two cells sharing the same location is unsolvable since the denominator would become zero. However, as just mentioned, in practice, this would never occur. 96 Figure 37: Cohesion-Avoidance combination phase plane plot of 2 cells. x and y represent the location of the 2 cells Figure 37 shows the phase plane plot for the combination of Cohesion and Avoidance of the two-cell system. There are two equilibrium lines which represent the separation distance of the Cohesion-Avoidance combination. The plot is symmetric about the origin since switching the location of the two cells (switching x and y) should not change the results of the system. Besides the points where the positions of the two cells are equal that cannot be solved, all points lead to the equilibrium lines. It is important to realize that these plots are only true when the cells are within each other’s neighborhood, otherwise there would be no influence for motion. The main point is that the combination of Cohesion and Avoidance produces a solvable separation distance. 97 Equal Cohesion-Avoidance combination Time step 20 Doubled Cohesion over Avoidance combination time step 20 Figure 38: Cohesion-Avoidance combination separation distance comparison. The red boundary lines show that the spacing is similar but groupings are tighter with greater Cohesion. Comparing the plots in figure 38, when Cohesion is increased, it can be observed that the cells have a smaller separation distance and the groups are slightly tighter. Thus the combination of Cohesion and Avoidance acts to maintain a separation distance between cells. Cohesion encourages a smaller separation distance while Avoidance promotes a greater separation distance. Although, with this thesis’s approach, the effects on separation distance from Cohesion and Avoidance are not equally linear since for Cohesion, the distance from other entities within the neighborhood does not matter while for Avoidance, the distance does matter. Moving forward to another combination, while Alignment may not be very interesting alone for a system at rest, in combination with Cohesion it is expected to have an impact. It is more difficult to predict exactly what will happen than in the case of Cohesion and Avoidance since Cohesion and Avoidance both act on positional measures while Alignment is based on velocity measures. However, Cohesion provides an initial source of movement, which will be to gather the cells together. Alignment will make the 98 cells want to follow the Momentum of their visible group, which is towards the centroid of the neighbor cells, thus gathering the cells together. For this reason, it should be expected that the cells will still gather to form groups. The results can be seen in the following figure. time step 1 time step 2 time step 3 time step 15 time step 20 time step 40 Figure 39: Cohesion-Alignment combination of 100 cell system As expected, the cells do form several local groups similar to the pure Cohesion case. The following figure is provided for comparison of the end results 99 Pure Cohesion time step 30 Cohesion-Alignment combination time step 40 Figure 40: Cohesion and Cohesion-Alignment combination result comparison The major groupings are similar although the specific configurations of some group are slightly different. The most visible difference is the joining of the three slightly separated groups into a more cohesive group circled in the figure. As the cells moved towards their cohesive targets, instead of stopping when reached, the cells continued to move due to the collective velocity of the neighborhood from the movement of the surrounding neighbors also moving towards cohesive targets. Basically, when a cell would normally stop after reaching a point of cohesive equilibrium based on pure Cohesion, the cell actually continues to move influenced by the collective Momentum of its neighborhood. This is the affect of Alignment: cells move in the direction of their neighborhoods collective Momentum. Another combination of interactive behaviors is Cohesion plus Randomness. 100 time step 1 time step 5 time step 10 time step 20 Figure 41: Cohesion and Randomness combination in 100 cell system Again, the system still reaches local gatherings of cells, although in different groupings than in the pure cohesive case. The differences are more noticeable than in the Cohesion and Alignment combination. This might be expected as the random effects will alter the locations of cells, thus constantly changing local neighborhood centroids. In addition, from one run to another, the locations of groupings may end up being different. Of course, the difference in locations of groupings are not completely dis-alike from the pure Cohesion case since Cohesion still has a large contribution and the initial random locations are the same. In the initially random cell locations used for this analysis, there 101 are already semi-groupings of cells establishing general neighborhood centroids for Cohesion. Of course, if the weight of Randomness was increased, then Cohesion would have a decreasingly significant contribution to the movement decision thus resulting in more random movement and positions. Although it is difficult to view with only time- step snapshots of the dynamical, time-evolving system, the cells never cease to move as the random contribution removes the possibility of equilibrium positions. Figure 42: Disorder entropy from Cohesion combinations of interactive behaviors In figure 42 the Cohesion and Avoidance combination is shown to not change much from the disorder measurement of the initial position of the system compared to the other combinations. Pure Cohesion definitely has a relatively greater decline in disorder while the Cohesion-Alignment combination reaches an even lower value. In addition, doubling the Cohesion weight in the Cohesion-Avoidance combination allows the Cohesion contribution to make a greater impact and decrease the disorder of the system 102 reinforcing the previously discussed separation distance. The Cohesion-Randomness combination does have an overall drop in disorder, but the random effect is definitely visible. The interesting result here is that the Alignment contribution in addition to Cohesion reaches a lower disorder. With Alignment, cells continued to move because of the collective velocity of their neighborhoods. Basically, when groups of cells would normally stop after reaching a point of cohesive equilibrium based on pure Cohesion, the cell and cell groups continued to move based on the collective Momentum of the neighborhood. However, when Alignment is added to the Cohesion-Avoidance combination, the end result between the two combinations of parameters do not produce significantly dissimilar results as emphasized by the following figures comparing the combination of Cohesion and Avoidance against the combination of Cohesion, Avoidance, and Alignment. Cohesion-Avoidance combination time step 20 Cohesion-Avoidance-Alignment time step 20 Figure 43: Cohesion-Avoidance and Alignment combination result comparison. The red boundary lines show the similarity in spacing between the two systems. 103 Figure 44: Disorder entropy of Cohesion Avoidance and Alignment While at first Alignment had no significant visible effect, this is due to the fact that the collective Momentums of the groupings were so low that the contribution from Alignment was dominated by the Cohesion and Avoidance contributions. At first, this may seem confusing, but it can be better clarified by considering the case where there is an increased amount of Alignment. After Alignment is increased to a greater contribution, a significant change in the collective behavior of the system becomes visible. Additionally, if instead of increasing Alignment, Momentum is added to each cell's profile, a similar significant change in the collective behavior of the system occurs. By increasing each cell’s Momentum, the collective velocity of each neighborhood is also increased. By increasing Alignment, the impact of the collective velocity of each Disorder Entropy: Cohesion & Avoidance with Alignment 7.546 7.547 7.548 7.549 7.550 7.551 0 5 10 15 20 25 30 Time Step Disorder Entropy (nats) Cohesion, Avoidance, Alignment Cohesion & Avoidance neighborhood is increased. The end result is that the domination of the Cohesion The below figures show the combinations with increased collective velocity. time step 1 time step 30 Figure 45: Cohesion-Avoidance The red and blue boundary lines help track the movements of the groups. neighborhood is increased. The end result is that the Alignment term can overcome the Cohesion and Avoidance contribution. The below figures show the combinations with increased collective velocity. time step 10 time step 20 time step 40 time step 60 Avoidance-Alignment combination with increased Alignment The red and blue boundary lines help track the movements of the groups. 104 term can overcome the The below figures show the combinations with increased collective velocity. time step 20 time step 60 Alignment in 100 cell system. The red and blue boundary lines help track the movements of the groups. 