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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 contactregion is a planar non-convex contact patch.  Such methods are useful in planning and control for robotic manipulation. Theplanar non-convex contact patch can either be a topologically connected set ordisconnected set. Most work in rigid body dynamic simulation assume that thecontact between objects is a point contact, which may not be valid in manyapplications. In this paper, by using the convex hull of the contact patch, webuild on our recent work on simulating rigid bodies with convex contact patchesfor simulating motion of objects with planar non-convex contact patches. Weformulate a discrete-time mixed complementarity problem where we solve thecontact detection and integration of the equations of motion simultaneously. Wesolve for the equivalent contact point (ECP) and contact impulse of eachcontact patch simultaneously along with the state, i.e., configuration andvelocity of the objects. We prove that although we are representing a patchcontact by an equivalent point, our model for enforcing non-penetrationconstraints ensure that there is no artificial penetration between thecontacting rigid bodies. We provide empirical evidence to show that our methodcan seamlessly capture transition among different contact modes like patchcontact, multiple or single point contact.

Modeling and Prediction of Rigid Body Motion with Planar Non-Convex Contact