Obstacle avoidance is a fundamental vision-based task essential for enabling quadrotors to perform advanced applications. When planning the trajectory, existing approaches both on optimization and learning typically regard quadrotor as a point-mass model, giving path or velocity commands then tracking the commands by outer-loop controller. However, at high speeds, planned trajectories sometimes become dynamically infeasible in actual flight, which beyond the capacity of controller. In this paper, we propose a novel end-to-end policy that directly maps depth images to low-level bodyrate commands by reinforcement learning via differentiable simulation. The high-fidelity simulation in training after parameter identification significantly reduces all the gaps between training, simulation and real world. Analytical process by differentiable simulation provides accurate gradient to ensure efficiently training the low-level policy without expert guidance. The policy employs a lightweight and the most simple inference pipeline that runs without explicit mapping, backbone networks, primitives, recurrent structures, or backend controllers, nor curriculum or privileged guidance. By inferring low-level command directly to the hardware controller, the method enables full flight envelope control and avoids the dynamic-infeasible issue.Experimental results demonstrate that the proposed approach achieves the highest success rate and the lowest jerk among state-of-the-art baselines across multiple benchmarks. The policy also exhibits strong generalization, successfully deploying zero-shot in unseen, outdoor environments while reaching speeds of up to 7.5m/s as well as stably flying in the super-dense forest. This work is released at https://github.com/Fanxing-LI/avoidance.
Figures & tables
Fig. 1: This section provides an overview of the proposed method. The policy is trained using backpropagation-through-time (BPTT) within a differentiable simulation that is aligned with real-world control responses. The high-fidelity simulation incorporates a series of precise dynamic computations, enabling successful policy training through straightforward training and inference pipelines, as well as zero-shot deployment on real-world robots.
Fig. 2: Training and inference pipeline of a state-of-the-art learning-based algorithm for collision-free flight without mapping. Our algorithm achieves true end-to-end control by eliminating intermediate trajectory representations in the reference frame. Direct generation of CTBR commands yields the shortest and most efficient inference chain, thereby avoiding dynamics-infeasible issues while improving maneuverability and stability.
Fig. 3: Multimodal representation supervision. Geometrical representation of one scene supervises the trajectory inferred by graphical representation. The gradient chain of differentiable simulation backpropagates the regulatory effect of the collision-based analytical reward.
Fig. 4: A schematic diagram of ESDF map reshaping. (A) : The shifting operation applied to the nearest obstacle point, which transforms the gradient direction from opposing the velocity to the lateral direction. (B) : The shifting angle Δa as a function of distance to the nearest obstacle d and incidence angle a . (C.1 and C.2) : The ESDF gradient field for scenes containing one round obstacle and one rectangular obstacle, where the ”death zone” with nearly uniform gradient direction is highlighted in red. (C.3) : An approximate visualization of the reshaped gradient field. (C.4) The gradient field after reshaping. Note that the gradient fields in (C) are not exact ESDFs; they are the same only without the shifting operation.
Fig. 5: Representative examples of the three groups of training scenes. The first group consists of boxes and pillars of varying shapes. The second group comprises short pillars. The third group contains tall pillars.
Fig. 6: Normalized training curves of SHAC and PPO.
Fig. 7: Large-scale forest environments at four obstacle densities: 0.02, 0.04, 0.06, and 0.08 obstacles/m 2 . For each density, we generate five map instances and evaluate each instance from five different start positions as fig. 9 .A, with the goal located on the opposite side of the forest.
Method
Dens.
v = 3 m/s
v = 6 m/s
v = 9 m/s
v = 12 m/s
S/T
Comp
Vel
Jerk
S/T
Comp
Vel
Jerk
S/T
Comp
Vel
Jerk
S/T
Comp
Vel
Jerk
EGO- Planner
0.02
25/25
1.000
2.49
4.92
24/25
0.963
4.72
22.06
11/25
0.651
6.05
45.13
9/25
0.632
7.15
81.32
0.04
24/25
0.963
2.48
9.23
18/25
0.863
4.64
26.08
8/25
0.601
5.79
50.78
4/25
0.570
7.07
79.58
0.06
23/25
0.946
2.48
9.60
18/25
0.816
4.58
35.48
7/25
0.526
5.51
62.11
3/25
0.444
6.58
78.70
0.08
25/25
1.000
2.47
11.43
12/25
0.737
4.51
45.23
4/25
0.498
5.64
64.68
0/25
0.370
6.67
80.89
Agile
0.02
17/25
0.854
2.96
18.44
15/25
0.815
5.39
52.26
13/25
0.776
6.88
124.22
12/25
0.754
7.65
218.38
TABLE I: Key Character Comparison of Baselines across All Velocities and Densities.
Fig. 8: (A) Trajectories of five test cases in one scene. (B) Trajectories of our policy. (C) Failure cases of baselines.
Fig. 9: Top: Comparison of success rates under varying obstacle densities (0.02–0.08 obs/m 2 ) and commanded speeds (3–12 m/s). Our method maintains near-perfect reliability even in the most aggressive and dense environments. Bottom: Probability density distribution of average jerk across speeds. Our end-to-end policy executes the smoothest maneuvers with consistently lower overall jerk compared to all baselines.
Fig. 10: Panoramic views of the super-dense environments at two obstacle densities: 0.16 and 0.25 obstacles/m 2 .
