Identifiability Analysis of Planar Rigid-Body Frictional Contact

Abstract

This paper addresses the identifiability of the inertial parameters and the contact forces associated with an object 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 forces, is indicative of the underlying dynamics that governs it. In this initial study we consider the cases of passive interaction, where an object free-falls under gravity, and active interaction, where known external perturbations act on the 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 closed-form relationship between inertial parameters, contact forces, and observed motions. 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 identifiability formulation both in simulation and with real experiments.