Provably correct continuous control for high-level robot behaviors with actions of arbitrary execution durations

Formal methods have recently been successfully applied to construct verifiable high-level robot control. Most approaches use a discrete abstraction of the underlying continuous domain, and make simplifying assumptions about the physical execution of actions given a discrete implementation. Relaxing these assumptions unearths a number of challenges in the continuous implementation of automatically-synthesized hybrid controllers. This paper describes a controller-synthesis framework that ensures correct continuous behaviors by explicitly modeling the activation and completion of continuous low-level controllers. The synthesized controllers exhibit desired properties like immediate reactiveness to sensor events and guaranteed safety of physical executions. The approach extends to any number of robot actions with arbitrary relative timings.