Timing Semantics for Abstraction and Execution of Synthesized High-Level Robot Control

The use of formal methods for synthesis has recently enabled the automated construction of verifiable high-level robot control. Most approaches use a discrete abstraction of the underlying continuous domain, and make assumptions about the physical execution of actions given a discrete implementation; examples include when actions will complete relative to each other, and possible changes in the robot's environment while it is performing various actions. Relaxing these assumptions give rise to a number of challenges during the continuous implementation of automatically synthesized hybrid controllers. This paper presents several distinct timing semantics for controller synthesis, and compares them with respect to the assumptions they make on the execution of actions. It includes a discussion of when each set of assumptions is reasonable, and the computational tradeoffs inherent in relaxing them at synthesis time.