Optimality equivalence and computational advantages of free-floating base dynamics compared to full-body dynamics

Abstract

Several transcription methods exist for predictive simulations of free-floating base motions like athlete performing twisting somersaults. Following a brief overview of the literature, we proposed two original direct multiple shooting optimal control problems: (1) with a reduced set of equations motion (free-floating base dynamics) and generalized accelerations as controls; and (2) with the dynamics enforced implicitly through algebraic constraints and generalized jerks as controls. To assess their performance (computational time, dynamic consistency, cost), we compared full-body vs free-floating base dynamics and explicit vs implicit formulations of an optimal control problem of a double straight somersault with three twists. We found that free-floating dynamics is relevant when bounds on joint torques are not required since it hastens the convergence up to 10 times and the optimal solutions are similar. Implicit dynamics also speeds up optimization compared to the explicit formulation, but dynamic consistency may be affected. Using joint jerks instead of accelerations as controls mitigates this limitation, especially when the mesh grid densifies.