Differentiable Dynamics Simulation Using Invariant Contact Mapping and Damped Contact Force

The gradient of typical differentiable simulation is uninformative for two reasons: 1) non-smoothness in contact dynamics not considered properly, and 2) excessive local minima generated from the smoothing procedure. To tackle this issue, we first propose differentiable contact dynamics with an invariant contact set and coordinate differentiation using a signed distance function (SDF). Also, to eliminate the undesirable jittering caused by the smoothing procedure, which induces extra local minima, and to achieve a smooth and informative gradient, we further endow our framework with a novel damped contact model. Various optimization problems are implemented to demonstrate the usefulness and efficacy of our differentiable framework.