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We present a principled method for motion prediction via dynamic simulationfor rigid bodies in intermittent contact with each other where the contact isassumed to be a planar non-convex contact patch. The planar non-convex contactpatch can either be a topologically connected set or disconnected set. Suchalgorithms are useful in planning and control for robotic manipulation. Mostworks in rigid body dynamic simulation assume that the contact between objectsis a point contact, which may not be valid in many applications. In this paper,by using the convex hull of the contact patch, we build on our recent work onsimulating rigid bodies with convex contact patches, for simulating the motionof objects with planar non-convex contact patches. We formulate a discrete-timemixed complementarity problem where we solve the contact detection andintegration of the equations of motion simultaneously. Thus, our method is ageometrically-implicit method and we prove that in our formulation, there is noartificial penetration between the contacting rigid bodies. We solve for theequivalent contact point (ECP) and contact impulse of each contact patchsimultaneously along with the state, i.e., configuration and velocity of theobjects. We provide empirical evidence to show that our method can seamlesslycapture the transition between different contact modes like patch contact tomultiple or single point contact during the simulation.

Rigid Body Motion Prediction with Planar Non-convex Contact Patch