Temporal Task and Motion Planning with Metric Time for Multiple Object Navigation

Integrating metric time into Task And Motion Planning (TAMP) is challenging, especially with simultaneous object motion. Existing work focuses on classical and numeric TAMP, not considering deadlines, motions overlapping in time, and other temporal constraints. In this paper, we fill this gap by formalizing Temporal Task and Motion Planning (TTAMP) for multi-object navigation. We propose a novel interleaved planning technique for this problem, which leverages incremental Satisfiability Modulo Theory to ensure efficient reasoning on deadlines and action duration coupled with a motion planner supporting simultaneous object motion. Geometric data on encountered obstacles prunes unreachable symbolic regions, while temporal bounds limit the geometric search space. For multiple moving objects, our algorithm contextualizes the conflicts learned from the motion planner on overlapping actions so that entire classes of temporal plans are pruned from the search space of the task planner, ensuring the eventual termination of the interplay. We provide a comprehensive benchmark suite and demonstrate the effectiveness of our solver in leveraging these scenarios.