@InProceedings{samy:rss:2021,
author = {Samy, Vincent and Ayusawa, Ko and Yoshida, Eiichi},
title = {Generalized Comprehensive Motion Theory for High-Order Differential Dynamics},
booktitle = {Robotics: Science and Systems},
year = {2021},
address = {Virtual},
month = {July 12-July 16},
url = {http://www.roboticsproceedings.org/rss17/p032.html},
doi = {10.15607/RSS.2021.XVII.032},
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 \"\tau . Thus; its gradient decomposed to; among other; the Jacobian \delta \"\tau /\delta q. 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 N{^2}.}
}