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An effective paradigm for simulating the dynamics of robots that locomote andmanipulate is multi-rigid body simulation with rigid contact. This paradigmprovides reasonable tradeoffs between accuracy, running time, and simplicity ofparameter selection and identification. The Stewart-Trinkle/Anitescu-Potra timestepping approach is the basis of many existing implementations. Itsuccessfully treats inconsistent (Painleve-type) contact configurations,efficiently handles many contact events occurring in short time intervals, andprovably converges to the solution of the continuous time differentialalgebraic equations (DAEs) as the integration step size tends to zero. However,there is currently no means to determine when the solution has largelyconverged, i.e., when smaller integration steps would result in only smallincreases in accuracy.  The present work describes an approach that computes the event times (whenthe set of active equations in a DAE changes) of all contact/impact events fora multi-body simulation, toward using integration techniques with error controlto compute a solution with desired accuracy.  We also describe a first-order, variable integration approach that ensuresthat rigid bodies with convex polytopic geometries never interpenetrate. Thisapproach permits taking large steps when possible and takes small steps whencontact is complex.

True Rigidity: Interpenetration-free Multi-Body Simulation with Polytopic Contact