New preprint: Set-Valued Rigid Body Dynamics for Simultaneous Frictional Impact

When objects collide, small changes in initial conditions can lead to dramatically different outcomes (imagine a pool break). Rigid models capture this via non-uniqueness. Typically, model-based controllers optimistically ignore these possibilities, sometimes leading to poor behavior around impact events. Using differential inclusions and complementarity problems, we describe and compute the set of possible outcomes for multiple, frictional impacts and provide guarantees of existence and completeness.