Exponential Tracking Control Using Backstepping Approach for Voltage-Based Control of a Flexible Joint Electrically Driven Robot

This paper addresses the design of exponential tracking control using backstepping approach for voltage-based control of a flexible joint electrically driven robot (EFJR), to cope with the difficulty introduced by the cascade structure in EFJR dynamic model, to deal with flexibility in joints, and to ensure fast tracking performance. Backstepping approach is used to ensure global asymptotic stability and its common algorithm is modified such that the link position and velocity errors converge to zero exponentially fast. In contrast with the other backstepping controller for electrically driven flexible joint robot manipulators control problem, the proposed controller is robust with respect to stiffness uncertainty and allows tracking fast motions. Simulation results are presented for both single link flexible joint electrically driven manipulator and 2-DOF flexible joint electrically driven robot manipulator. These simulations show very satisfactory tracking performances and the superiority of the proposed controller to those performed in the literature using simple backstepping methodology. 1. Introduction As demonstrated in [1], actuator dynamics constitute an important component of the complete robot dynamics. If actuator dynamics is ignored, the designed controller may not yield good system overall performance. In recent years, controls for robot manipulators, including the actuator dynamics, have received considerable attention and several control schemes have been developed [2–10]. In the early works Tarn et al. [2] proposed a nonlinear feedback robot controller that incorporates the robot manipulator dynamics as well as the robot joint motor dynamics. This study shows that the proposed controller gives better performance than nonlinear feedback robot controller based on the manipulator dynamics only. Carroll et al. [3] introduce a robust corrective tracking controller for rigid link electrically driven (RLED) robot manipulators operating under motion constraints, to overcome consideration of actuators dynamics and task space control problem. The controllers proposed in [2, 3] required full knowledge of system dynamics. If there are uncertainties in the dynamics, these controllers proposed may give a poor performance and may even cause instability. To overcome the uncertainties in the dynamics, robust controllers have been proposed in [4–10]. Stepanenko and Su [4] presented a simple robust nonlinear control law that incorporates the manipulator dynamics as well as dynamics of actuators. In contrast to the known methods, the presented design