Optimal Control of Robot Behavior Using Language Measure

Summary

This chapter presents optimal discrete-event supervisory control of robot behavior in terms of the language measure μ, presented in Chapter 1. In the discrete-event setting, a robot’s behavior is modelled as a regular language that can be realized by deterministic finite state automata (DFSA). The controlled sublanguage of a DFSA plant model could be different under different supervisors that are constrained to satisfy different specifications [6]. Such a partially ordered set of sublanguages requires a quantitative measure for total ordering of their respective performance. The language measure [10] [8] serves as a common quantitative tool to compare the performance of different supervisors and is assigned an event cost matrix, known as the $\tilde \Pi$-matrix and a state characteristic vector, X-vector. Event costs (i.e., elements of the $\tilde \Pi$-matrix) are based on the plant states, where they are generated; on the other hand, the X-vector is chosen based on the designer’s perception of the individual state’s impact on the system performance. The elements of the $\tilde \Pi$-matrix are conceptually similar to the probabilities of the respective events conditioned on specific states; these parameters can be identified either from experimental data or from the results of extensive simulation, as they are dependent on physical phenomena related to the plant behavior. Since the plant behavior is often slowly time-varying, there is a need for on-line parameter identification to generate up-to-date values of the $\tilde \Pi$-matrix within allowable bounds of errors. The results of simulation experiments on a robotic test bed are presented to demonstrate efficacy of the proposed optimal control policy.