Serialized Red-Green-Gray: Quicker Heuristic Validation of Edges in Dynamic Roadmap Graphs

We present the dynamic rotation-stacked visibility graph (dRVG), an online motion planner that guides polygonal robots to specified goals in initially unknown, static environ- ments. It merges local roadmaps from successive observations to plan collision-free translations and rotations without a uniform position grid. A spatial quadtree schedules sensing goals across regions to reduce repeated visits while retaining all orientation configurations for routing. Under exact sensing and geometric computation and star-shaped robot and envelope assumptions, dRVG with center scans is resolution-complete relative to full- map RVG at the same angular resolution. In experiments using footprint scans, dRVG solves all 140 cases across 20 difficult maps and seven angular resolutions within a 20 s planning budget, with a median planning time of 1.18 s at 360 orientation layers. Six microMVP demonstrations illustrate the complete online planning loop on a physical robot.

This paper develops the Rapidly-iterating kinoDynamic Grid (RDG) algorithm, an asymptotically near-optimal kinodynamic motion planning algorithm that produces high quality solutions through rapid iteration. The algorithm leverages a state space grid decomposition to perform node selection, dynamics propagation, and graph revision in constant time complexity with respect to the number of nodes in the trajectory tree. Through a covering ball sequence induction proof, the algorithm is shown to be asymptotically near-optimal and probabilistically complete. Different subsystems of the algorithm are evaluated against common nearest-neighbor search-based methods at generating exploration bias. The RDG algorithm is evaluated through simulated trials in complex, kinodynamic motion planning problem environments up to 10 DOF relative to similar sparse, kinodynamic planning algorithms with optimality guarantees, SST and DIRT. The RDG algorithm outperforms both SST and DIRT in mean final solution quality by up to 104% and 40% respectively. Additionally, RDG maintained a 100% success rate, even on a 10-DOF test case where both SST and DIRT did not.

Image-goal navigation requires a global planner that connects visually specified endpoints while providing observations that a local policy can follow. Three-dimensional Gaussian Splatting (3DGS) provides map-registered RGB, opacity, and depth renderings, but does not explicitly encode navigable topology. We introduce GS-PRM, a Gaussian visual roadmap whose milestones, local connections, and visual references are constructed directly through 3DGS rendering without deriving an occupancy grid or signed distance field. We define render-based collision-free (RC-free) configurations and paths. Panoramic depth supplies conservative clearance for milestone validation and adaptive coverage, while edge-aligned orthographic rendering tests the robot's swept volume. We establish conditional soundness and sufficient conditions for deterministic query completeness and probabilistic construction completeness of GS-PRM. To validate the performance of GS-PRM, we conduct experiments in both simulated and real-world environments, demonstrating long-horizon navigation using goal-conditioned policies guided by GS-PRM. Compared with a state-of-the-art 3DGS-based navigation system, our GS-PRM-based navigation system achieves up to a twice higher average success rate and reduces travel time by up to 57.2% when both systems complete the navigation task.