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We present non-convex maximal dissipation principle (NMDP), a time integration scheme for articulated bodies with simultaneous contacts. Our scheme resolves contact forces via the maximal dissipation principle (MDP). Whereas prior MDP solvers assume linearized dynamics and integrate using the forward multistep scheme, we consider the coupled system of nonlinear Newton-Euler dynamics and MDP and integrate using the backward integration scheme. We show that the coupled system of equations can be solved efficiently using a novel projected gradient method with guaranteed convergence. We evaluate our method by predicting several locomotion trajectories for a quadruped robot. The results show that our NMDP scheme has several desirable properties including: (1) generalization to novel contact models; (2) stability under large timestep sizes; (3) consistent trajectory generation under varying timestep sizes.

Implicit Integration for Articulated Bodies with Contact via the Nonconvex Maximal Dissipation Principle