Flexible Robotic Arm Control: Nonlinear Ultimate Boundedness and Linear Stabilization

We treat the question of control of an elastic robotic arm of two links. Ofcourse this approach can be extended to other elastic arms. A nonlinear ultimate boundedness controller (UBC) is synthesised such that in the closed-loop system, the joint angle tracking error is uniformly bounded, and tends to a certain small neighborhood of the origin. The controller includes a reference joint angle trajectory generator and integral error feedback. Although, the joint angles are controlled using the UBC, elastic modes are excited. A feedback stabilizer is designed for the linearized model including the UBC about the terminal state which is switched only in the vicinity of the equilibrium state for stabilization. Simulation results are presented to show that in the closed-loop system including the UBC and the stabilizer, accurate joint angle trajectory following and elastic mode stabilization are accomplished in the presence of uncertainty.