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

TL;DR

This paper introduces a novel multi-body simulation method that accurately detects contact events and guarantees interpenetration-free motion for convex polytopic bodies, improving simulation reliability and efficiency.

Contribution

It presents an event detection technique for contact changes and a first-order variable step integrator ensuring no interpenetration in multi-body simulations.

Findings

Accurately detects contact/impact event times.

Guarantees no interpenetration for convex polytopic bodies.

Enables larger time steps when contact is simple.

Abstract

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