Muscle-actuated control of articulated body systems in operational space remains challenging due to the lack of analytical methods for kinematics and dynamics resolution. A fundamental problem is resolving the redundancy of complex articulation mechanisms in the context of non-negative actuation by (even more redundant) muscle actuators. A second fundamental problem is to maintain continuity of the kinematics and dynamics redundancy resolution over a given time-window - a 'good' solution must resolve redundancy in a manner that limits noise in higher derivatives. Such mechanisms include muscle-actuated robots, as well as models of the human musculoskeletal system. Using the latter as an exemplar, the fundamental problems we discussed can resolve to: developing a differentiable model of muscle articulation; computing the muscle-to-generalized coordinate Jacobian; computing muscle-to-operational space Jacobians; and computing task-to-muscle Jacobians. Finally, we note that it is important to do the previous computations in a manner that the re-computation of local linearization from time-step to time-step does not introduce large changes. The last point is important to develop stable control and simulation.
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