@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}.}
}