Rigid Body Dynamic Simulation with Line and Surface Contact

TL;DR

This paper introduces a physics-consistent, unified method for simulating rigid body dynamics with line and surface contact by solving a mixed nonlinear complementarity problem, ensuring accurate contact modeling and seamless contact transition.

Contribution

The paper presents a novel approach that models line and surface contact using a convex set of contact points and solves contact detection and dynamics simultaneously, ensuring physical consistency.

Findings

Unique solutions for contact points and wrenches for any velocity

Seamless transition between point, line, and surface contact

Validated through simulation examples

Abstract

In this paper, we develop a principled method to model line and surface contact with point contact (we call this point, equivalent contact point) that is consistent with physics-based models of surface (line) contact. Assuming that the set of contact points form a convex set, we solve the contact detection and dynamic simulation step simultaneously by formulating the problem as a mixed nonlinear complementarity problem. This allows us to simultaneously compute the equivalent contact point as well as the wrenches (forces and moments) at the equivalent contact point (consistent with the friction model) along with the configuration and velocities of the rigid objects. Furthermore, we prove that the contact constraints of no inter-penetration between the objects is also satisfied. We present a geometrically implicit time-stepping scheme for dynamic simulation for contacts between two bodies with convex contact area, which includes line contact and surface contact. We prove that for surface and line contact, for any value of the velocity of center of mass of the object, there is a unique solution for contact point and contact wrench that satisfies the discrete-time equations of motion. Simulation examples are shown to demonstrate the validity of our approach and show that with our approach we can seamlessly transition between point, line, and surface contact.