Robot manipulator control by accelaration feedback: Stability, design and performance issues

The acceleration feedback control law is shown to be stable. Stability is proven using a Lyapunov approach under rigid body and LQ assumptions. Under LQ assumptions, the control law can be designed to be joint coordinate decoupled, allowing for a simple, inexpensive servo mechanism implementation. Under rigid body assumptions, the high gain feedback can be increased without bound, causing a decrease of the bounds on the steady state error towards zero. However under non-rigid body assumptions and with high frequency unstructured uncertainties, the high gain feedback must be frequency weighted. A linearized frequency domain analysis shows that there is no gain margin, and only a maximum 180 degrees of phase margin. Frequency weighting of the high gain feedback provides the means with which gain and phase margins can be achieved and robustness enhanced. The inherent penalty is that high gain feedback must be traded-off against the system bandwidth. Translated into practical terms, steady state error performance must be traded-off against manipulator response time due to the necessary frequency weighting of the high gain feedback.