Teardrop Risk Field-Based Spatiotemporal Path Planning Method for Mobile Robots in Dynamic Environments

Navigating dynamic environments requires autonomous robots to balance computational efficiency with safety. Traditional isotropic risk fields ignore obstacle velocities, causing overly conservative lateral avoidance or insufficient margins against head-on collisions. To address this, we propose TRF-ST-RRT, a spatiotemporal RRT framework driven by our core innovation: a velocity-based "teardrop" risk field (TRF). By constructing an anisotropic safety corridor, the TRF dynamically extends its leading edge based on kinematic constraints. This explicitly forces the planner to navigate behind or alongside dynamic obstacles, ensuring robust spatial buffers against oncoming threats. To efficiently deploy this field, a supporting three-layer probabilistic hybrid sampling strategy is integrated to accelerate the real-time 3D spatiotemporal search. Finally, line-of-sight path simplification and subsequent temporal reconstruction, combined with segmented Bézier smoothing, are applied to guarantee trajectory executability. Extensive ablation studies and ROS2 simulations demonstrate that, compared to individual state-of-the-art baselines such as ORCA, MPPI, and ST-RRT*, TRF-ST-RRT substantially reduces planning time and iteration counts while delivering notable improvements in both overall driving efficiency and dynamic evasion success rates.