From Robots to Humans: towards Efficient Forward Dynamics Simulation and Optimization Exploiting Structure and Sensitivity Information

The locomotion of quadruped and humanoid robots shares some characteristics with the one of animals and humans: a kinematic tree structure and a free-floating base, switches in the model due to different contact situations and a high number of degrees of freedom consisting of many links and many actuated joints. One main difference is in actuation: while robots commonly are driven by (at most) one motor for each joint, animals and humans usually use much more than one muscle for each joint. Although a single muscle may also be connected to several joints, the tree-like structure of the multibody system may be preserved. This enables the use of efficient, recursive dynamics modeling methods exploiting tree structure which have already been successfully developed for legged robots . Optimization techniques for exploiting redundancy in dynamic motions are presented. Biomechanical systems inhibit two levels of redundancy. First, the motion (e.g. point-to-point) of a whole limb or body can be realized by many different joint trajectories. This is common for robots with legs and arms as well as for animals and humans. Second, the joint torques (and as a result the joint motions) can be generated by different forces of the individual muscles involved in the motion of the joint. Several optimization hypotheses exist how the participating muscles are actuated during joint motion. The backward dynamics simulation and optimization starts from measured joint trajectories to compute an approximation of the required control for the observed motion. The forward dynamics simulation and optimization results in a high dimensional, nonlinear optimal control problem. In principle, it enables the forecast of a free motion for a validated model but is much more computationally expensive. Compared to current approaches reach a computational speed-up by two orders of magnitude using tailored, efficient dynamics modeling, recursively obtained, explicit sensitivity information of the system dynamics and efficient direct transcription methods for solving the optimal control problem by direct collocation (already successfully used for optimization of gaits of legged robots). Numerical results are presented for walking robots and for the kicking motion of a leg with two joints and five muscle-tendon-groups.