105 time step 1 time step 5 time step 10 time step 20 time step 30 time step 40 Figure 46: Cohesion-Avoidance-Alignment-Momentum combination of 100 cell system. The red boundary line helps track the movement of the group. As exhibited by the figures, the system still forms clear gatherings of cells, and the gatherings have a continual movement that flows in the direction of the collective Momentum due to the Alignment impact. Furthermore, because of the continual movement, the groups are no longer separated in several smaller groups. As the cells move, the different groups intersect and merge together to form a larger single group. This continual flow of a cohesive group is the beginning of the collective behavior called flocking. 106 Figure 47: Disorder Entropy of Flocking The above figure shows that disorder reaches a lower limit than has previously been observed. This is because the continual movement of the flocking cells allows the group to decrease the distance from other groups of cells. Stated differently, the global system forms a few groups of flocking cells rather than many separated and static groups of cells, thus the global system’s disorder entropy decreases as the collective ordering of the cells becomes tighter. This section examined the simple behaviors defining the interaction between cells. As shown, many of the simple behaviors are intuitive and easily understood individually; however, by combining the simple behaviors, the collective behavior of the system can have non intuitive results. While using simple interactive behaviors to structure the local interactions between cells provides a more easily understood control mechanism, the complexity resulting from many interacting agents cannot yet be completely evaded. Disorder Entropy in Flocking 7.46 7.47 7.48 7.49 7.5 7.51 7.52 7.53 7.54 7.55 7.56 0 20 40 60 80 100 Time Step Disorder Entropy (nats) Cohesion, Avoidance, & 3xAlignment Cohesion, Avoidance, Alignment, & Momentum 107 4.4.1 Flocking The synchronized but adaptable flocking behavior has been recognized as one of the key collective behaviors. Self-organized flocking behavior can be observed in many different natural system examples such as locust swarms, starling flocking, and fish schooling. Simply by altering the rules of interaction, the system can exhibit adaptive changes either in system structure or function. This coordination of multiple entities often deals with synchronized complex motion planning thus a major research challenge is developing methods for agent action synchronization in a robust and reliable way. In order to compare behavioral profiles and simulated trials of emergent flocking behavior, system behavior is characterized by the standard deviation (σ) of direction. The idea is that structured synchronized motion becomes qualitatively visible when groups of cells move harmoniously in roughly equivalent directions, or in other words, exhibit directional Alignment. Assuming a normal distribution, if the standard deviation of direction of the system is 0.5 radians, then roughly 70% of the cells are moving within about 30 degrees of each other. The maximum degree differential two cells can have is 180 degrees, which is in exactly opposite directions. 108 Figure 48: Standard deviation of direction over 300 steps The data for the standard deviation as it changes with each simulation step is also smoothed using a 30-step running average. This suppresses small spikes that do not represent the general behavior of the system. Most trials start at around 2 standard deviations, so the 1.5 mark will represent the onset of synchronized motion when the standard deviation begins to drop. It's used to compare profiles that have sharp decline in standard deviation versus those that have a gradual one as exhibited in the above figure. The total time τ for the system to drop below 0.5 radians can be separated into two parts: τ 1 the time to reach 1.5 radians, and τ 2 the time in between 1.5 and 0.5 radians. A steeper descent will have a smaller τ 2 . τ = τ 1 + τ 2 τ τ Each profile was run throug list of all the profiles can be found in the appendix. synchronized motion exhibited in standard deviation in direction below 0.5 radians. the left never reached this minimum while Set σ min > 0.5 rad A B C Figure 49: Comparison of profiles based on profile was run through many trials with each trial containing list of all the profiles can be found in the appendix. Centralizing the interest around the synchronized motion exhibited in flocking, the goal is to find the profiles that reach a in direction below 0.5 radians. In the following figure, the profiles on the left never reached this minimum while the profiles on the right did. σ min < 0.5 rad : Comparison of profiles based on minimum standard deviation 109 containing 300 steps. A Centralizing the interest around the , the goal is to find the profiles that reach a In the following figure, the profiles on minimum standard deviation Set σ min > 0.5 rad D E Figure 49, continued Set A shows that synchronized motion can be obtained by sufficiently applying Alignment such that it can overcome the contribution from the separation distance defined by the Cohesion and major driver of flocking behavior without Alignment to the separation distance can also achieve synchronized motion, but σ min < 0.5 rad , continued: Comparison of profiles based on minimum standard deviation Set A shows that synchronized motion can be obtained by sufficiently applying such that it can overcome the contribution from the separation distance and Avoidance combination. This Alignment behavior flocking behavior. Set B shows that adding a little bit of Momentum to the separation distance can also achieve synchronized motion, but 110 : Comparison of profiles based on minimum standard deviation Set A shows that synchronized motion can be obtained by sufficiently applying such that it can overcome the contribution from the separation distance behavior is a Momentum to the separation distance can also achieve synchronized motion, but 111 that adding too much Momentum will make the motion again sporadic. The separation distance from the Cohesion and Avoidance combination maintains the groupings of the cells while the little bit of Momentum provides the continuous movement, thus resulting in the flocking motion. Alignment is not an absolutely necessary component behavior to achieve flocking. But when the Momentum contribution starts to overpower the cohesive behavior, separation distance cannot be maintained and the cells do not exhibit flocking movement. In set C, the random contribution breaks the Alignment behavior. Not until the Alignment behavior suppresses the random movement can the system reach a standard deviation below 0.5 radians. Again, a little bit of Momentum can assist Alignment in maintaining the flocking behavior over the randomness, but too much destabilizes the flocking. Set D shows that combinations of only Randomness and Momentum do not result in lower standard deviations. Without the Alignment behavior or cohesive behavior, the system cannot achieve the desired synchronized motion. Every profile that exhibits flocking motion carries some contribution from either Cohesion, Alignment, or both. Set E reiterates the above findings. While it was found that some trials for certain combinations can reach a minimum standard deviation below 0.5 radians, not all the trials reached and maintained such minimum. The following table presents the percentage of trials that could reach but not maintain the 0.5 radian minimum. The following figures analyze seven of the analyzed profiles that showed strong flocking behavior, reaching a minimum standard deviation in cell direction below 0.5 112 radians in addition to maintaining the lower standard deviation at the end of the trial for one hundred percent of the time. These profiles can be compared for performance by analyzing the time in number of simulation steps it took to first reach 1.5 standard deviations, and then to reach 0.5 standard deviations. Profile Figure σ min < 0.5 rad. σ step300 < 0.5 rad. 16% 4% 0.95 ± 0.51 84% 84% 0.36 ± 0.48 100% 93% 0.18 ± 0.19 93% 93% 0.19 ± 94% 88% 0.25 ± 0.33 94% 94% 0.12 ± 0.09 9% 9% 0.86 ± 0.20 40% 30% 0.73 ± 0.42 Figure 50: Profiles at the edge of synchronized motion 113 σ step300 0.95 ± 0.51 0.36 ± 0.48 0.18 ± 0.19 0.19 ± 0.12 0.25 ± 0.33 0.12 ± 0.09 0.86 ± 0.20 0.73 ± 0.42 P1 P2 P3 P4 P5 P6 P7 Figure 51: Time performance comparison. Error bars represent one standard deviation P1 P2 P3 P4 P5 P6 P7 : Time performance comparison. Error bars represent one standard deviation 114 P1 P2 P3 P4 P5 P6 P7 : Time performance comparison. Error bars represent one standard deviation Profile C-O-A-R-M P1 1-1-3-0-0 P2 1-1-2-0-0 P3 1-1-3-0-1 P4 3-3-1-0-1 P5 2-2-1-0-1 P6 1-1-1-0-1 P7 1-1-2-0-2 Figure M Visualization σstep300 0.05 ± 0 0.07 ± 0 0.07 ± 0 0.16 ± 0 0.11 ± 0 0.12 ± 0.12 ± Figure 52: Profiles used for performance comparison 115 σstep300 ± 0.03 ± 0.02 ± 0.07 ± 0.08 ± 0.07 ± 0.07 ± 0.09 116 These profiles finish their trials at much lower standard deviations. A standard deviation of 0.12 signifies that most of the cells are moving in directions within 7 degrees of the average direction of all the cells. The speed at which each profile drops below 1.5 standard deviations seems to correlate well with the speed from subsequently dropping below 0.5 standard deviations, except for P4. This shows that while the increased Cohesion-Avoidance of P4 helps initially drops the standard deviation, the increased Alignment of P5 accelerates the decreasing of the standard deviation to drop below 0.5 such