In this paper, the global stability problem for constrained robot motions in the presence of constraint uncertainties is investigated. We focus on the uncertainties in the constraint functions and their effects on the global stability. PD type controllers are used and conditions for global stability are developed using Lyapunov's direct approach. In the presence of the constraint uncertainties under investigation, the desired position and constraint force can be guaranteed with global asymptotic convergence. The developed conditions for feedback gain selections clearly show the effects of the constraint uncertainties. For the case when the velocity measurements are not available, conditions for global stability regulation are also established and the robot controller uses only the measurements of the position angles. Finally, we consider the case where the robot joints are flexible and global stability conditions are given.
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