Adaptive Control of Manipulators Forming Closed Kinematic Chain With Inaccurate Kinematic Model

The problem of self-tuning control of cooperative manipulators forming closed kinematic chain in the presence of inaccurate kinematics model is addressed in this paper. The kinematic parameters pertaining to the relative position/orientation uncertainties of the interconnected manipulators are updated online by two cascaded estimators in order to tune a cooperative controller for achieving accurate motion tracking with minimum-norm actuation force. This technique permits accurate calibration of the relative kinematics of the involved manipulators without needing high precision end-point sensing or force measurements, and hence, it is economically justified. Investigating the stability of the entire real-time estimator/controller system reveals that the convergence and stability of the adaptive control process can be ensured if 1) the direction of angular velocity vector does not remain constant over time, and 2) the initial kinematic parameter error is upper bounded by a scaler function of some known parameters. The adaptive controller is proved to be singularity-free even though the control law involves inverting the approximation of a matrix computed at the estimated parameters. Experimental results demonstrate the sensitivity of the tracking performance of the conventional inverse dynamic control scheme to kinematic inaccuracies, while the tracking error is significantly reduced by the self-tuning cooperative controller.