Robust adaptive control of manipulators with application to joint flexibility

Citation

Lee, Ho-Hoon (1992) Robust adaptive control of manipulators with application to joint flexibility. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ks5z-8e20. https://resolver.caltech.edu/CaltechETD:etd-08072007-073507

Abstract

This thesis discusses the model-based adaptive trajectory control of commercial manipulators whose dynamics are well known with uncertainties confined to parameters. This thesis emphasizes the importance of the transient behavior as well as robust stability of a system and takes it into account in the design of adaptive control laws. The basic idea is to search for compensators in the direction of minimizing a quadratic performance index, and then analyze the stability and robustness of the selected compensators in the presence of bounded disturbances, sensor noises, and unmodelled dynamics. With this idea, centralized and decentralized adaptive control schemes are proposed for rigid-joint manipulators. Stability bounds for disturbances, control and adaptation gains, and desired trajectories and their time-derivatives are derived for the proposed schemes. These bounds are sufficient conditions for robust stability of the proposed schemes in the presence of unmodelled dynamics such as feedback delays in the digital control systems and the coupled dynamics in the decentralized scheme. A flexibility compensator is designed to treat the problem of joint flexibility. With the flexibility compensator, a manipulator having flexible joints is transformed to that having rigid joints with high-frequency dynamics of joint couplings representing unmodelled dynamics. In this way, control of flexible-joint manipulators is converted to that of the corresponding rigid-joint manipulators. Accordingly, the robust adaptive control schemes proposed for rigid-joint manipulators are applied. Then, through stability analysis, stability bounds for disturbances, control and adaptation gains, and desired trajectories and their time-derivatives are derived for the scheme with the flexibility compensator, in the presence of the unmodelled dynamics. Under the constraint of these bounds, the proposed adaptive scheme is not only almost independent of the gear-reduction ratios, flexibilities of joint couplings, and characteristics of actuators, but also free from the requirements of measuring angular accelerations and jerks of links.

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