that the total time to fall below 0.5 is very similar. The faster speeds of P1 and P2 over the other profiles, as well as the faster speed of P1 over P2, shows that the Alignment contribution definitely accelerates the emergence of flocking motion. It is also possible that P5 is initially slightly slower than P4 due to the increased Momentum of P5. From previous examples, increased amounts of relative Momentum were shown to break the emergence of the synchronized motion behavior. The increased Momentum of P6 and P7 would also defend Momentum leading to slower emergence. This makes sense since Momentum creates inertia for the system to continue in the same direction as the previous time step. The results point to a correlation between the end standard deviation and system speed performance such that a lower end standard deviation matches with a faster system. Also, some contribution from either Cohesion or Alignment is necessary for structured flocking motion. Although Alignment is not an absolutely necessary factor, it greatly increases the speed and stability of reaching and maintaining lower standard deviations in 117 flocking motion. Alignment is a major driving factor for flocking. While the Alignment contribution was expected to hold such effect, its contribution must be significant enough such that it is not suppressed by other interactive factors. Avoidance can increase the minimum resistance level while too much Randomness definitely acts to break up the structured synchronized motion. 4.4.2 Stability of Flocking Behavior Complex systems provide adaptive behaviors but also lack the deterministic stability exhibited in classically designed systems. This is the design tradeoff between the approaches as previously discussed. Complex systems without stochastic contributions are fully deterministic from a set of given initial conditions, meaning the same system will produce the same results from the same initial conditions every time. The uncertainty arises from not understanding the full space of responses based on initial conditions due to the massive possibilities. The non-linearity of complex systems allows for small changes to consequence in large global effects. Small changes in initial conditions can produce large effects. While this leads to the unintuitive global behaviors, it can also destabilize the system away from functional behaviors, thus the need for guided emergence. A profile that can reach low standard deviations may not necessarily maintain such directional Alignment. Profiles were found that can both reach low minimal standard deviations and maintain those minimums. While it is difficult to prove convergence for the flocking behavior through theoretical equations, it can be shown statistically through many simulations. The previous analysis of repeated computer 118 simulation trials provides a statistical study by characterizing the resultant global behavior from many different initial conditions and profiles to ensure a statistical confidence of expected guided behaviors. It was shown that profiles matching strong behavioral patterns are statistically confident in resulting in the desired global behaviors. With the Alignment-Random profile, only 16% of the trials reached a minimum standard deviation below 0.5 radians and only 4% ended the trial with σ step300 < 0.5 radians. This questions the stability of the flocking motion exhibited within the system using such profile. In the above table, it is also shown that the 1-1-3-0-3 profile of the Cohesion-Avoidance-Alignment-Momentum combination lacks stability in maintaining a standard deviation below 0.5 radians although 100% of the trials did reach the minimum. The Cohesion-Avoidance-Momentum profile shows 84% that reached the 0.5 radian minimum in addition to a greater stability in maintaining the behavior, but is still lacking a smaller confidence interval in the expectation of the flocking motion. While some profiles cannot provide much assurance, seven of the analyzed profiles do reach a 0.5 minimum standard deviation in cell direction and maintain it until the end of the trial for one hundred percent of the time. As shown in the previous discussion, these profiles all had the strongest flocking behavior both in emergence quickness and flocking performance. This provides some statistical confidence of expected behaviors from the same parameter profiles. Although absolute stability is not proven, the statistical support provides a basis of expectation that certain profile combinations will reach specifically desired emergent collective behaviors. 119 In the MIM approach for CSO systems, there is a major difference than with many traditional complex systems because the end functionality is based on the collective behavior as oppose to specific structural formations. Because of this, it is difficult to use traditional stability approaches based on coordinate positions to identify attractors, basins of attraction, stable cycles, and sink nodes. The current mathematical techniques provide limited capability towards developing complex systems. Furthermore, the MIM approach designs for uncertainty by designing with uncertainty. Emergence is guided through the meta-model, but not absolutely specified. The space of uncertainty is exactly what allows for the width of functional capacity, so in a sense, the system is designed with limited stability. The instability can give rise to new functions that could only be reached by breaking out of stable cycles. 4.4.3 Searching Searching is a common application connected to CSO systems. CSO search involves distributed team of autonomous agents in searching for target. CSO searching exploits parallelism with many entities searching concurrently and can be implemented without a central commander in a fully distributed fashion. Looking at the natural systems of ant colonies, bee hives, and immune cells, none of these employ systematic searches such as breadth-first-search or depth-first-search. Observing a single entity in any of these systems may lead one to believe that the search progression is almost random. But in complex systems, the individual is not the whole picture and the total collective system must be properly grasped in order to understand the advantages of the complex system search. 120 Searching is often necessary because one of the difficulties in only giving each cell a small locality of sensing is that there may be no cell that is even aware of a target. Moreover, because of the large open space where the cells are free to roam, even after many time steps, the system may never discover the target. Contrast the two different locations for a passive object exhibited in the figure below. In order to simplify the analysis, the number of cells considered in the system is eight. The grayed areas represent environmental obstacles. Figure 53: Foraging: two contrasting locations for a passive object The two locations contrast varying difficulties for the cell group to discover the object. The cells can generally discover a passive object at location 1 more easily than an object at location 2 because the obstacles push the cells away from location 2. Basically, due to the Avoidance contribution, the cells are less inclined to explore the space in 121 between the two obstacle blocks. An increased average Avoidance weight in the system would produce a system with a wider search net. Increasing the average Avoidance weight of the system would produce a system with a wider search net, which may help to discover some locations quicker. However, because of the position of the passive object at location 2 within the obstacles, increasing the Avoidance weight of cells might push the cells away from the passive object since they are pushed away from the obstacles. Because of this decreasing the overall system Avoidance weight may increase the likelihood that the system discovers the object quicker. However, decreasing the Avoidance weight to a minimal amount results in a very tightly gathered system with a small net of exploration, in addition to poorer obstacle Avoidance. Of course, analyzing the system behavior is not as simple as tuning a single weight. Avoidance works in conjunction with Cohesion to define the separation distance between cells. Increasing Cohesion yields similar results to low Avoidance where the system tightly gathers and has a smaller sensor net field. Intuitively, to increase the search field, a lower Cohesion weight should be used. However with low Cohesion, if one cell were to discover the passive object, the other cells would not be as inclined to follow, never discovering the object. 