Efficient Contact Mode Enumeration in 3D

In a hybrid dynamical system with multiple rigid bodies, the relative motions of the contact points on two colliding bodies may be classified as separating, sticking (moving together), or sliding. Given a physical contact model, the active contact modes determine the dynamic equations of motion. Analogously, the set of all possible (valid) contact mode assignments enumerates the set of all possible dynamical flows of the hybrid dynamical system at a given state. Naturally, queries about the kinematics or dynamics of the system can be framed as computations over the set of possible contact modes. This paper investigates efficient ways to compute this set.