SACE-Bi-RRT: Sobol-Adaptive Connection-Gated Expansion with Tangent-Plane Deflection for Three-Dimensional UAV Path Planning*

Planning collision-free paths for unmanned aerial vehicles in cluttered three-dimensional environments requires balancing path length, smoothness, and consistency across repeated queries. However, existing bidirectional RRT* planners generally do not exploit two sources of information generated during the search: the length and visibility of the gap between the two trees, and the local obstacle geometry revealed when an extension is blocked. This paper proposes SACE-Bi-RRT*, a bidirectional RRT* planner that feeds the connection state and the collision geometry back into the search. A dual-tree guided expansion strategy regulates the probability and the target of the guided extension by the incrementally maintained closest node pair and its line-of-sight visibility. A tangent-plane deflection strategy projects the blocked extension onto the tangent plane of the hit obstacle, which converts the collision into a deterministic detour. The step length follows the local clearance; scrambled Sobol sequences with an in-obstacle-triggered bridge test supply the exploratory samples, and the trees merge with the pair of minimum seam cost. In 100 independent runs in each of three simulated environments, SACE-Bi-RRT* shortens the final path by 12.1% to 31.3% relative to five baselines, whose average turning angle is 1.3 to 2.6 times its own. The coefficient of variation of its path length stays below 1.9%, against 3.8% to 12.1% for the baselines, and the converged planning time remains below 0.7 s.