Velocity
EGO-Planner
Agile
Newton
YOPOv2
Ours
S/T
Comp
Vel
Jerk
S/T
Comp
Vel
Jerk
S/T
Comp
Vel
Jerk
S/T
Comp
Vel
Jerk
S/T
Comp
Vel
Jerk
Density: 0.16 obstacles/m 2
2 m/s
5/5
1.000
1.66
10.99
0/5
0.350
1.97
24.78
5/5
1.000
2.00
7.68
3/5
0.827
1.79
4.03
5/5
1.000
2.39
5.16
4 m/s
4/5
0.917
3.29
58.08
0/5
0.221
3.36
55.49
5/5
1.000
3.46
14.07
2/5
0.756
3.31
11.45
5/5
1.000
3.54
9.69
6 m/s
1/5
0.774
4.60
45.10
0/5
0.438
4.80
90.23
5/5
1.000
4.15
28.90
2/5
0.609
4.48
31.54
5/5
1.000
4.64
15.16
8 m/s
1/5
0.452
5.30
57.37
0/5
0.249
4.35
147.81
4/5
0.877
4.31
61.58
2/5
0.543
5.89
46.61
5/5
1.000
5.26
20.06
TABLE II: Key Character Comparison of Baselines in Superdense Scenes (Density 0.16 and 0.25)
Fig. 11: Real-world experiment in a regular forest environment with an obstacle density of 0.1 m -2 . (A) Reconstructed scene and flight trajectory. (B) Velocity profile during flight. (C) Jerk profile during flight. (D) Real-world scene and flight trajectory. (E) First-person view of the drone at the time steps indicated in (A).
Fig. 12: Real-world experiment in a super-dense forest with an obstacle density of approximately 1m−2 . (A) Reconstructed three-dimensional scene and the actual flight trajectory. (B) Velocity profile recorded during the flight. (C) Jerk profile recorded during the flight. (D) Photograph of the real-world environment alongside the corresponding flight trajectory. (E) First-person view (FPV) captured at the time steps indicated in (A) .
Fig. 13: Multiple experiments for testing policy generalization in various environments including wild and urban scenes.
Differentiable simulation enables efficient policy optimization through analytic gradients, yet safety is commonly incorporated as a weighted penalty, requiring manual tuning of the trade-off between task performance and constraint satisfaction. We instead formulate obstacle avoidance as an explicit constraint and train quadrotor policies using primal--dual gradient descent--ascent through a differentiable simulator. We introduce two key components to enable effective constrained training. First, we propose a bounded clearance-based constraint function that provides informative gradients around the safety boundary while preventing large violations from destabilizing primal--dual optimization. Second, we introduce log-mean-exp (LME) aggregation to smoothly emphasize critical per-step safety violations across a trajectory and training batch within a single constraint governed by one dual variable. Together, these components enable the desired safety level to be specified directly while balancing constraint satisfaction and task completion. We theoretically prove that the proposed optimization with differentiable simulation converges to feasible policy under mild assumptions. Experiments demonstrate improved safety--performance trade-offs over fixed-penalty and existing policy-learning baselines, as well as generalization to denser out-of-distribution environments. Finally, the learned policy transfers zero-shot to Gazebo/PX4 and a physical quadrotor without additional fine-tuning.
Yan Rui Tan, Praveen Krishnapur, Zeyu Feng +3
National University of Singapore, Singapore. · Agency for Science, Technology and Research (A*STAR), Singapore.
First-order reinforcement learning with differentiable simulation is promising for quadrotor control, but practical progress remains fragmented across task-specific settings. To support more systematic development and evaluation, we present a unified differentiable framework for multi-task quadrotor control. The framework is wrapped, extensible, and equipped with deployment-oriented dynamics, providing a common interface across four representative tasks: hovering, tracking, landing, and racing. We also present the suite of first-order learning algorithms, where we identify two practical bottlenecks of standard first-order training: limited state coverage caused by horizon initialization and gradient bias caused by partially non-differentiable rewards. To address these issues, we propose Amended Backpropagation Through Time (ABPT), which combines differentiable rollout optimization, a value-based auxiliary objective, and visited-state initialization to improve training robustness. Experimental results show that ABPT yields the clearest gains in tasks with partially non-differentiable rewards, while remaining competitive in fully differentiable settings. We further provide proof-of-concept real-world deployments showing initial transferability of policies learned in the proposed framework beyond simulation.
Precise aggressive maneuvers with lightweight onboard sensors remains a key bottleneck in fully exploiting the maneuverability of drones. Such maneuvers are critical for expanding the systems' accessible area by navigating through narrow openings in the environment. Among the most relevant problems, a representative one is aggressive traversal through narrow gaps with quadrotors under SE(3) constraints, which require the quadrotors to leverage a momentary tilted attitude and the asymmetry of the airframe to navigate through gaps. In this paper, we achieve such maneuvers by developing sensorimotor policies directly mapping onboard vision and proprioception into low-level control commands. The policies are trained using reinforcement learning (RL) with end-to-end policy distillation in simulation. We mitigate the fundamental hardness of model-free RL's exploration on the restricted solution space with an initialization strategy leveraging trajectories generated by a model-based planner. Careful sim-to-real design allows the policy to control a quadrotor through narrow gaps with low clearances and high repeatability. For instance, the proposed method enables a quadrotor to navigate a rectangular gap at a 5 cm clearance, tilted at up to 90-degree orientation, without knowledge of the gap's position or orientation. Without training on dynamic gaps, the policy can reactively servo the quadrotor to traverse through a moving gap. The proposed method is also validated by training and deploying policies on challenging tracks of narrow gaps placed closely. The flexibility of the policy learning method is demonstrated by developing policies for geometrically diverse gaps, without relying on manually defined traversal poses and visual features.
Tianyue Wu, Guangtong Xu, Zihan Wang +6
Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University, Hangzhou, China. · Huzhou Institute of Zhejiang University, Huzhou, China. · Differential Robotics Technology Co., Ltd., Hangzhou, China.