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Robot robust path tracking. (English) Zbl 0864.93078
Summary: A new discontinuous robust control law for a rigid manipulator with bounded parameter uncertainties to track a desired trajectory, is presented. Global exponential stability is proved by the use of a natural Lyapunov function based on a transformation of the manipulator’s differential equation due to J. J. E. Slotine and W. Li [“On the adaptive control of robot manipulators”, Int. J. of Robotics Research 6, 49-59 (1987)]. Convergence is to a sliding mode along which the tracking error is reduced at an arbitrary exponential rate. It is also shown how adaptation of bounds on uncertainties, and parameter adaptation, can be incorporated. For a continuous approximation of the discontinuous control law, practical stability (essentially, global uniform ultimate boundedness) of the tracking error is proved. Simulation results for the continuous control law exhibit excellent robust tracking.
MSC:
93C85 Automated systems (robots, etc.) in control theory
93B12 Variable structure systems
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