TRAIN: Terrain-Aware Interactive Navigation for Quadruped Robots via Reinforcement Learning

Wei Zhu; Irfan Tito Kurniawan; Ye Zhao; Mitsuhiro Hayashibe

cs.ROFeb 13, 2026

TRAIN: Terrain-Aware Interactive Navigation for Quadruped Robots via Reinforcement Learning

Authors: Wei Zhu, Irfan Tito Kurniawan, Ye Zhao, Mitsuhiro Hayashibe

Organizations: Department of Robotics, Graduate School of Engineering, Tohoku University, 980-8579, Sendai, Japan. · Laboratory for Intelligent Decision and Autonomous Robots, Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30313, USA.

Abstract

This study introduces TRAIN: TeRrain-Aware Interactive Navigation, a deep reinforcement learning (DRL)-based framework for quadrupedal navigation across unstructured terrain and human-populated environments. Conventional quadrupedal navigation typically separates motion planning from locomotion control, neglecting whole-body constraints and terrain awareness. On the other hand, end-to-end methods are more integrated but require high-frequency sensing, which is often noisy and computationally costly. In addition, most existing approaches assume static environments, limiting their use in human-populated settings. To address these limitations, we propose a two-stage training framework with three DRL pipelines. (1) TRAIN-Loco employs an asymmetric actor-critic (AC) model for quadrupedal locomotion, enabling agile traversal of uneven terrains without explicit terrain or contact observations. (2) TRAIN-Nav applies a symmetric AC framework for navigation with interactive pedestrians, directly mapping transformed LiDAR data to ego-agent actions under differential-drive kinematics. (3) A unified pipeline, TRAIN, integrates TRAIN-Loc and TRAIN-Nav, supporting terrain-aware quadrupedal navigation in uneven and interactive environments. Comprehensive benchmarks against quadrupedal locomotion and robot navigation baselines demonstrate the effectiveness of TRAIN. Hardware experiments further confirm its potential for sim-to-real transfer.

Figures & tables

Fig. 1: Terrain-aware navigation of quadruped robots in interactive environments. The top panel illustrates simulation training scenarios, while the bottom panels show real-world implementations.

Fig. 2: Overall framework with a two-stage training architecture. In the first stage, a quadrupedal locomotion policy and a navigation policy with interaction awareness are trained separately. In the second stage, these two policies are unified into a single quadrupedal navigation policy, which is further retrained in uneven and interactive environments.

Fig. 3: Terrain height map and contact points visualized in IsaacSim.

Reward	Equation ( $r_{i}$ )	Weight ( $w_{i}$ )
Linear $\mathrm{vel}$ track	$\exp\{-4\left(\mathbf{v}_{xy}^{\mathrm{cmd}}-\mathbf{v}_{xy}\right)^{2}\}$	$1.5$
Angular $\mathrm{vel}$ track	$\exp\{-4\left(w_{z}^{\mathrm{cmd}}-w_{z}\right)^{2}\}$	$0.75$
Linear $\mathrm{vel}$ ( $z$ )	$v_{z}^{2}$	$-2.0$
Angular $\mathrm{vel}$ ( $xy$ )	$\boldsymbol{w}_{xy}^{2}$	$-0.05$
Torque	$\boldsymbol{{\tau}}^{2}$	$-2\times 10^{-4}$
Angular acceleration	$\boldsymbol{\ddot{{\theta}}}^{2}$	$-2.5\times 10^{-7}$

TABLE I: Reward function for quadrupedal locomotion

Type	Domain	Noise
System dynamics	Friction coefficient	[0.65, 1.25]
	Body mass	[-1.0, 3.0] kg
	CoM $xy$	[-0.05, 0.05] m
	CoM $z$	[-0.01, 0.01] m
Observations	Body linear $\mathrm{vel}$ $\mathbf{v}_{t}$	[-0.1, 0.1] m/s
	Body angular $\mathrm{vel}$ $\boldsymbol{\omega}_{t}$	[-0.2, 0.2] rad/s

TABLE II: Locomotion Domain Randomization

Fig. 4: LiDAR scan transformation. The red filled circle represents the ego-agent, blue filled circles denote static obstacles of varying sizes, and blue hollow circles indicate pedestrians with a fixed radius. The left panel shows the LiDAR scan (solid beams) at time

t-k

, while the right panel illustrates the scan (solid beams) at the current time

t

. Dashed lines in the right panel correspond to the transformed LiDAR beams from

t-k

t

. Each point

P_{i}

retains the same global position in both panels.

