  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).
Prior MDP solvers compute contact forces via convex programming by assuming
linearized dynamics integrated using the forward multistep scheme. Instead, we
consider the coupled system of nonlinear Newton-Euler dynamics and MDP, which
is time-integrated using the backward integration scheme. We show that the
coupled system of equations can be solved efficiently using the 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) superior stability under large
timestep sizes; (3) consistent trajectory generation under varying timestep
sizes.
