Learning control and its applications. I: Elements of general theory (Q1287263)

The term ``learning control'' means a specific approach intended to improve the performance of robots used to carry out cyclic working operations. The author considers the basic approaches used to design learning control algorithms that primarily differ in the type of the a priori information on the behavior of an object. Initially, the patterns (procedures) that rely only on the hypothesis that the ``input-output'' relationship is sufficiently smooth are presented. The approach is based on an improved procedure of Newton-Gauss type. It is found out that if there is some a priori information, the same scheme can be applied without ``identification'' testing if the influence of unknown factors is small in some sense. The author focuses on two ideas: to use the a priori information contained in the dynamic model of the object, and to introduce strong feedback as the way of preliminary reduction of the role of unknown factors and of improvement of object properties, ensuring, in turn, learning efficiency. Convergence conditions for the learning procedure for sufficiently general objects are presented. The best results are obtained for objects in Frobenius form. The classical strong feedback with a parameter specifying the passband of the nonperturbed system is used, and the convergence conditions for learning are expressed through values of this parameter and Lipschitz constants bounding the influence of the a priori unknown perturbation factors. The possible applications to robotics are further stated. It is demonstrated that the mathematical models of manipulation robots can be expressed in Frobenius form both in the case of rigid designs and taking account of flexibility in the kinematic connections. For the ``rigid'' scheme the convergence conditions are detailed. Algorithms with position feedback and ``high-speed'' algorithms are presented. The author shows both analytically and with the help of numerical experiments the advantage of ``position'' algorithms ensuring the absence of error accumulation.