  The problem of self-tuning control of cooperative manipulators forming a
closed kinematic chain in the presence of an inaccurate kinematics model is
addressed using adaptive machine learning. 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 i) the direction of the angular
velocity vector does not remain constant over time, and ii) 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.
