Efficient PID Tracking Control of Robotic Manipulators Driven by Compliant Actuators

This brief aims to show that a linear proportional–integral–derivative (PID) controller is theoretically valid for tracking control of robotic manipulators driven by compliant actuators. The control problem is formulated into a three-time-scale singular perturbation formula, including a slow time scale at the rigid robot dynamics, one actual fast time scale at the actuator dynamics, and another virtual fast time scale at the controller dynamics. A PID-type controller is derived to guarantee semiglobal practical exponential stability of the rigid robot dynamics, and a derivative-type controller is applied to establish global exponential stability of the actuator dynamics. Based on a state transformation to the closed-loop rigid robot dynamics and the extended Tikhonov’s theorem, it is proven that the entire system has semiglobal practical exponential stability under a proper choice of control parameters. The proposed controller is not only structurally simple and model-free resulting in low implementation cost, but also robust against external disturbances and parameter variations. The current design is only valid while the spring stiffness is relatively large compared with other parameters of the robot dynamics. Experimental results based on a single-link compliant robotic manipulator have verified effectiveness of the proposed approach.