Fig. 5: Reward structure and scenarios. The left panel illustrates the geometric representation used for defining the reward function, while the right panel depicts four possible ego-agent scenarios: collision, goal arrival, discomfort, and open space.

Fig. 6: Progression of terrain difficulty levels over training iterations across five independent random seeds. The solid line indicates the mean, while the shaded region denotes the minimum and maximum bounds.. The Privilege method yields an ideal performance reference (upper bound) rather than a direct baseline.

Fig. 7: Locomotion ablation results evaluated across five random seeds. DreamWaQ-A1 is omitted because all five runs collapsed (terrain difficulty converged to zero) at the early training stage.

Method	$\Delta v_{x}$ m/s	$\Delta v_{y}$ m/s	$\Delta w_{z}$ rad/s
DreamWaQ-Go2	0.12 $\pm$ 0.15	0.12 $\pm$ 0.15	0.15 $\pm$ 0.15
L2T-Go2	0.17 $\pm$ 0.18	0.17 $\pm$ 0.17	0.28 $\pm$ 0.28
SLR-Go2	0.13 $\pm$ 0.18	0.13 $\pm$ 0.17	0.10 $\pm$ 0.11
TAR-Go2	0.45 $\pm$ 0.68	0.31 $\pm$ 0.60	0.27 $\pm$ 0.34
TRAIN-Loco-MLP-Go2	0.13 $\pm$ 0.15	0.12 $\pm$ 0.14	0.16 $\pm$ 0.17
TRAIN-Loco-Go2 (Ours)	0.10 $\pm$ 0.12	0.11 $\pm$ 0.13	0.13 $\pm$ 0.12

TABLE III: Command tracking errors for quadrupedal locomotion on uneven terrains.

Fig. 8: Velocity tracking performance along with simulation scenes. The commanded velocities, $[v_{x},v_{y},w_{z}]$ , change from $[0.0,0.0,0.0]$ , to $[0.6,0.6,1.0]$ , to $[-0.6,-0.6,-1.0]$ , and to $[0.0,0.0,0.0]$ . The top left two scenes correspond to the peak tracking errors for our approach, and the other four illustrate the erroneous tracking for DreamWaQ.

Fig. 9: Learning efficiency comparison with five random seeds. The learning curve for HEIGHT is plotted separately in the bottom panel due to its significantly lower learning efficiency (approximately 20 times slower). The remaining learning curves are depicted in the top panel, where DRL-VO achieves an efficiency comparable to our method when utilizing our proposed network architecture.

	Method	SR	CR	TR	NT
Reactive	DWA	0.946	0.014	0.040	18.81 $\pm$ 3.36
	ORCA	0.848	0.004	0.148	20.33 $\pm$ 5.59
	AVOCADO	0.830	0.044	0.126	18.56 $\pm$ 4.61
MPC	N-MPC	0.242	0.002	0.756	19.89 $\pm$ 3.85
	NeuPAN	0.004	0.020	0.976	40.20 $\pm$ 0.85
	T-MPC	0.326	0.586	0.106	19.50 $\pm$ 7.31

TABLE IV: Navigation evaluations with 500 random tests.

Panel of Figure 14 — Fig. 10: Trajectories of the ego-agent and pedestrians. The red circle is the ego-agent, the green represents the goal, the cyan circles are static obstacles, and others are pedestrians. As time goes by, the color of the circle changes from light to dark. N-MPC fails due to navigation timeout, while RGL and AVOCADO fail because of collisions.

