Control and stabilization of nonlinear uncertain elastic robotic arm

An approach is presented to the control of an uncertain nonlinear flexible robot arm (PUMA-type) with three rotational joints. The third link is assumed to be elastic. A torquer control law, which is a function of the trajectory error, is derived for controlling the joint angles. The knowledge of the system dynamics is not required for the derivation of the controller. This controller includes a reference model to generate command joint angle trajectories, and a dynamic system in the feedback path which requires only joint angle and rate for feedback. The torquer controller asymptotically decouples the elastic dynamics into two subsystems, representing the transverse vibration of the elastic link in two orthogonal planes. For the damping of the elastic vibration, a force control law using modal velocity feedback is synthesized. Simulation results are presented to show that the combination of the torque and force control law accomplishes reference joint angle trajectory tracking and elastic mode stabilization despite the uncertainty in the system