122 Figure 54: Search comparison with the standard profile chosen as equal contributions from Cohesion, Avoidance, Alignment, and Momentum while having no Randomness. Figure 54 compares the average amount of time steps the system needed in order to discover the passive object at location 2. There are four different combinations of parameter weights: Standard, which is similar weights of Cohesion, Avoidance, Consistency, and Momentum with no Randomness; Double Cohesion, which is the standard setting with doubled Cohesion contribution; Double Avoidance, which is the standard with doubled Avoidance contribution; and Standard Plus Random, which is the standard in addition to a similar weight of Randomness. The figure shows that the Standard Plus Random setting will give the most efficient search with Double Avoidance and Double Cohesion following close behind. This means that the increased disorder from Avoidance does yield a quicker search, although not by much to the increased Cohesion. Of course, Double Cohesion still has a lower disorder measure than the Standard setting. Adding Randomness has the best 1422 736 616 537 0 200 400 600 800 1000 1200 1400 1600 Standard Double Cohesion D ouble A voidance Standard + Random Param eter C o nfig uratio n Search Efficiency ( loc a tion 2) Average Number of Steps 123 overall effect which indicates that increased uncertainty helps deal with the uncertainty in search applications. While disorder does seem to have some relation to search ability, because of the coupled nature of disorder with obstacle Avoidance, depending on the environment, the relationship between disorder and search efficiency is not directly proportional. 4.5 COARM Behavioral Model Relationship Findings The behavioral examination was initiated in order to gain insights into the relationship of the COARM BM. This simulation based study helps describe the Meta- Behavioral matrix. The following key points and representative profiles summarize the different findings. This resultant information builds the base of design information that can be used in manipulating adaptability into CSO systems using the COARM MIM. Avoidance is required for managing obstacles For aggregation, compaction, and centering increase cohesion For scattering and dispersion increase avoidance Specific group demand requires decreased disorder thus profile combinations of greater cohesion, greater alignment, or less avoidance Momentum gives continuous fluidity Alignment is the major driver for synchronized fluidity Random uncertainty in the system helps manage application search uncertainty 124 Using these insights, the designer can identify interaction behaviors for different functional capacities. Essentially, by controlling the parametric variables, the system’s mechanical implications can be manipulated. In most cases, different ratios and combinations of interactive behaviors will be required. It will rarely be as simple as using a single behavior. The hard task is simultaneously handling both uncertainty and a specific demand. As pointed out earlier, obstacle evasion is impossible without Avoidance. Thus any system that is possibly concerned with unforeseen obstacles or unpredictable terrains must have some level of Avoidance. However, Avoidance increases disorder, and any system that may require a specific group demand requires decreased disorder. Specific group demands, such as requiring four individuals to transport an object, depend on cohesive collectiveness of a group, thus when disorder is too high, the group may not operate as one. Towards extreme levels of disorder, individual cells cannot even perceive other cells outside of their neighborhood in order to interact with. Beyond disorder, many applications may require continuous movement of the cells and groups of cells. As demonstrated, with only Cohesion and Avoidance, the cells eventually reach relative equilibrium at some separation distance. Continuous fluidity is achieved by introducing Momentum into the system such that the cells will maintain some speed. Furthermore, Alignment will drive collective synchronized motion. Finally, while disorder does seem to have some relation to searchability, because of the coupled nature of disorder with obstacle Avoidance, depending on the environment, both decreasing and increasing disorder may have a positive impact on 125 search efficiency. Search efficiency is important for any search or exploration application. It is also important if the system needs to discover a beacon in order to define a new task or target function, especially when in an idle state of global desire. One way to deal with the task uncertainty is by increasing uncertainty into the system, which is done through Randomness. The increased uncertainty assists in circumstances when the system needs to discover new paths or new locations. Random approaches and instantiations are often used within uncertain applications such as in the Monte Carlo method, randomized repetitions of hill climbing, and even genetic algorithms. 4.6 Concluding Remarks of Major Findings A Meta-Interaction Model approach with Interactive Behavioral Based Design is given in order to design adaptability into CSO systems. The COARM BM design space represented by the MIM was explored. It was analyzed focusing on synchronized flocking behavior. The relationships between the COARM simple behaviors of Cohesion, Avoidance, Alignment, Momentum, and Randomness were investigate and the major findings from the interactive behaviors were discussed. An analytical study at this level of detail has not previously been completed from a design perspective. The concept is to understand the space of possible collective behaviors by focusing on the simplified classes of observable group behavioral constrained by the interactions of the individuals. This describes the parameter gradients and trends that will be used to guide emergent capacities. 126 The COARM BM is spatially defined. As such, the local constraint of each cell's neighborhood was a definite limitation for certain mechanical applications. Some profiles also shows stability concerns in obtaining certain target collective behaviors. These are weak profiles with respect to the target behavior and show the transition zone between collective behaviors. Alignment is definitely the main attractor for stabilizing synchronized fluidity. However, the addition of the Momentum interactive behavior shows Alignment is not the only attractor. Adding Momentum results in increased fluidity although it can also decrease the speed of emergence. Expanding the BM set size results in a more complex collective behavioral space, and thus a wider system capacity space. A wider capacity space comes with a greater uncertainty, but this is the tradeoff a designer must make. It was also found that increasing a system's random uncertainty helps deal with application search uncertainty. Essentially, introducing Randomness allows the system to be open-minded to behaviors that can encourage discovery. This result combined with the analysis of Alignment and Momentum can make an extreme parallel with another very complex system, human society. Alignment, or the behavior to follow the behaviors of others, propels efficiency in the group. Japanese culture and society emphasizes the human nature to follow the direction of others. It also shows a culture pride of efficiency and optimized processes. American culture, on the other hand, emphasizes individuals. America has shown the strength to continuously move forward although carries the tendency to not change directions until absolutely required. Americans carry greater individual momentum rather than focusing on the efficiency of the greater global result. 127 Furthermore, the lack of directional Alignment is also emphasized with random behaviors in many directions from the diverse American individuals of varying cultures. This Randomness results in a society that has lead many modern innovations and discoveries. Through this simple study, findings connected with bigger complex systems could be discussed. The MIM approach has lead us to new insights towards complex systems. The COARM MIM is the representation abstracted on the BM set. The MIM approach uses the insights from the simulation based study to guide the tuning of the design variables. It provides a method to design adaptability into the system by exploiting dynamic variables that can be easily manipulated to change the collective behavior of the system. The MIM profiles link the local behaviors to the collective behavior and provide heuristics the designer can use in connecting the local interactions with global functionality. The MBM based on parametric behavioral variables can straightforwardly and quickly be applied towards systems with Behavioral Models. The MBM approach also lends itself well to further developments in using control feedback design, learning methods, or evolutionary algorithms, especially those that require heuristic guidance. The next chapter will further demonstrate multi-functionality through mechanical task applications. 128 Chapter Five: Example Applications Using the COARM Meta-Interaction Model 5.1 Introduction This chapter will exemplify IBD using the MIM with several task applications. A single BM is not expected to be the solution for every mechanical task; different function capacities will demand different behavioral sets. COARM is just one point in the MIM behavioral design space. Using the MIM approach as developed for the COARM BM, some of the simple function capacities that might be achieved are: synchronized group motion, exploration or searching, coverage, containment, surrounding, pursuit, evasion, and following. These are all typical spatial, mechanical tasks that are required for real world applications that demand complex adaptive systems such as search-and-surround, foraging, missile flocking, and material fills. Different combinations of global behaviors are required for each application, and the dynamical variables must be tuned in order for those behaviors to emerge. Moreover some task demands will require not only parallel combinations, but temporal combinations of interactions they may need to occur in sequential phases. An example demonstrating temporal sequence combinations is natural disaster rescue. The problem first demands exploration with evasion and then would require transporting. The first phase would utilize added Randomness and Avoidance while the second phase uses Cohesion and Avoidance. This chapter will further discuss application examples. 