Control of Robotic Manipulators under Time-Varying Sensing-Control Delays

Time-varying input/output delays in a control system can significantly degrade the stability and performance of the closed loop system. Recently, passivity based control has emerged as a promising candidate to guarantee delay independent stability of passive systems with delays in the input-output channel. In this paper we study set point control of rigid robots with time-varying sensing/control delays. We first show that the classical PD controller can be modified to regulate the robotic manipulator, provided scattering transformation along with additional gains are used in the communication path. While this results in a stable system, asymptotic regulation cannot be guaranteed. Hence, a (delay dependent) gain margin for a proportional position feedback controller is provided to guarantee stability and asymptotic convergence of the regulation error to the origin. To improve closed loop performance, scattering transformation based design of a damping injection scheme is also discussed. The proposed algorithms are numerically verified on a two-degree-of-freedom manipulator.