From Field to Planning: Learning Temporal Polar Gradient Fields for Vision-based AAV Trajectory Planning in Dynamic Environments

Haowen Gao; Zhan Chen; Yinuo Xu; Yifeng Niu; Mengyun Wang; Chao Yan

cs.ROOct 10, 2026

From Field to Planning: Learning Temporal Polar Gradient Fields for Vision-based AAV Trajectory Planning in Dynamic Environments

Authors: Haowen Gao, Zhan Chen, Yinuo Xu, Yifeng Niu, Mengyun Wang, Chao Yan

Organizations: College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China · College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Abstract

Autonomous Aerial Vehicle (AAV) trajectory planning requires real-time and accurate safety gradient guidance, especially in dynamic environments. Existing methods typically rely on static maps and dynamic obstacle tracking to construct gradient fields, imposing heavy computational burdens and yielding conservative trajectories. To address these limitations, we propose a two-stage Field-to-Planning (F2P) learning framework to provide accurate and efficient safety gradients for trajectory planning in dynamic environments. In the first stage, we introduce an Ego-centric Polar Occupancy (EPO) representation that naturally matches the geometry of the onboard camera frustum, while supporting unstructured scene modeling. Subsequently, we formulate a Temporal Polar Gradient Field (TPGF) via multi-kernel separable Gaussian convolution to provide unified safety gradients, without explicitly distinguishing between static and dynamic obstacles. To mitigate the inherent spatial ambiguity introduced by applying convolutions within the polar grid, we propose an ESDF-guided offline learning strategy that incorporates geometric priors into TPGF. In the second stage, we employ the calibrated TPGF to guide the trajectory planning policy in a self-supervised learning manner. Comparative results with other approaches demonstrate the superiority of our method. Extensive real-world experiments within various cluttered dynamic environments validate the real-time performance and robustness on resource-constrained onboard systems.

Figures & tables

Fig. 1: Snapshot of the customized AAV and its trajectory flying through outdoor forest corridors using the proposed framework. The robot achieves safe autonomous flight, effectively executing collision-avoidance maneuvers against approaching pedestrians.

Fig. 2: Overview of the proposed two-stage Field-to-Planning (F2P) framework. The first stage learns an ego-centric Temporal Polar Gradient Field (TPGF) from privileged point clouds. In the second stage, the calibrated TPGF is utilized as a differentiable safety field to guide the self-supervised learning of the trajectory planning policy.

Fig. 3: Illustration of the TPGF generation and trajectory evaluation process. Blue and red cubes represent static and moving obstacles, respectively. First, obstacle points within the FoV are projected into the polar coordinate grid to construct the EPO, followed by a convolution operation to generate the TPGF. Finally, spatiotemporal sampling points along the planned trajectory are projected into the corresponding TPGF slices to query risk values, thereby yielding the differentiable safety loss.

Panel of Figure 4 — Fig. 4: Offline data collection scenarios for training and testing scenarios for planning benchmark comparisons.

Config. ( $B\times N_{\tau}$ )	Frames	TPGF Runtime (ms)	ESDF Runtime (ms)	Speedup (ESDF / TPGF)
$1\times 1$	1	0.454	1.854	4.09 $\times$
$8\times 30$	240	1.093	351.69	321.91 $\times$
$32\times 30$	960	3.515	1438.02	409.36 $\times$
$128\times 30$	3840	14.076	5695.21	404.90 $\times$

TABLE I: Computational Efficiency Comparison between TPGF and ESDF

Configuration	Method	SR $\uparrow$	TC $\downarrow$	SPL $\uparrow$	SNT $\uparrow$	ET $\downarrow$	RT $\downarrow$
Scenario 1 25 Dynamic 75 Static Speed: 0.5 m/s	Ours	1.00	0.00	0.96	0.75	29.75	4.77
	VIGO [ 7 ]	0.96	1.00	0.93	0.44	58.12	45.58
	IPD-MPC [ 10 ]	0.76	7.00	0.68	0.72	27.75	25.20
	YOPO [ 16 ]	0.92	2.00	0.91	0.73	28.81	3.44
	EGO-Planner [ 21 ]	0.80	6.00	0.77	0.46	37.53	42.34
Scenario 2 75 Dynamic 25 Static Speed: 0.5 m/s	Ours	0.96	1.00	0.92	0.73	29.00	4.65

TABLE II: QUANTITATIVE BENCHMARKS IN VARIOUS SCENARIOS

Fig. 5: Visualization of a single flight trial for the evaluated methods. The methods share identical start and goal points, as well as consistent dynamic obstacle trajectories. (a) Spatiotemporal AAV trajectories, with enlarged views of three collision regions. The historical trajectories of moving obstacles are represented by connected transparent cuboids. (b) Velocity-time curves.

