Lyapunov-based control of a robot and mass-spring system undergoing an impact collision

The control of a dynamic system with impact conditions is an interesting problem with practical importance. One difficulty in controlling systems subject to impact collisions is that the equations of motion are different when the system status changes suddenly from a non-contact state to a contact state. In this paper a nonlinear controller is designed to regulate the states of two dynamic systems that collide. The academic example of a planar robot colliding with an unactuated mass-spring system is used to represent a broader class of such systems. The control objective is to command a robot to collide with an unactuated mass-spring system and regulate the spring-mass to a desired compressed state. Lyapunov-based methods are used to develop a continuous controller that yields global asymptotic regulation of the spring-mass and robot links. Unlike some other results in literature, the developed continuous force controller does not depend on sensing the impact, measuring the impact force, or the measurement of other acceleration terms.