Efficiently learning safe and agile quadruped navigation in densely cluttered environments remains difficult: existing methods often lack safety and agility, or become conservative in complex scenes and require long training schedules. We propose SEA-Nav (Safe, Efficient, and Agile Navigation), a safe reinforcement learning framework for quadruped navigation in cluttered environments. A differentiable control barrier function (CBF) shield constrains the policy to produce safe velocity commands. An adaptive collision-state initialization mechanism increases the probability of learning from safety-critical near-collision experience. An action regularization term further suppresses infeasible commands for physical deployment. The policy converges after about one hour of training on a single RTX 4090 and transfers zero-shot to real-world cluttered scenes.
Figures & tables
Fig. 1: SEA-Nav is trained in about one hour on a single RTX 4090 and deployed zero-shot in a previously unseen maze. The robot successfully escapes using the built-in MPC controller and onboard sparse LiDAR, both unseen during training.
Fig. 2: Overview of the proposed SEA-Nav pipeline. Historical observations are encoded into a latent feature, which is concatenated with the current observation to form the joint state representation. In the Actor, the joint state passes through a shared Backbone into a navigation action head and a safety-gain α head, producing a nominal velocity command and an adaptive gain; the LSE-CBF Shield then solves for a safe velocity command. The Critic takes the joint state representation xt=[ot,zt] as input and directly predicts the state value V(xt) . The Actor and Critic are optimized jointly with PPO, shield intervention, and kinematic regularization losses.
Fig. 3: SEA-Nav trajectories in three navigation scenarios of increasing difficulty. Each subfigure shows two distinct start-goal trials. SEA-Nav successfully traverses narrow passages and performs timely maneuvering adjustments to avoid entrapment in cluttered environments.
Method
Easy
Medium
Hard
SR (%)↑
CR (%)↓
TR (%)↓
SR (%)↑
CR (%)↓
TR (%)↓
SR (%)↑
CR (%)↓
TR (%)↓
SEA-Nav (Ours)
100.00 (±0.00)
0.00 (±0.00)
0.00 (±0.00)
97.00 (±0.82)
1.00 (±0.82)
2.00 (±0.00)
90.00 (±1.63)
5.00 (±0.82)
5.00 (±0.82)
SEA-Nav w/o ACSI
100.00 (±0.00)
0.00 (±0.00)
0.00 (±0.00)
93.00 (±0.82)
2.33 (±0.47)
4.67 (±0.47)
83.00 (±2.45)
8.00 (±2.16)
9.00 (±1.63)
SEA-Nav w/o Shield
97.67 (±0.47)
1.33 (±0.47)
1.00 (±0.00)
90.00 (±0.82)
2.67 (±0.94)
7.33 (±1.70)
74.33 (±3.30)
11.67 (±1.70)
14.00 (±2.16)
SEA-Nav w/o Lreg
96.33 (±0.47)
2.67 (±0.47)
1.00 (±0.00)
82.33 (±2.05)
6.00 (±0.82)
11.67 (±1.25)
57.00 (±4.08)
18.00 (±2.16)
25.00 (±2.16)
ABS [ 7 ]
95.00 (±0.00)
4.67 (±0.47)
0.33 (±0.47)
75.33 (±1.25)
9.33 (±0.47)
15.33 (±1.70)
45.33 (±3.40)
22.00 (±1.41)
32.67 (±2.05)
TABLE I: Different difficulty levels are evaluated; mean and standard deviation are reported over 3 evaluation runs of 100 randomized trials each.
Fig. 4: (Left) Trajectory plot; (right) velocity profiles. SEA-Nav maintains larger obstacle clearance and smoother speed variations. The safety gain α decreases in hazardous regions so the CBF Shield dominates, and increases in safe regions where the nominal navigation command takes the lead.
Fig. 5: Real-world experimental environments. Ten trials are conducted in each environment.
Method
Cluttered Room
Dynamic Obstacle
Obstacle Course
S-Blend Track
SR (%)↑
CR (%)↓
AS (m/s) ↑
SR (%)↑
CR (%)↓
AS (m/s) ↑
SR (%)↑
CR (%)↓
AS (m/s) ↑
SR (%)↑
CR (%)↓
AS (m/s) ↑
SEA-Nav
100
10
1.6
90
20
1.5
100
10
1.2
100
10
1.4
SEA-Nav-b
100
10
0.9
100
20
0.8
90
10
0.7
100
10
0.5
ABS [ 7 ]
70
50
2.1
60
10
1.7
0
100
0.6
80
20
0.8
OCR [ 23 ]
90
20
1.7
90
10
1.5
30
100
1.0
90
20
1.3
REASAN [ 14 ]
90
20
1.3
90
10
1.3
40
100
0.9
90
30
0.9
TABLE II: Real-world deployment results. AS: average speed (m/s); SEA-Nav-b: built-in MPC controller and onboard sparse LiDAR.