Method	Learned Parameters $[\eta,\ \boldsymbol{s}_{c,b,h},\ \boldsymbol{w}_{c,b,h}]$	Planning Performance
Method		SR $\uparrow$	TC $\downarrow$	SPL $\uparrow$	SNT $\uparrow$	ET $\downarrow$
Core only	$[4.37,\{2.19,0.00,0.00\},$ $\{1.00,0.00,0.00\}]$	0.20	48.00	0.18	0.16	28.32
Body only	$[4.40,\{0.00,9.26,0.00\},$ $\{0.00,1.00,0.00\}]$	0.00	83.00	0.00	0.00	29.16
Halo only	$[4.39,\{0.00,0.00,10.42\},$ $\{0.00,0.00,1.00\}]$	0.28	35.00	0.25	0.21	29.52
w/o $\mathcal{L}_{\mathrm{corr}}$	$[2.46,\{1.17,4.95,7.52\},$ $\{2.17,1.95,1.41\}]$	0.04	66.00	0.03	0.03	28.79
w/o $\mathcal{L}_{\mathrm{safe}}$	$[2.46,\{1.18,4.96,7.51\},$ $\{2.16,1.95,1.41\}]$	0.08	61.00	0.07	0.06	28.80

TABLE III: Ablation Study on Parameter Configurations and Planning Performance in Dynamic Scenarios

Panel of Figure 9 — Fig. 6: Generalization and performance boundaries. (a) Success rates across diverse unseen scenarios. (b) Success rate degradation under scaled obstacle density and maximum velocity.

Panel of Figure 10 — Fig. 7: AAV trajectories and generalization testing. The AAV successfully avoids all obstacles in the three cases. (a) and (b) illustrate the corresponding trajectories in the static forest and cluttered indoor. (c) demonstrates the Gazebo simulation and the corresponding AAV and dynamic-pedestrian trajectories. The AAV trajectory is color-coded by speed, while solid obstacle positions mark the closest approaches to the AAV during the flight.

Fig. 8: The real-world experimental system.

Fig. 9: A sequence of snapshots captures the quadrotor as it flies through different cluttered environments. (a) demonstrates evasive maneuvers against an actively approaching pedestrian in a cluttered indoor scene. (b) displays the corresponding depth observations and the real-time planned trajectories of the quadrotor. (c)-(e) showcase evasive flights in an outdoor forest scenario (with the quadrotor highlighted by a yellow circle), where (c) illustrates the continuous avoidance of pedestrians crossing both laterally and longitudinally; (d) depicts the quadrotor evading two pedestrians walking side-by-side while flying through the gap between a pedestrian and the trees; and (e) presents the continuous avoidance of multiple trees and pedestrians within the forest.

Panel of Figure 13 — Fig. 10: Flight trajectory and the corresponding velocity profiles for the indoor scenario. (a) Executed 2D trajectory, where the purple curve represents the actual flight path of the quadrotor, blue voxels indicate static obstacles, and red cuboids denote dynamic pedestrians. (b) Corresponding velocity profiles over time. The 3-axis velocities are directly output from the odometry, representing the quadrotor’s velocities in the world coordinate frame.

Panel of Figure 14 — Fig. 11: Flight trajectory and the corresponding velocity profiles for the outdoor forest scenario.

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SPOT: Spatio-Temporal Obstacle-free Trajectory Planning for UAVs in Unknown Dynamic Environments

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We address the problem of reactive motion planning for quadrotors operating in unknown environments with dynamic obstacles. Our approach leverages a 4-dimensional spatio-temporal planner, integrated with vision-based Safe Flight Corridor (SFC) generation and trajectory optimization. Unlike prior methods that rely on map fusion, our framework is mapless, enabling collision avoidance directly from perception while reducing computational overhead. Dynamic obstacles are detected and tracked using a vision-based object segmentation and tracking pipeline, allowing robust classification of static versus dynamic elements in the scene. To further enhance robustness, we introduce a backup planning module that reactively avoids dynamic obstacles when no direct path to the goal is available, mitigating the risk of collisions during deadlock situations. We validate our method extensively in both simulation and real-world hardware experiments, and benchmark it against state-of-the-art approaches, showing significant advantages for reactive UAV navigation in dynamic, unknown environments.

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