129 5.2 Search-and-surround As an example task application, consider the case of search-and-surround. Search- and-surround applications include hazardous waste cleanup, bomb detection and removal, and disaster survival rescues. A natural system parallel would be the human immune system where white blood cells continuously swarm through the body searching for foreign substances to eliminate. Complex systems provide many advantages to the search-and-surround problem. First of all, as the number of agents multiplies, it will become impossible for a central commander to coordinate the search task for the numerous agents. The MIM approach is fully distributed not relying on any central control or global information. In addition, the search-and-surround applications often occur in hostile and unpredictable environments whether in enemy territories, unexplored regions of the space and the ocean, or natural disasters like earthquakes and storms. The multi-agent system must be able to adapt to the situation without the need for a prior knowledge of the specific hazards that might be encountered. The search-and-surround mission requires function capacities to achieve exploration and searching. This will occur in a generally open environment but there may be some hills and valleys that create boundary limitations. There may also be possible enemy aggressors or other non-hostile entities that exist in the environment. Because of the nature of the exploration and search task, the target location is also unknown but only identified after discovery. This task requires the general function capacity of motion. In a massive homogeneous system, the cells would be self-propelling particle net in its exploration. The particle net also assists in the surround task as the second-phase task 130 requires many particles to successfully discover the object, not just one. The main uncertainties are the environment layout although a generally expected terrain type is given. There is a huge uncertainty in the target location. Another uncertainty is in not knowing the possible dangers and enemy aggressors that might exist. However, the general function class is simply self-propelled movement. Once the loosely defined functional requirements and unknowns have been outlined, the designer's next task is modeling, with the first phase in selecting a behavioral interaction model. The COARM behavioral interaction can maintain a separation distance to create a particle search net and also demonstrate continuous motion of search. The COARM model requires a very simple cell form for implementation, which aligns with the goals of using simple, non-intelligent agents. The intelligence of the system results from the combined global behavior. And finally, the MIM for the selected BIM can be developed. For COARM, this was done in the previous chapter and preliminary insights that outline the heuristic relationships were found. This information can be used for later growth implementations such as learning and genetic algorithms. Extended-Boids models have been well-studied and have actually already been shown to work for specific search-and-surround situations. 131 Planning with Uncertainty BM CM MIM General Environment Definition: Open terrain may have hills and dips General Function Capacity: Movement, self propulsion Particle net Uncertainties: Necessary direction (uncertain target location) Terrain layout Hostilities or enemy aggressors Requirements: Search net or separation distance Continuous movement of search → Use COARM Interaction Model Simple mechanical cell 2-D motion Limited local sensor Senses relative position and velocity Sense foreign objects (boundaries) Limited long-term memory (only MIM parameter weights) Preliminary tests and simulations Justify working behavior Behavioral heuristics Introduce evolution algorithms Finalize Figure 55: Search and Surround CSO Design Process Phase 1: Exploring / Searching Behavior: Synchronized Continuous Motion + Uncertain Directions Parameter Profile: + = Phase 2: Surrounding Behavior: Following Parameter Profile: Figure 56: Representative profile for phases of search-and-surround This task requires two phases, the first of searching and the second of following. Many cells following a stationary object has the consequence of surrounding. Again, since the second phase will require cohesive groups, the first phase can utilize flocking 132 motion to have preemptive groups built. Tuning with a reliance on Randomness, Momentum and Alignment, which transfers to a dominance of Cohesion after the object is found, should result in search-and-surround. Just to note, some Avoidance is required so that individuals do not run into each other. initial time step 5 time step 9 time step 16 time step 20 time step 36 time step 82 time step 106 time step 142 Figure 57: Search-and-Surround example: 100 cells searching to surround 5 big red objects. A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E 133 Figure 57 exhibits an example simulation of 100 cells searching to surround 5 big red objects in an open environment. Just to restate, the simulation has toroidal boundaries such that the top and bottom are linked and the left and right are linked. From the initial positioning, object D and C are quickly discovered and surrounded. Consequently, the cohesive group behavior of the cells draws more entities to the general location. However, since the objects have already been surrounded, the new cells cannot latch onto the position of the objects and continue moving in search of other objects. In step 36, this grouping of cells is observed and object A has already been surrounded. The group quickly discovers object E which leaves object B as open prey. By step 82, the remaining group discovers object B. In step 142, the five objects have been surrounded and the extra cells continue to flock as group searching for any other objects. With higher entropy through random movements and increased separation, the cells can quickly discover objects. Furthermore, because the cells are constantly interacting implicitly through the collective behaviors, objects can be quickly surrounded rather than waiting for each individual cell to discover the object on its own. When an object is located, it is quickly encompassed because cells move as a group rather than individual. The group behavior of the cells increases effectiveness and does not rely on the individual abilities of each cell. The method is fully distributed without any explicit cooperation between the simple cells. This search-and-surround simulation is a simple demonstration of one application for complex, adaptive systems. 134 5.2.1 Foraging: Search-and-Surround Extended As described earlier, the search-and-surround application can be extended many other tasks. One exhibited in ant colonies is foraging where cells must go out and search for a specific type of object, then transport it to a target destination. Ants forage for food. Moving and transporting other non-system objects is a common function required for applications such as rubble clearing or search-and-rescue. However, for the concept of simple small cells, one robot may not have the individual power to move an object by itself, and instead, needs the help of several cells to work together. Furthermore, if the cells have no global coordinate system, unless they already know where the object to be moved is located, they have to search for the object. For the next study, the global objective will be to move a passive object to a target location. The passive object will require at least four cells around it to be moved. Initially, one cell is not enough to move the object, but as other cells come into contact with the object they will help the first cell to move the object. With Cohesion, when a single cell is near the object, it is expected that the other cells would more likely move in that direction, even if the other cells do not see the object. The figure below shows the initial position of eight cells and the initial position of the passive object in between the two obstacles. The object will have a target location, which is denoted by the ‘X.’ 135 Figure 58: Initial system state with eight circular cells, two obstacles, and one passive object on the field. 'X' denotes the desired location of the object. This study does not focus on the mechanism of attaching or physically pushing the object. It is only important that the cells are near the object. Cells maintain their proximity to the object by considering a magnified weight for the passive object when calculating the cohesiveness vector contribution. This has the effect of gravitating cells to the passive object when the object is within the viewable neighborhood of the cells. Although it may seem obvious that the system would have no apparent global functionality if the cells did not consider Cohesion, Avoidance, or Alignment, the figure below is presented to confirm that the simulation would produce this expected result. 