A contact model for geometrically accurate treatment of polytopes in simulation

Abstract

I herein present a formulation of non-penetration constraints between pairs of bodies which accounts for all possible combinations of active contact. This is the first formulation that accurately models the body geometries near points of potential contact, simultaneously preventing interpenetration while allowing bodies to traverse accurately through the surrounding free space. Unlike the standard approach, this method does not need to guess at which contacts to enforce. This new formulation is easy to incorporate into existing simulation methods, improves accuracy by many orders of magnitude, and is stable for even large time steps.

Simulation can be an invaluable tool, particularly in fields such as robotics where physical experiments can be extremely expensive, time consuming, and even dangerous. However, the value of a simulator is directly related to its ability to accurately and reliably model physical phenomena such as intermittent contact. In virtually all multibody simulators available today, the standard methods of contact identification and response treat the free space between pairs of bodies as a convex set, when it is in fact non-convex. To reconcile, simulators typically use very small time steps and employ numerous ad hoc corrections, many of which have become commonplace and include allowing interpenetration to occur, arbitrarily limiting response forces, misrepresenting body geometries, and "freezing" bodies with relatively low velocities. Indeed, a vast body of literature exists addressing the many symptoms of dynamic instability due to poor contact determination.

Additionally, I present the RPI-MATLAB-Simulator (RPIsim), an open source tool for efficient research and practical teaching in multibody dynamics. RPIsim is designed to be easy to use and easily extended. Students being introduced to dynamics for the first time have no problem creating and running simulations, even with a limited programming background. Researchers can utilize the existing code base to support work on specific areas since it is easy to replace or extend individual modules of the simulator.