Variable structure control of a robot arm with flexible links

The authors treat the question of the control of an elastic, two-link robotic arm using variable structure system (VSS) theory and the pole assignment technique for stabilization. A discontinuous joint angle control law that accomplishes asymptotic decoupled joint-angle-trajectory tracking is designed. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. Although joint angles are controlled using a variable structure control (VSC) law, the flexible modes of the links are excited. Starting with a linearized model of the terminal state, a stabilizer is designed using the pole assignment technique to control the elastic oscillation of the links. A control logic is included to switch the stabilizer the instant the joint angle trajectory enters a specified neighborhood of the terminal state. Simulation results show that the closed-loop system can achieve accurate trajectory tracking and elastic mode stabilization