Optimality equivalence and computational advantages of free-floating base dynamics compared to full-body dynamics. (March 2023)

• Record Type: Journal Article
• Authors: Puchaud, Pierre; Charbonneau, Eve; Michaud, Benjamin; Begon, Mickaël
• Is Part Of: Mechanism and machine theory. Volume 181(2023)
• Publication Date: 2023-03
• Subjects: Optimal control -- Direct multiple shooting -- Predictive simulation -- Biomechanics -- Acrobatics; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2022.105164
• Languages: English
• ISSNs: 0094-114X

Abstract

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. Highlights: Free-floating base dynamics is 10 times faster than full-body dynamics in explicit. Free-floating base dynamics is recommended when constraining torques is not wanted. Implicit dynamics may work with direct multiple shooting when jerks are the controls. Implicit dynamics also speeds up optimization compared to the explicit formulation.