Nonsmooth Impact Mechanics

The field of nonsmooth impact dynamics and its applications to the control of robotic systems is examined in this monograph. The mathematical foundations of the dynamics of systems of rigid bodies submitted to a set of unilateral constraints are introduced. Following on from this the macroscopic physical laws of shocks (restitution roles) are described and commented on. In view of the applications to feedback control, stability properties of trajectories of various types of measure differential equations are reviewed. This includes a general stability analysis framework suitable for a class of impacting robotic systems performing complete tasks. Finally, feedback control of manipulators subject to unilateral constraints (which consist of a class of hybrid systems) is studied.