Stability analysis of adaptively controlled flexible joint manipulators
- 1 January 1990
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 2538-2544 vol.4
- https://doi.org/10.1109/cdc.1990.203465
Abstract
The composite slow/fast control strategy, consisting of a slow adaptive controller designed for a rigid robot together with a fast control to damp the elastic oscillations of the joints, was previously derived by the authors. In this paper, mathematical details of the algorithm are presented. By using the composite Lyapunov theory for singularly perturbed systems, sufficient conditions are obtained for adaptive trajectory tracking. For point-to-point motion it is shown that there is always a range of joint stiffness for which convergence is achieved, and the region of convergence is quantified. For tracking (smooth and bounded) reference trajectories, sufficient conditions for closed-loop stability and uniform boundedness of the tracking error are given. A residual set to which the tracking error converges is quantified. It is also shown that for special classes of trajectories, which include step responses generated from reference models and certain joint interpolated trajectories, asymptotic tracking can be achieved.Keywords
This publication has 17 references indexed in Scilit:
- Adaptive control of flexible joint manipulatorsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Adaptive motion control of rigid robots: a tutorialPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Adaptive control of flexible joint manipulatorsSystems & Control Letters, 1989
- Adaptive computed torque control for rigid link manipulationsSystems & Control Letters, 1988
- Modeling and Control of Elastic Joint RobotsJournal of Dynamic Systems, Measurement, and Control, 1987
- On the Adaptive Control of Robot ManipulatorsThe International Journal of Robotics Research, 1987
- A robust direct adaptive controllerIEEE Transactions on Automatic Control, 1986
- Integral manifolds of slow adaptationIEEE Transactions on Automatic Control, 1986
- Quadratic-type Lyapunov functions for singularly perturbed systemsIEEE Transactions on Automatic Control, 1984
- Robustness of adaptive control algorithms in the presence of unmodeled dynamicsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1982