Parameter and contact force estimation of planar rigid-bodies undergoing frictional contact

Abstract

This paper addresses the identification of the inertial parameters and the contact forces associated with objects making and breaking frictional contact with the environment. Our goal is to explore under what conditions, and to what degree, the observation of physical interaction, in the form of motions and/or applied external forces, is indicative of the underlying dynamics that governs it. In this study we consider the cases of passive interaction, where an object free-falls under gravity, and active interaction, where known external perturbations act on an object at contact. We assume that both object and environment are planar and rigid, and exploit the well-known complementarity formulation for contact resolution to establish a constrained optimization-based problem to estimate inertial parameters and contact forces. We also show that when contact modes are known, or guessed, the formulation provides a closed-form relationship between inertial parameters, contact forces, and observed motions, that turns into a least squares problem.

Consistent with intuition, the analysis indicates that without the application of known external forces, the identifiable set of parameters remains coupled, i.e. the ratio of mass moment of inertia to mass and the ratio of contact forces to the mass. Interestingly the analysis also shows that known external forces can lead to decoupling and identifiability of mass, mass moment of inertia, and normal and tangential contact forces. We evaluate the proposed algorithms both in simulation and with real experiments for the cases of a free falling square, ellipse, and rimless wheel interacting with the ground, as well as a disk interacting with a manipulator.