Sampling-based synthesis of maximally-satisfying controllers for temporal logic specifications

Sampling-based methods have advanced the state of the art in robotic motion planning and control across complex, high-dimensional domains. With few exceptions, such approaches only admit simple constraints and objectives, such as collision-avoidance and reaching a goal state. In this work we leverage the best of two worlds: the scalability of sampling-based motion planning and the precise formal guarantees of temporal logic. We present an incremental sampling-based algorithm that synthesizes a motion control policy satisfying a bounded Signal Temporal Logic formula over properties of a given environment. Our key insight is that we can bias the selection of samples using a quantitative measure of how well the best path in the current tree of samples satisfies the specification. This allows us both to converge to a path that satisfies the specification, and to improve upon an existing path, i.e. to satisfy the specification with maximum robustness. We illustrate the performance of our method in several case studies.