Solving Models of Controlled Dynamic Planar Rigid-Body Systems with Frictional Contact

Abstract

Effective modeling and control of multibody systems interacting with their environment through frictional contact remains a challenging problem. In this paper, we address the planar version of this problem by developing a general method to compute the instantaneous dynamic solution for planar rigid bodies interacting with their environment through Coulomb frictional contacts. The resulting analytical forward solution is represented in piecewise linear form, which admits tractable inversion for implementing behavioral control. We address the inherent problem of ambiguity in the resulting model (both between and within a particular linear model) by resorting to enumeration techniques and solve for the complete collection of possible model solutions in the presence of both contact constraints and additional task-specific linear constraints. We illustrate the application of these techniques by developing a controller to reliably achieve the dynamic self-righting of a hexapod robot.