On-line, Reflexive Constraint Satisfaction for Hybrid Systems: First Steps (Invited Presentation)

Abstract. We can achieve guaranteed constraint satisfaction of a hybrid dynamical system (which takes into account the underlying continuous dynamics) in a simple, hierarchical control algorithm. Two layers of functionality, (1) piece-wise viable servo controllers and (2) a “reflex controller,” are required for guaranteed constraint satisfaction. The resulting control structure allows higher-levels of “intelligence ” or functionality to be added which don’t have to worry about guaranteeing constraints. The structure acts as an on-line filter which approves any actions that will maintain constraints but denies any requests that would result in behavior outside that specified. In this note, we lay down the notation and theory of this hierarchy in a broad, abstract setting. Minimal properties to assure constraint satisfaction are given. The incorporation of such a model with higher planning levels and its associated convergence properties are discussed. The philosophy has been successfully applied to a robot’s maintaining collision avoidance while under higher-level control, viz. path planners and teleoperation. The system operates on-line in real-time; in executing collisionfree motions, the robot uses its full mechanical bandwidth.