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• W3176145953 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." @default.
• W3176145953 created "2021-07-05" @default.
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• W3176145953 date "2021-07-12" @default.
• W3176145953 modified "2023-10-16" @default.
• W3176145953 title "Generalized Comprehensive Motion Theory for High-Order Differential Dynamics" @default.
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• W3176145953 doi "https://doi.org/10.15607/rss.2021.xvii.032" @default.
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