Scalable Coverage Trajectory Synthesis on GPUs as Statistical Inference

Coverage motion planning is essential to a wide range of robotic tasks. Unlike conventional motion planning problems, which reason over temporal sequences of states, coverage motion planning requires reasoning over the spatial distribution of entire trajectories, making standard motion planning methods limited in computational efficiency and less amenable to modern parallelization frameworks. In this work, we formulate the coverage motion planning problem as a statistical inference problem from the perspective of flow matching, a generative modeling technique that has gained significant attention in recent years. The proposed formulation unifies commonly used statistical discrepancy measures, such as Kullback-Leibler divergence and Sinkhorn divergence, with a standard linear quadratic regulator problem. More importantly, it decouples the generation of trajectory gradients for coverage from the synthesis of control under nonlinear system dynamics, enabling significant acceleration through parallelization on modern computational architectures, particularly Graphics Processing Units (GPUs). This paper focuses on the advantages of this formulation in terms of scalability through parallelization, highlighting its computational benefits compared to conventional methods based on waypoint tracking.