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It is hypothesized that the nonlinear muscle characteristic of biomechanical systems simplify control in the sense that the information the nervous system has to process is reduced through off-loading computation to the morphological structure. It has been proposed to quantify the required information with an information-entropy based approach, which evaluates the minimally required information to control a desired movement, i.e., control effort. The key idea is to compare the same movement but generated by different actuators, e.g., muscles and torque actuators, and determine which of the two morphologies requires less information to generate the same movement. In this work, for the first time, we apply this measure to numerical simulations of more complex human movements: point-to-point arm movements and walking. These models consider up to 24 control signals rendering the brute force approach of the previous implementation to search for the minimally required information futile. We therefore propose a novel algorithm based on the pattern search approach specifically designed to solve this constraint optimization problem. We apply this algorithm to numerical models, which include Hill-type muscle-tendon actuation as well as ideal torque sources acting directly on the joints. The controller for the point-to-point movements was obtained by deep reinforcement learning for muscle and torque actuators. Walking was controlled by proprioceptive neural feedback in the muscular system and a PD controller in the torque model. Results show that the neuromuscular models consistently require less information to successfully generate the movement than the torque-driven counterparts. These findings were consistent for all investigated controllers in our experiments, implying that this is a system property, not a controller property. The proposed algorithm to determine the control effort is more efficient than other standard optimization techniques and provided as open source. |
