Inverse Trajectory Control and Zero Dynamics Sensitivity of an Elastic Manipulator

The question of control of the end effector trajectory and stabilization of a two-link flexible robotic arm is considered. A control law based on the inversion of an input-output map is obtained. The outputs are chosen as the sum of the joint angle and tip elastic deformation times a constant factor for each link. The stable maneuver of the arm critically depends on the stability of the zero dynamics of the system. Stability of the zero dynamics is shown to be sensitive to the choice of the constant multiplying factor, which explains the difficulty in controlling the tip position. A critical value of the constant factor for control is obtained and this corresponds to a coordinate in the neighbourhood of the actual tip position. Although the inverse controller accomplishes output control, this excites the rigid and elastic modes. A linear stabilizer is designed for final capture of the terminal state and stabilization of the elastic modes. Simulation results are presented to show that in the closed-loop system, large maneuvers can be performed in the presence of payload uncertainty.