136 Figure 59: Purely random system without Cohesion, Alignment, or Avoidance. Figure 59 shows a purely random system without Cohesion or Alignment after 300 time steps. The foraging goal was never reached because not enough cells discovered the object at the same time, although it is possible that after a larger amount of time, enough cells would discover the object through their random movement. However, due to the lack of Cohesion, the cells may only move the object a small amount before venturing off. The cells never develop a coherent flock and thus provide no definite global functionality since one cell is not enough to move the passive object. This shows the necessity of the cohesively collective behavior of the system. 137 (a) (b) (c) Figure 60: Eight cells moving a passive object. In this run (a) is time step when the cells have gathered, (b) is time step when the cells discovers the object, and (c) is time step when the object gets to its desired location. Figure 60 shows the system performing collective foraging: locating the object, moving it, and bringing it to a target location. Similar weights were given each to Cohesion, Avoidance, Alignment, and Momentum, which will be the default initial parameter setting. In figure 60a, the cells have organized together into the single cohesive flock. In figure 60b, the cells have discovered the passive object, and in figure 60c the cells bring the passive object to the target location. Currently, the passive object dictates the target location since the cells have no global positioning information. This study shows that the CSO system using the MIM approach is capable of completing the global foraging task. The next examples will continue to use the same CM and BIM models in order to show the functional versatility of the CSO system with the MIM model. 138 5.3 Missile Grouping Modern warfare has been sharply defined by technological advances. Many recent missions and conflicts have relied on guided weapons such as missiles. The purpose of the guidance and control system is to secure a direct hit upon a selected target. “Guidance” is defined as the strategy for how to steer a missile in order to intercept, while “control” is defined as the tactics of using the missile actuators to implement such strategy (Berglund, 2001). Guidance can be divided into two main categories: target related guidance, where the missile receives real-time target tracking data, and non-target related guidance, where the missile navigates to some predetermined point, which can be the target or the position where target related guidance initiates (Berglund, 2001). There are three main phases of guidance: the Boost phase, the Midcourse Phase, and the Terminal Phase. The objective of the boost, or launch phase, is to position the missile so that it can receive guidance signals to reach the target. The midcourse phase is the second phase of guidance and places the missile near the target where the final phase can begin. This is often the longest phase. The terminal phase brings the missile to intercept with the target. This phase often has the highest demand on guidance accuracy and missile maneuverability. Different guidance-control laws can be used in the different guidance phases. Many air missiles use trajectory optimization during the mid-course phase; however, trajectory optimization can only avoid known obstacles. Most trajectory optimization is done pre-launch, although it is possible to re-plan during missile flight assuming there is an active communication with the missile. 139 The self-organizing approach lends itself well to the midcourse phase where essentially the missile, or in this case many missiles, must get from some point A after the boost phase to some point B where the target is located. In the case that obstacles and the foreign terrain may be unknown and no active communication link can persist with the missile, no pre-launch trajectory optimization can be done. In addition, when there are many missiles in flight together, trajectory optimization becomes more and more complex. The MIM approach will not always be the best choice, especially if the flight route is completely determined. However, the approach provides adaptive benefits to dynamic environments that carry unforeseen dangers. In addition, the approach scales well for increasing number of missile that may need to flock together. Pre-planned trajectories would normally be planned for each missile in order for the missiles to avoid collisions. With a self-organizing approach, missiles can be given simple rules of interaction in order to execute a successful flight. A natural system analogy would be bird flocking or fish schooling. Planning with Uncertainty General Environment Definition: Open air space Possible terrain formation obstacles General Function Capacity: Movement, self propulsion Flocking Uncertainties: Path's Obstacles Hostilities Figure 61: Planning with Uncertainty for Missile Grouping Grouped missile flight relies on synchronized fluidity, evasion, and target location thus the parameters are heavy also not expected to hurt here distances of the missiles. implement the target locati target’s relative direction is unavoid obstacles that may exist in the path of the missile flight. Another uncertainty is in not knowing the possible dangers and enemy aggressors that might exist. Phase 1: Exploring / Searching Behavior: Continuous Motion + Flocking + Obstacle Avoidance Parameter Profile: = Figure 62: Representative profile for phases of Grouped missile flight relies on synchronized fluidity, evasion, and target location thus the parameters are heavy on Momentum, Alignment, and Avoidance also not expected to hurt here and may be used to help define different separa In this case, there is some "desire" that is necessary in the target location. Unless the missile can freely roam, having to know the target’s relative direction is unavoidable. The main unknown is the environmental obstacles that may exist in the path of the missile flight. Another uncertainty is in not dangers and enemy aggressors that might exist. Phase 1: Exploring / Searching Continuous Motion + Flocking + Obstacle Avoidance + + : Representative profile for phases of search-and-surround 140 Grouped missile flight relies on synchronized fluidity, evasion, and target location Avoidance. Cohesion is define different separation that is necessary in order to Unless the missile can freely roam, having to know the the environmental obstacles that may exist in the path of the missile flight. Another uncertainty is in not surround 141 initial position after boost phase time step 25 time step 50 time step 69 time step 80 time step 95 time step 111 time step 130 time step 177 Figure 63: Example flight of 10 self-organizing missiles Figure 63 shows the implementation of applying self-organizing principles from complex system to missile group flight. Initially, the 10 missiles are evenly separated as they might be from the launch phase. They know that their target lies somewhere to the right so they proceed in that direction. However, at approximately step 50, the missile 142 group comes into contact with the grey obstacles. Due to the obstruction, which could be representative of mountain ranges, buildings, etc., the missiles must reshape their formation in order to safely pass through the opening between the obstacles. Steps 69 through 95 show the tightening of the formation in order to meet the constraints of the passage way and at step 111 the missile group is safely passing through the obstacles. At step 130, the missile group begins to re-separate in order to create better separation between the missiles as space opens up. Step 177 shows the more distributed spacing as the missiles have passed through the toroidal boundary taking advantage of the more open environment. The figure shows the successful flight execution of the missile grouping as they avoid possibly unknown obstacles without any central controller optimizing the trajectories of each individual missile. 