Learning control theory for robotic motion

A new concept of learning control for the improvement of robot motions is proposed, which can be referred to a mathematical modelling of learning and generation of motor programmes in the central nervous system. It differs from conventional classical and modern control techniques. It stands for the repeatability of operating a given robotic system and the possibility of improving the command input on the basis of actual measurement data acquired at the previous operation. Hence adequate conditions on the repeatability and invariance of the system dynamics are assumed, but no precise description of the dynamics is required for construction of the learning algorithms. Two types of iterative learning algorithm are proposed: one uses a PD-type (proportional and differential) update of input commands and the other a PI-type (proportional and integral) update where velocity signals are regarded as outputs. It is shown that in both types a better performance is realized at every attempt of operation, provided a desired motion is given a priori and the actual motion (velocity signals) can be measured at every operation. Further, the robustness of such learning control algorithms with respect to the existence of perturbed errors of initialization of the robot, disturbances and measurement noise during operation is analysed in detail. It is shown that in PD-type learning laws such errors are neither amplified nor aggregated in later consecutive trials of operation. In the case of PI-type learning laws it is shown that such a robustness property is assured if a forgetting factor is adequately introduced into the repetitive learning law.