Robotics: Science and Systems XVII

Generalized Comprehensive Motion Theory for High-Order Differential Dynamics

Vincent Samy, Ko Ayusawa, Eiichi Yoshida

Abstract:

We address the problem of calculating complex Jacobian matrices that can arise from optimization problems. An example is the inverse optimal control in human motion analysis which has a cost function that depends on the second order time-derivative of torque ̈τ. Thus; its gradient decomposed to; among other; the Jacobian δ ̈τ/δq. We propose a new concept called N-order Comprehensive Motion Transformation Matrix (N-CMTM) to provide an exact analytical solution of several Jacobians. The computational complexity of the basic Jacobian and its N-order time-derivatives computed from the N-CMTM is experimentally shown to be linear to the number of joints Nj. The N-CMTM is based on well-known spatial algebra which makes it available for any type of robots. Moreover; it can be used along classical algorithms. The computational complexity of the construction of the N-CMTM itself is experimentally shown to be N².

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Bibtex:

  
@INPROCEEDINGS{Samy-RSS-21, 
    AUTHOR    = {Vincent Samy AND Ko Ayusawa AND Eiichi Yoshida}, 
    TITLE     = {{Generalized Comprehensive Motion Theory for High-Order Differential Dynamics}}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2021}, 
    ADDRESS   = {Virtual}, 
    MONTH     = {July}, 
    DOI       = {10.15607/RSS.2021.XVII.032} 
}