5.4 Material Fill Another critical application that has been connected with CSO systems is the material reinforcement task. This class of applications manifests in several varieties including self-growing support columns, material shields, self-repairing covers, or even signal nodal nets. CSO systems are excellent solutions for these challenges because of the distributed approach and simple, inexpensive components. In this study, we will consider the simple case of a material fill where the design objective is to minimize void space, which requires a function capacity of a dispersed particle net. Essentially, given a boundary of open space, the CSO system needs to maximize coverage through the space at all times. Thus the top-down imposed function will be to distribute through the space 143 but to maintain some cohesiveness. If the cells get too far apart, then a void is created, but if the cells are too clumped together, there will be large open spaces. Planning with Uncertainty General Environment Definition: Open terrain Possible scattered obstacles General Function Capacity: Dispersed particle net Uncertainties: Void Locations Terrain layout Figure 64: Planning with Uncertainty for Material Fill The simulated system will consider a square open space with the system composed of 100 cells. The space is divided into a 10-by-10 grid representing void spaces. The fill rate can then be measured by counting the percentage of voids occupied by at least one cell of the system. In order to fill one-hundred-percent of the void spaces, the cells would have to perfectly distribute one cell for each and every void space. This is difficult considering the cells do not even know where the void spaces are and do not communicate to each other location directives. The below figure shows the10-by-10 grid with red x-marks pointing out unfulfilled void spaces. This application will definitely require scattering and dispersion, but what makes it interesting compared to the previously studied applications is that motion may not be required. In many of the previous applications, the synchron was beneficial. However, this application relies more on static equilibrium positions as oppose to constant motion. interactive behaviors. The mission environment is generall may be obstacles scattered through the field. Material Fill Behavior: Scattering, Dispersion Parameter Profile: Figure 66: Representative profile for phases of search Figure 65: 10-by-10 grid for material fill This application will definitely require scattering and dispersion, but what makes it interesting compared to the previously studied applications is that motion may not be required. In many of the previous applications, the synchronized motion of was beneficial. However, this application relies more on static equilibrium positions as oppose to constant motion. In the COARM BM, Cohesion and Avoidance The mission environment is generally known to be open, but there may be obstacles scattered through the field. Scattering, Dispersion : Representative profile for phases of search-and-surround 144 This application will definitely require scattering and dispersion, but what makes it interesting compared to the previously studied applications is that motion may not be ized motion of CSO systems was beneficial. However, this application relies more on static equilibrium positions as Avoidance are the static y known to be open, but there surround 145 The needed profile is a simple pure Avoidance profile. This will create the most dispersed material net without separating too much. The question is why Cohesion is not optimal. Once the cells move outside the range of other cells, they no longer have any need to move since there is no continuous motion for Momentum or Alignment. The neighborhood size consequently is what defines the separation between each layer of material and Cohesion is not needed to maintain groupings. The below figure shows the performance comparison for four different profiles with pure Avoidance as the best. Figure 67: Percentage of voids filled comparison The real major limitation is the number of cells as compared to the space that requires filling. The fewer cells that are used in the system, then clearly the more difficult it will be to fill the voids. In the case that there are very few cells as compared to the size of the void area, then increasing the neighborhood size will create increasing distances of Standard Cohesion-Avoidance Cohesion-2xAvoidance Pure Avoidance 146 separation between the cells. If the a shorter distance is preferred over covering a wider overall area, then the Cohesion weight may need to be increased. 5.5 Implications and Concluding Remarks This section has demonstrated multiple applications and achievable function capacities from the CSO system. The different effects of the COARM interactive behaviors were utilized. The COARM BM was able to adapt to several task requirement by generally specifying the task environment. It has demonstrated multi-functionality from collective behaviors that spawn from simple interactive behaviors and simple cells. In order to design complex systems for uncertain applications, the designer must design by allowing for the uncertainty, but then guiding it. The exhibited applications are building blocks for many more elaborate real- world applications. Studying these applications of the meta-model approach for CSO systems can provide insights guiding us for the design of future systems. Search-and- surround is a preliminary situation for other applications such as planetary exploration and mine removal. As technology advances, search-and-surround also leads toward nano- robotic systems that can be deployed within bio-systems such as in the human bloodstream. Group flocking is a major stepping stone towards team robotics and unmanned vehicle squadrons, whether aerial, aquatic, or land based. The material fill application can have implications on amorphous materials, signal nodes, reconfigurable circuitry, support columns, material shields, and self-repairing covers. 147 The extension towards future applications is not about giving specific internal profiles to computational agents but realizing the implications of changing interactive behaviors. For example, instead of specifying an exact Avoidance or Cohesion contribution, engineers can control the interaction through magnetic manipulation. Or instead of specifying Momentum within a profile, the scientist can change thermal characteristics in order to effect interaction changes. Understanding the trends within the meta-model design space can help engineers and scientists develop new systems by realizing new implementation and control mechanisms. The MIM approach is about the relative gradients in behavior manipulation to guide emergent response, not specifying absolute parameter profiles. Furthermore, the behavioral manipulation can be achieved by different mechanical techniques beyond computational memory, depending on the system. This is a major implication of the new design space based on behaviors. The self-organizing method allows for the system to alter its function simply by manipulating the parameter profiles. This is the assistance that the MIM approach provides in designing complex adaptive systems. By using BBD to design the CSO system and develop the MIM, the system multi-functionality can easily be controlled and adjusted. Furthermore, the MIM approach provides direct access to the adaptive change that can work in conjunction with other learning, evolutionary, and feedback methods. Of course, the classical engineering approach may still be ideal when the environment and functional specification can be well-defined. Self-organizing based complex systems excel in environments containing unforeseeable circumstances when engineers cannot predict all the possible contingencies that may be encountered. CSO 148 systems can provide the adaptability in order to manage such uncertainties that classical systems cannot. On the other hand, the adaptability is gained at the compromise of predictable determinism. Engineers must balance these tradeoffs in their design solutions. 149 Chapter Six: Contributions and Future Direction The Meta-Interaction Model using parametric behavioral weights has been introduced and applied to representative multi-robotic applications. The Behavioral Based Design approach can quickly be applied towards systems with conceived Behavioral Models. It provides a method to manage multi-functional adaptability by exploiting dynamical variables that can be easily manipulated to change the overall behavior of the system. This approach lends itself well to further developments in using control feedback design, learning methods, or evolutionary algorithms, especially those that require heuristic guidance. Concluding this dissertation, the intellectual contributions are asserted and future research directions are discussed. 6.1 Contributions 1. COARM: CSO System Design and Application The COARM system and computer simulation was developed in order to analyze the use of the MIM. The multi-agent computer model demonstrates system multi- functionality through MIM manipulation. This system implementation and simulation provides an alternative approach of a CSO system implementation. The system achieves functionality while maintaining the following characteristics: The approach to agent interaction to create global functionality relies only on local interactions with absolutely no global awareness. Cell algorithms are robust as they do not rely on global coordinates, centralized control, explicit cooperation, or specific sequences of team actions. 150 Cells are simple without long-term memory, complex decision making, large data streams, or explicit modeling of other agents. Varieties of collective functions are achieved. Users have a direct control mechanism through the parameter manipulation. 2. The Meta-Interaction Model Approach This work presented the Meta-Interaction Model. It uses parameterization as a method to manage and manipulate multi-functionality of cellular, self-organizing systems. The tunable dynamical variables provide control over the global pattern dynamics. This approach grants direct top-down control over system capacity emergence. It combines the top-down guidance with bottom-up cellular self-organization. The Meta-Interaction Model is an abstracted layer on the Behavioral Model. As such, to evaluate the abstract, theoretical approach, the COARM BM was used to demonstrate the use of the MIM. The study has revealed trends and relationships between different COARM behavioral interaction types as well as the connection to global functionality. This gives the design information that can assist the designer and the system user to manage and guide the system functionality. It is also the heuristic information that would be applied in learning and other artificially intelligence algorithms leading towards system evolution and growth. Consequently, the meta-model approach lends itself well for explicit system controls methods, learning algorithms, and genetic algorithms. 