Stability Analysis of a Visual PID Controller Applied to a Planar Parallel Robot

This work analyses the stability of a standard PID controller fed by measurements provided by a vision system, and applied to a planar parallel redundant manipulator for constant set point tracking. The stability analysis considers uncertainty in the Jacobian matrix associated to the manipulator active joints, and constant disturbances perturbing these joints. The disturbances appear as time-varying at the visual level. Asymptotic stability of the closed loop system is proven using a Strict Lyapunov Function. The above allows directly applying the Lyapunov second method without resorting on the LaSalle-Krassovsky invariance theorem. The analysis also provides an upper bound on the allowable uncertainty in the Jacobian matrix. Experiments on a laboratory prototype permit evaluating the performance of a PID controller applied to a planar parallel robot.