  We present a principled method for motion prediction via dynamic simulation
for rigid bodies in intermittent contact with each other where the contact is
assumed to be a planar non-convex contact patch. The planar non-convex contact
patch can either be a topologically connected set or disconnected set. Such
algorithms are useful in planning and control for robotic manipulation. Most
works in rigid body dynamic simulation assume that the contact between objects
is 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 on
simulating rigid bodies with convex contact patches, for simulating the motion
of objects with planar non-convex contact patches. We formulate a discrete-time
mixed complementarity problem where we solve the contact detection and
integration of the equations of motion simultaneously. Thus, our method is a
geometrically-implicit method and we prove that in our formulation, there is no
artificial penetration between the contacting rigid bodies. We solve for the
equivalent contact point (ECP) and contact impulse of each contact patch
simultaneously along with the state, i.e., configuration and velocity of the
objects. We provide empirical evidence to show that our method can seamlessly
capture the transition between different contact modes like patch contact to
multiple or single point contact during the simulation.