151 Ultimately, the MIM approach introduces a new design space based on interactive behaviors. The space links emergent function capacity with local interactions. Using this design space can lead to developments of new CSO systems and can provide a method to guide emergent functional capacities. 3. Interactive Behavioral Based Design for Cellular Self-Organizing Systems The MIM approach is centered on Behavioral-Based Design of CSO systems. It is focused on interaction with no pre-conceived forms. This work has outlined the BBD approach for designing CSO systems. It decouples the system's function from its form. This allows for multiple structure solutions rather than relying on human generated pre- specified solutions. The global functionality is connected to the emergent behavior as oppose to an emergent structure. Focusing on behaviors provides an easy way for the designer to focus on the complex interactions of the system. It also hides low-level details allowing for the designer to concentrate on the high-level problem and solution. This combines human based top-down directive with the advantages of natural processes of bottom-up self- organization. Using such a hybrid approach allows for the designer and the user to balance top-down targeted functionality with the system's bottom-up adaptability to dynamically changing problem requirements. 152 4. Alternative Design Approach for Cellular Self-Organizing Systems The final result of using the MIM technique centered on BBD is a new approach for multi-agent system design. The classical design process limits the advantages gained by using complex systems. Others have recognized the need for a new paradigm but have not yet outlined the context for that new paradigm. In this work, shifting towards system based on artificial nature, the concepts that the new paradigm must center around have been discussed. Because of expanding system size and changing demands, the complex designer must design in the realm of the unknown and accept that not every minute detail can be specifically addressed. The complex system must be designed with the ability to grow after launch. This can be done by relying on self-organization rather than on the traditional functional breakdown with piece-by-piece design. In order to design the context of self-organization, the designer must focus on the interactions between cells, which are the intrinsic source of the system's complexity. By designing with complexity, the solution can match the multi-functional demands of the problem. Complexity gives the solution its source of adaptability. Traditional design attempts to simplify and strip this complexity, thus removing adaptability. Retaining complexity within the solution system increases the system's total number of achievable states, or variety, resulting in the capability of fulfilling multiple challenges. This work takes just one small step in pushing the envelope of design towards an artificial nature. In this space we design for uncertainty with uncertainty rather than relying only on certain knowledge. This envelope extension is exhibited below. 153 Figure 68: Extending the Design Envelope Towards Artificial Nature 6.2 Future Directions This thesis has introduced a novel concept towards the design of CSO systems, but many future extensions are still waiting to be discovered. This research paves the path towards several research directions. 1. The study has so far only considered homogeneous systems. A future step would introduce heterogeneous cells. There are two levels of heterogeneity with the CSO system, internal and external. The internal heterogeneity would result from cells carrying differing profiles as oppose to every system cell sharing the same profile. This would be a necessary extension as cells gain the ability to internally evolve in different directions. The MBM method easily leaves open the possibility of internal evolution, and actually expects it. What happens if a single system carries two different dominant parameter sets? 154 The external level of heterogeneity would consider a system with cells that are mechanically and physically different. Increased individual functionality in the cell model may give rise to a bigger behavioral space and thus expanded collective functional capacities. Increased interfaces results in greater complexity. The approach may be extended to explore varying levels of communication, memory, mechanical functions, and other individual capabilities. Including either internal or external heterogeneity would explore further into the MBM space. 2. As mentioned previously, the meta-model approach easily lends itself to combine together with other intelligence methods. The level of technology would greatly benefit from expanding and further developing an approach to include learning, feedback or evolutionary methods. This could lead to a system that would self-generate the MBM matrix, rather than having the designer examine the MBM matrix. The system could use fitness functions or other methods to dynamically evaluate and extend the MBM matrix. Future research can combine these techniques such that the system can self-discover new component or system behaviors, and thus functionality. Currently, the system objective is defined extrinsically by a human programmer, but it can be adjusted to be intrinsic based on fitness functions or even simply survival. 155 3. 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Abstract (if available)
Abstract
The Cellular Self-Organizing (CSO) system takes the nature inspired biological processes of self-organization and emergence towards complex, multi-agent systems. Self-organization can be observed in many natural systems, and researchers hope to harness the biological advantages of simple individuals, versatile collective functionality, and robustness. The point in being cellular is to emphasize the simple nature of each agent and the idea of a large system population. A single simple cell may not be successful on its own, but a collective system of cells can be extremely adaptable and functional. ❧ Technological development is facing increased challenges as design engineers begin to tackle problem domains with greater uncertainty. Future engineered systems must be able to function in unpredictable environments such as deep ocean, rough terrain, and outer space while performing uncertain tasks like hazardous waste cleanup and search-and-rescue missions. CSO systems can provide the adaptability in order to manage uncertainties that traditional systems cannot. As the uncertainty of the problem domain increases, engineering design methods must be advanced in order to properly address the changing needs and constraints. ❧ This thesis details a new CSO approach inspired by natural phenomena in order to extend the design envelope towards an artificial nature. While natural systems had the luxury of evolution over millions of years, achieving bottom-up adaptability by design represents a major challenge to the systems engineering and design research community. Two fundamental issues must be addressed: one is the analysis problem of predicting the global emergence from local interactions
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Asset Metadata
Creator
Chiang, Winston Wen
(author)
Core Title
A meta-interaction model for designing cellular self-organizing systems
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
07/30/2012
Defense Date
05/01/2012
Publisher
University of Southern California
(original),
University of Southern California. Libraries
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Tag
bio-inspired design,cellular,emergence,mechanical design,modular,OAI-PMH Harvest,robotic design,robotics,self-organizing,self-organizing swarm,swarm,swarm engineering,team robotics
Language
English
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Electronically uploaded by the author
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Jin, Yan (
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), Chen, Yong (
committee member
), Flashner, Henryk (
committee member
)
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wwchiang@usc.edu
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https://doi.org/10.25549/usctheses-c3-76138
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etd-ChiangWins-1061.pdf
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76138
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Chiang, Winston Wen
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texts
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University of Southern California Dissertations and Theses
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The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
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Tags
bio-inspired design
cellular
emergence
mechanical design
modular
robotic design
robotics
self-organizing
self-organizing swarm
swarm
swarm engineering
team robotics