New class of parameter identification algorithms and their application to robot control

A system performs various tasks over its lifetime. The problem of optimal tracking performance for the entire lifetime of a robotic system with parametric uncertainty is considered. The classical adaptive control methods minimize the tracking error of the current task without making an effort to learn about the system parameters. We show that knowledge of the desired future tasks and the system parameters is necessary for design of the optimum controller. Therefore, identification of system parameters is a crucial task to be accomplished. In adaptive robot control if the input signal for a task is persistently exciting (PE), in accordance with the classical definition, then the parameters estimated by the classical methods of adaptive control/parameter estimation are guaranteed to converge to their true values. This PE signal is required for infinite horizon. This has been the case for the plants considered here which have constant parameters linearly related to the computable variables. A class of algorithms is proposed, both in open and closed loop, that guarantees identification of the parameters while requiring less stringent conditions on the input. The closed loop algorithm ensures asymptotic stable tracking of the desired trajectory as well. These algorithms are derived and demonstrated.; We are specifically interested in robot control, where the state of the art algorithms employ gradient based methods. We show that the model based controller (e.g. Slotine and Li (2)) has the structure of optimal tracking controller. Examples providing quantitative results from robotics and linear time invariant systems are demonstrated, comparing the results with an enhancement of a classical approach of gradient type algorithm and least squares algorithm respectively. The overall effect is superior tracking performance over the lifetime of the system resulting in reduced cost of operation through improved quality of product, less wear tear, low input energy levels, longer life of the plant etc. We also discuss and demonstrate application of the proposed algorithms in case of step changes in plant parameters. It is expected that the results presented here will be applicable to a large class of dynamic systems, including discrete time systems and sampled data systems.