Synthesis of hybrid constraint-based controllers

Abstract

A robot is an integrated system, with a controller embedded in its plant. We take a robotic system to be the coupling of a robot to its environment. Robotic systems are, in general, hybrid dynamic systems, consisting of continuous, discrete and event-driven components. We call the dynamic relationship of a robot and its environment the behavior of the robotic system. The problem of control synthesis is: given a requirements specification for the behavior, and given dynamic models of the plant and the environment, generate a controller so that the behavior of the robotic system satisfies the specification. We have developed a formal language, Timed Linear Temporal Logic (TLTL) [17], for requirements specification. We have also developed a semantic model, Constraint Nets [19], for modeling hybrid dynamic systems. In this paper, we study the problem of control synthesis using these representations. Control synthesis in general is difficult. We first focus on a special class of requirements specification, called constraint-based specification, in which constraints are associated with properties such as safety, reachability and persistence. Then we develop a systematic approach to synthesizing controllers using constraint methods, in which controllers are embedded constraint solvers that solve constraints in real-time. Finally, we consider hierarchical control structures, in which the higher levels embody digital/symbolic event-driven control derived from discrete constraint methods and the lower levels incorporate analog control based on continuous constraint methods. We illustrate these techniques using a robot soccer player as a running example.