Task and Motion Policy Synthesis as Liveness Games

We present a novel and scalable policy synthesis approach for robots. Rather than producing single-path plans for a static environment, we consider changing environments with uncontrollable agents, where the robot needs a policy to respond correctly over the infinite-horizon interaction with the environment. Our approach operates on task and motion domains, and combines actions over discrete states with continuous, collision-free paths. We synthesize a task and motion policy by iteratively generating a candidate policy and verifying its correctness. For efficient policy generation, we use grammars for potential policies to limit the search space and apply domain-specific heuristics to generalize verification failures, providing stricter constraints on policy candidates. For efficient policy verification, we construct compact, symbolic constraints for valid policies and employ a Satisfiability Modulo Theories (SMT) solver to check the validity of these constraints. Furthermore, the SMT solver enables quantitative specifications such as energy limits. The results show that our approach offers better scalability compared to a state-of-the-art policy synthesis tool in the tested benchmarks and demonstrate an order-of-magnitude speedup from our heuristics for the tested mobile manipulation domain