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8.1 Index fingers biomechanics
The skeleton of the human index finger consist of 3 joints connected with 3 rigid links.
The two joints (proximal interphalangeal (PIP) and the distal interphalangeal (DIP)) are
described as hinge joints that can generate both flexion-extension. The metacarpopha-langeal
joint (MCP) is a saddle joint and it can generated flexion-extension as well as
abduction-adduction.
Fingers have at least 6 muscles, and the index finger is controlled by 7. Starting with
the flexors, the index finger has the Flexor Digitorum Profundus (FDS) and the Flexor
Digitorum Superficialis (FDP). The the Radial Interosseous (RI) acts on the MCP joint.
Lastly, the extensor mechanism acts on all three joints. It is an interconnected network of
tendons driven by two extensors Extensor Communis (EC) and the Extensor Indicis (EI),
and the Ulnar Interosseous (UI) and Lumbrical (LU). There are also 4 passive tendon
elements that complete this network. These passive tendons are the Terminal Extensor
(TE), the Radial Band (RB) the Ulnar Band (UB) and the Extensor Slip (ES).
Active tendons are connected to muscles and therefore they directly actuate the finger.
Passive tendons are connected with other tendons(active) and ligaments and their role
for the case of the index finger is to transform the applied tensions to the distal join. In
our work we will consider only the active tendons.
8.2 Iterative stochastic optimal control
We consider the nonlinear dynamical system described by the stochastic differential equa-tion
that follows:
237
Object Description
| Title | Iterative path integral stochastic optimal control: theory and applications to motor control |
| Author | Theodorou, Evangelos A. |
| Author email | etheodor@usc.edu; theo0027@umn.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Computer Science |
| School | Viterbi School of Engineering |
| Date defended/completed | 2011-01-11 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-04-29 |
| Advisor (committee chair) | Schaal, Stefan |
| Advisor (committee member) |
Valero-Cuevas, Francisco Sukhatme, Gaurav S. Todorov, Emo Schweighofer, Nicolas |
| Abstract | Motivated by the limitations of current optimal control and reinforcement learning methods in terms of their efficiency and scalability, this thesis proposes an iterative stochastic optimal control approach based on the generalized path integral formalism. More precisely, we suggest the use of the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parameterized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton Jacobi Bellman (HJB) equation, policy improvements can be transformed into an approximation problem of a path integral which has no open algorithmic parameters other than the exploration noise. The resulting algorithm can be conceived of as model-based, semi-model-based, or even model free, depending on how the learning problem is structured. The new algorithm, Policy Improvement with Path Integrals (PI2), demonstrates interesting similarities with previous RL research in the framework of probability matching and provides intuition why the slightly heuristically motivated probability matching approach can actually perform well. Applications to high dimensional robotic systems are presented for a variety of tasks that require optimal planning and gain scheduling.; In addition to the work on generalized path integral stochastic optimal control, in this thesis we extend model based iterative optimal control algorithms to the stochastic setting. More precisely we derive the Differential Dynamic Programming algorithm for stochastic systems with state and control multiplicative noise. Finally, in the last part of this thesis, model based iterative optimal control methods are applied to bio-mechanical models of the index finger with the goal to find the underlying tendon forces applied for the movements of, tapping and flexing. |
| Keyword | stochastic optimal control; reinforcement learning,; robotics |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3804 |
| Contributing entity | University of Southern California |
| Rights | Theodorou, Evangelos A. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Theodorou-4581 |
| Archival file | uscthesesreloadpub_Volume14/etd-Theodorou-4581.pdf |
Description
| Title | Page 251 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | 8.1 Index fingers biomechanics The skeleton of the human index finger consist of 3 joints connected with 3 rigid links. The two joints (proximal interphalangeal (PIP) and the distal interphalangeal (DIP)) are described as hinge joints that can generate both flexion-extension. The metacarpopha-langeal joint (MCP) is a saddle joint and it can generated flexion-extension as well as abduction-adduction. Fingers have at least 6 muscles, and the index finger is controlled by 7. Starting with the flexors, the index finger has the Flexor Digitorum Profundus (FDS) and the Flexor Digitorum Superficialis (FDP). The the Radial Interosseous (RI) acts on the MCP joint. Lastly, the extensor mechanism acts on all three joints. It is an interconnected network of tendons driven by two extensors Extensor Communis (EC) and the Extensor Indicis (EI), and the Ulnar Interosseous (UI) and Lumbrical (LU). There are also 4 passive tendon elements that complete this network. These passive tendons are the Terminal Extensor (TE), the Radial Band (RB) the Ulnar Band (UB) and the Extensor Slip (ES). Active tendons are connected to muscles and therefore they directly actuate the finger. Passive tendons are connected with other tendons(active) and ligaments and their role for the case of the index finger is to transform the applied tensions to the distal join. In our work we will consider only the active tendons. 8.2 Iterative stochastic optimal control We consider the nonlinear dynamical system described by the stochastic differential equa-tion that follows: 237 |
