Guiding Vector Field Generation via Score-based Diffusion Model

Many diffusion-based planners enforce safety through inference-time guidance, but such interleaved trajectory deformations often degrade kinematic feasibility due to manifold rupture. We propose Graph-Guided Safe Diffuser (G2SD), a hierarchical framework that leverages a high-level topological graph planner to guide a low-level diffusion model. G2SD enforces safety at a structural level by abstracting the data manifold into a learned latent graph, on which high-level planning is performed. Continuous trajectories are generated by diffusion planners, which are conditioned on the graph node representations selected by the high-level planner. Theoretical analyses demonstrate conditions under which manifold rupture occurs in diffusion planners, and show that G2SD improves safety by reducing the constraint violation probability as the number of segments increases. Experiments demonstrate that G2SD substantially outperforms baselines, increasing goal-reaching rate without any collision from 40-50% to 98% in Maze2D navigation and also achieving superior task scores in locomotion.

This paper develops a singularity-free guiding vector field (SF-GVF) for path following on the special orthogonal group SO(3). First, we lift the Euclidean SF-GVF construction to SO(3), integrating the augmented-state approach with the intrinsic Lie-group geometry and obtaining a closed-form geometric guidance law whose integral curves converge to a designer-specified attitude path. The field is defined on a dense open subset of SO(3), excluding only the measure-zero antipodal set - a manifestation of the topological obstruction to continuous global stabilization on SO(3). The construction requires no per-step optimization and produces a control input intrinsically in so(3) as body angular rates. Second, we formalize the progression behavior along the path as a designer-supplied function ν(ξ), promoting the parametric speed from an implicitly resolved degree of freedom to a first-class design specification. In contrast to the Euclidean condition v = 0, which excludes vehicles with minimum-speed constraints, the corresponding condition ω= 0 on SO(3) is physically admissible for most platforms with active attitude control, making the progression behavior a design freedom structurally available on SO(3) but absent in the Euclidean setting. The framework's structural results are established under a bi-invariant Riemannian metric and hold uniformly across choices of path, progression, and Lyapunov gain. The framework is illustrated in simulation on self-intersecting paths under both constant and point-convergence progression behaviors.

Safe and agile trajectory planning is essential for autonomous systems, especially during complex aerobatic maneuvers. Motivated by the recent success of diffusion models in generative tasks, this paper introduces AeroTrajGen, a novel framework for diffusion-based trajectory generation that incorporates control barrier function (CBF)-guided sampling during inference, specifically designed for unmanned aerial vehicles (UAVs). The proposed CBF-guided sampling addresses two critical challenges: (1) mitigating the inherent unpredictability and potential safety violations of diffusion models, and (2) reducing reliance on extensively safety-verified training data. During the reverse diffusion process, CBF-based guidance ensures collision-free trajectories by seamlessly integrating safety constraint gradients with the diffusion model's score function. The model features an obstacle-aware diffusion transformer architecture with multi-modal conditioning, including trajectory history, obstacles, maneuver styles, and goal, enabling the generation of smooth, highly agile trajectories across 14 distinct aerobatic maneuvers. Trained on a dataset of 2,000 expert demonstrations, AeroTrajGen is rigorously evaluated in simulation under multi-obstacle environments. Simulation results demonstrate that CBF-guided sampling reduces collision rates by 94.7% compared to unguided diffusion baselines, while preserving trajectory agility and diversity. Our code is open-sourced at https://github.com/RoboticsPolyu/CBF-DMP.