On state and inertial parameter estimation of free-falling planar rigid bodies subject to unscheduled frictional impacts

Abstract This paper addresses the problem of simultaneous state estimation and inertial and frictional parameter identification for planar rigid-bodies subject to unscheduled frictional impacts. The aim is to evaluate to what level of accuracy, given noisy captured poses of an object free-falling under gravity and impacting the surrounding environment, it is conceivable to reconstruct its states, the sequence of normal and tangential impulses and, concurrently, estimate its inertial properties along with Coulomb’s coefficient of friction at contacts.  To this aim we set up a constrained nonlinear optimization problem, where the unscheduled impacts are handled via a complementarity formulation. To assess the validity of the proposed approach we test the identification results both (i) with respect to ground truth values produced with a simulator, and (ii) with respect to real experimental data. In both cases, we are able to provide accurate/realistic estimates of the inertia-to-mass ratio and friction coefficient along with a satisfactory reconstruction of systems states and contact impulses.