Parameter Estimation of Nonsmooth Frictionless Impacts Through a Hybrid Observer

Estimating the velocity of a mass involved in nonsmooth impacts is a challenging problem because of their hybrid nature, especially when the restitution coefficient and the orientation of the tangent line at the point of impact are unknown. In this article, various hybrid observers are proposed for some families of mechanical systems to estimate the velocities, the restitution coefficient, and the orientation of the constraint, under the assumption that only the positions are measured. The stability properties of the corresponding error dynamics are proved, showing semiglobal exponential convergence to zero. First, the performance of the proposed observer is tested in some simulation runs. Second, the analysis is carried out in experimental tests, by measuring the position of the impacting body through slow and fast camcorders, with a post-processing of the recorded video. A final experimental evaluation is done in real-time with a hardware architecture based on a Raspberry Pi.