Scalable Coverage Trajectory Synthesis on GPUs as Statistical Inference

TL;DR

This work reframes coverage motion planning as a statistical inference problem by formulating trajectory generation as flow matching, aligning the trajectory distribution $p_s(x)$ with a reference $q(x)$ through gradient flows. It introduces two gradient-flow strategies—Stein variational gradient flow and Sinkhorn divergence gradient flow—computed in parallel on GPUs, and couples them with a linear-quadratic regulator (LQR) based control synthesis to enforce dynamic feasibility. The approach demonstrates substantial scalability improvements over traditional waypoint-based methods, especially for long-horizon tasks, while remaining compatible with existing waypoint-based approaches. The results suggest that combining modern generative-inference techniques with GPU acceleration can enable efficient, large-scale coverage planning in robotics, with potential applications to autonomous exploration and search tasks.

Abstract

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.

Figures (6)

• Figure 1: Our method adapts flow-based generative inference methods to generate dynamically feasible flow directions on the state trajectory. Reference flow on the state trajectory is generated using standard methods from machine learning and accelerated through GPU parallelization. Lastly, we synthesize control gradients that generate dynamically feasible flow on the state trajectory by solving a linear quadratic regulator (LQR) problem.
• Figure 2: Our linear quadratic flow matching formula generates dynamically feasible flow on the state trajectory that closely matches the reference flow.
• Figure 3: Example coverage trajectories generated by the TSP baseline and our flow matching method based on the Stein variational gradient flow for a differential-drive robot.
• Figure 4: Example coverage trajectories generated by the TSP baseline and our flow matching method based on the Sinkhorn divergence gradient flow for an aircraft robot.
• Figure 5: Time efficiency comparison of our method using the Stein variational gradient flow (on GPU and CPU) and the TSP baseline. The TSP baseline is not tested beyond 1000 time steps due to the high computation time.