Least-violating control strategy synthesis with safety rules

We consider the problem of automatic control strategy synthesis, for discrete models of robotic systems, to fulfill a task that requires reaching a goal state while obeying a given set of safety rules. In this paper, we focus on the case when the said task is not feasible without temporarily violating some of the rules. We propose an algorithm that {synthesizes} a motion which violates only lowest priority rules for the shortest amount of time. Although the proposed algorithm can be applied in a variety of control problems, throughout the paper, we motivate this problem with an autonomous car navigating in an urban environment while abiding by the rules of the road, such as "always stay in the right lane" and "do not enter the sidewalk." We evaluate the algorithm on a case study with several illustrative scenarios.