Tracking Control with Robotic Systems for a Moving Target: A Vector Lyapunov Function Approach

Abstract In this paper, we develop a controller for tracking a moving target using a manipulator equipped with a vision-sensor at the end-effector. The proposed control system is composed of a target velocity observer, a position-based visual servo (PBVS) and a proportional-derivative (PD+) tracking controller. This control scheme is analyzed as an interconnected system where input-to-state stability is proved for PBVS and PD+ subsystems, and the overall stability is proved using vector Lyapunov functions. The analysis technique further aids the determination of control parameters which defines the response of the whole system. A simplified notion of a manipulator is used to develop the theory and the application is demonstrated through simulation results in the context of on-orbit servicing where the objective is to track a non-cooperative tumbling satellite with a free-floating space manipulator.