TDO-MSF: A turn-deviation optimized multi-stage framework for smooth three-dimensional UAV trajectories

Abstract

Path planning remains a major challenge for the autonomous navigation of Unmanned Aerial Vehicles (UAVs). Despite significant advances in graph-based, sampling-based, metaheuristic, and learning-based path-planning approaches, many existing methods still produce excessive turning points, large path deviations, and trajectories that are misaligned with UAV maneuverability constraints. To address these limitations, this paper presents a Turn-Deviation Optimized Multi-Stage Framework (TDO-MSF) for UAV path planning. The proposed framework integrates a bidirectional A* search algorithm, a turn-deviation reduction strategy, and a direction-constrained neighborhood expansion mechanism to reduce unnecessary directional changes during path generation. A multiscale inflection correction method is employed to eliminate redundant turning points, while a curvature-constrained adaptive-radius smoothing technique is applied to improve trajectory continuity and maneuverability. In addition, a trajectory-guided Enhanced Artificial Potential Field (E-APF) algorithm is incorporated for obstacle avoidance, along with constraints on velocity, acceleration, jerk, and turning radius. The proposed framework is evaluated in various 3D benchmark environments with different obstacle densities and configurations. Its performance is compared with those of the original A*, Improved A*, Improved RRT, Improved PSO, ICSSA, and the baseline MSF-MTPO algorithms using both conventional path-planning and trajectory-quality metrics. Experimental results indicate that the proposed TDO-MSF achieves an average path-length reduction of approximately 2.08% and a 29.25% reduction in the number of turns compared with the benchmark methods. Furthermore, it improves trajectory smoothness and obstacle-avoidance performance while maintaining curvature-constrained and trajectory-guided obstacle-avoidance capabilities.