Set-Valued Rigid Body Dynamics for Simultaneous Frictional Impact
There are many nuanced and complicated discrepancies that contribute to the simulation-to-reality gap in robotics, but one is fairly basic: some models are unable to predict any outcome from some initial conditions (non-existence), while in reality, some systems produce many different outcomes from indistinguishably similar conditions (non-uniqueness). We derive models with existence guarantees by capturing this non-uniqueness as a differential inclusion.