Automata-based supervisory control logic design for a multi-robot assembly cell

Supervisory control logic design for a complex automated manufacturing system, a multi-robot assembly cell is discussed. A complex multi-robot assembly cell should be controlled to repeat a work cycle that satisfies the control requirements such as obeying an assembly sequence, and freedom from deadlocks, livelocks, collisions and wasteful behaviour. Recent automata-based control theories for discrete event dynamic systems focus on deriving a maximally permissible control logic, called a supremal controllable sublanguage, from a priori given automata-based control logic specification for the desirable system behaviour, called a legal language, when uncontrollable events may cause undesirable behaviour. However, it is not trivial to develop a legal language for a complex system like a multi-robot assembly cell. The computational procedure is subject to state explosion. In this paper, we propose a practical way of specifying and constructing the legal language from the given control requirements, and of obtaining the control logic that minimizes the cycle time. We first develop automata models for specifying each control requirement and generic behaviour of each component device, except the deadlock-free and livelock-free control requirements, which are hard to specify in automata. We discuss modelling strategies for controlling the multi-robot assembly cell. We propose a computational strategy for efficiently composing the automata and trimming out dead-ended states to enforce the deadlock-free control requirement and obtain the legal language. We derive an optimal control logic from the legal language that minimizes the cycle time by searching the randomly generated feasible state trajectories of the system that is controlled by the legal language. The livelock cycles are eliminated by minimizing the cycle time.