Term
Purpose
Compact expression
Weight
rterm
episode termination cost
1[terminated]
−100
rreach
tight goal reaching
1+2d211[d<0.5]
+10
rvelo
move toward goal
cosθvx+1+2d21
+15
rclear
clearance-aware motion
1[d>1]cosϕvx+1[d≤1]1+2d21
+15
rstuck
penalize getting stuck
1[d>1]1[Δpmax<0.1]1[vx>0.0]1[∣ωz∣<1.0]
−5
rcoll
penalize collisions
(1+4(∥v∥22+ωz2))∑kβk1[∥fk∥>0.1]
−4
TABLE III: Reward terms and weights.
Fig. 6: Comparison of LiDAR point clouds. The robot’s position and orientation are indicated by the gray arrow. (a): The robot’s actual environment. (b): Sparse point cloud from the Unitree Go2 robot’s onboard LiDAR, consisting of approximately 1,000 3D points per frame. (c): Denser point cloud from the RPLIDAR A2, consisting of approximately 2,000 2D points per frame.
Navigating dynamic and crowded environments presents significant challenges for quadruped robots due to severe sensor occlusion and unpredictable human motion. Existing approaches face a trade-off: model-based methods, such as Velocity Obstacles (VO), theoretically guarantee safety but rely on accurate obstacle motion estimates that often fail in dense crowds, while end-to-end learning methods offer robustness but lack motion prediction capability of obstacles, leading to collisions or conservative behaviors. To solve this, we propose VOP-Nav, a novel navigation system that combines the geometric safety of VO with the agile adaptability of end-to-end learning. Using only local onboard observations, our system avoids explicit obstacle detection and tracking pipelines. The VOP-Net processes multi-frame LiDAR data to implicitly encode dynamic constraints and predict a safe velocity region derived from Velocity Obstacle theory. Importantly, the VO predictions serve a dual role: they are used as input to the navigation policy during inference and as a reward signal during training to encourage safe motion. Evaluations in Isaac Gym demonstrate that VOP-Nav achieves higher success rates than all baselines while balancing locomotion speed and collision avoidance. Real-world deployment on a Unitree Go2 quadruped robot further validates the system's robustness and efficiency in complex indoor and outdoor dynamic environments.
Shuyu Wu, Zeyu Liu, Tianbao Zhang +6
Shanghai Jiao Tong University, Shanghai 200240, China · State Key Laboratory of High-end Heavy-load Robots, Midea Group, Foshan 528300, China
Learning-based quadruped controllers achieve impressive agility but typically lack formal safety guarantees under model uncertainty, perception noise, and unstructured contact conditions. We introduce SafeMind, a differentiable stochastic safety-control framework that unifies probabilistic Control Barrier Functions with semantic context understanding and meta-adaptive risk calibration. SafeMind explicitly models epistemic and aleatoric uncertainty through a variance-aware barrier constraint embedded in a differentiable quadratic program, thereby preserving gradient flow for end-to-end training. A semantics-to-constraint encoder modulates safety margins using perceptual or language cues, while a meta-adaptive learner continuously adjusts risk sensitivity across environments. We provide theoretical conditions for probabilistic forward invariance, feasibility, and stability under stochastic dynamics. SafeMind is deployed on Unitree A1 and ANYmal C at 200~Hz and validated across 12 terrain types, dynamic obstacles, morphology perturbations, and semantically defined tasks. Experiments show that SafeMind reduces safety violations by 3--10x and energy consumption by 10--15% relative to state-of-the-art CBF, MPC, and hybrid RL baselines, while maintaining real-time control performance.
Zukun Zhang, Kai Shu, Mingqiao Mo
The University of Hong Kong, Pokfulam, Hong Kong, China · Alibaba, Beijing, China · University of Chinese Academy of Sciences, No.1 Yanqihu East Rd, Huairou District, Beijing, China
Safe quadrotor navigation in cluttered and dynamic environments depends not only on instantaneous geometric perception, but more critically on anticipating collision risks induced by relative motion. Conventional modular pipelines frequently suffer from perception latency, while end-to-end learning methods relying on implicit scalar rewards often struggle to extract reliable spatio-temporal features without physics-grounded supervision. To address this, we propose an anticipatory risk-guided reinforcement learning framework. Leveraging privileged simulator states, we construct a directionally aligned future collision risk map based on the Closest Point of Approach (CPA). Through an asymmetric actor-critic architecture, the network is trained to self-predict this structured risk, which explicitly guides the visual policy during deployment. A lightweight spatio-temporal encoder extracts motion cues directly from onboard depth sequences, bypassing explicit object tracking or optical flow estimation. Extensive simulated and real-world experiments demonstrate that our method effectively improves safety margins and flight efficiency in dense dynamic clutters compared to existing baselines. Furthermore, the learned policy achieves robust zero-shot Sim-to-Real transfer on a physical quadrotor, relying purely on abstracted spatio-temporal depth sequences and its self-predicted risk priors, validating the effectiveness of our approach and its robust generalization from simulation to reality.
Yuchao Mei, Guohao Zhang, Luxia Ai +2
National Key Laboratory of Science and Technology on Multi-spectral Information Processing, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China