Method	SR	CR	NT
TRAIN-Nav-CNN	0.892	0.108	18.96 $\pm$ 1.40
TRAIN-Nav-Direct	0.956	0.064	20.66 $\pm$ 2.83
TRAIN-Nav-Noise	0.960	0.040	18.75 $\pm$ 1.48
TRAIN-Nav (Ours)	0.972	0.028	19.26 $\pm$ 1.29
TRAIN-Nav-Reverse (Ours)	0.980	0.020	18.81 $\pm$ 2.29

TABLE V: TRAIN-Nav: Ablation evaluations with 500 random tests.

Method	SR	CR	TR	NT
Nav-Loco	0.924	0.076	0.000	19.62 $\pm$ 2.20
Train-Nav-Loco	0.930	0.066	0.004	19.54 $\pm$ 2.26
TRAIN-Direct	0.924	0.076	0.000	19.60 $\pm$ 2.15
TRAIN-Warm-Start	0.954	0.042	0.004	20.39 $\pm$ 2.81
TRAIN-Clip	0.916	0.076	0.008	21.28 $\pm$ 3.38
TRAIN-Loco-DWA	0.894	0.078	0.028	18.90 $\pm$ 3.23

TABLE VI: TRAIN: Ablation evaluations and benchmark with 500 random tests.

Panel of Figure 17 — Fig. 11: Trajectories and simulation environments for representative failure cases. (a) Top row: A head-on collision between the robot and a dynamic pedestrian. (b) Middle row: A scenario where a pedestrian rear-ends the robot due to reactivity differences. (c) Third row: Trajectory analysis of a collision with a static obstacle. (d) Bottom row: Corresponding 3D simulation snapshots for the obstacle collision cases presented in (c).

Fig. 12: Overview of the hardware deployment pipeline. Visual data for pedestrian tracking is acquired via the onboard camera, while localized navigation is achieved through LiDAR-IMU fusion. These data streams are processed on an external PC to execute the real-time perception-to-action mapping.

Fig. 13: Unseen pedestrian environments. The robot starts at (-4, 0) m with a goal position of (4, 0) m. Static obstacles of varying sizes are randomly distributed along the robot’s path. The initial group of pedestrians is distributed in a circular formation, while the upper and lower rectangles define the movement zones for additional pedestrians.

Scenarios	flat	uneven	slopes	stairs
Success/Failure	3/0	4/1	3/0	6/4

TABLE VII: Hardware implementations.

Fig. 14: Real-world terrain configurations. The top panel displays the indoor rough terrain, while the bottom panels illustrate the stair scenarios.

Method	SR	NT	Fall	Collision	Timeout
DWA	0.82	16.40	3/50	2/50	4/50
TRAIN (ours)	0.92	19.15	3 /50	1 /50	0 /50

TABLE VIII: Hardware implementations with simulated pedestrians and obstacles.

	Success	Collision	Fall	NT
Descending	9	1	0	17.38
Ascending	8	1	1	22.65

TABLE IX: Hardware implementations with simulated pedestrians and obstacles on stairs.

Networks	Input shape	Hidden layers	Output shape
Actor	(64,)	$512\times 256\times 128$	(12,)
Critic	(286,)	$512\times 256\times 128$	(1,)
Decoder	(19,)	$64\times 128$	(45,)

TABLE X: Locomotion networks: actor, critic, and decoder

Layer	Operation
1	Conv2d(1, 16, kernel - size=3, stride=1, padding=1)
2	MaxPool2d(kernel - size=2, stride=2, padding=0)
3	Conv2d(16, 32, kernel - size=3, stride=1, padding=1)
4	MaxPool2d(kernel - size=2, stride=2, padding=0)
5	Conv2d(32, 64, kernel - size=3, stride=1, padding=1)
6	Flatten with output shape (1408,)

TABLE XI: Locomotion networks: encoder

Networks	Input shape	Hidden layers	Output shape
Actor	(54)	$1024\times 1024$	(4,)
Critic	(56,)	$1024\times 1024$	(1,)

TABLE XII: Navigation networks: actor, critic, and decoder

Layer	Operation
1	Conv2d(1, 32, kernel - size=(2, 20), stride=(1, 10))
2	MaxPool2d(kernel - size=(1, 5))
3	Conv2d(32, 32, kernel - size=2, stride=1)
4	MaxPool2d(kernel - size=(1, 2))
5	Flatten with output shape (2176,)
6	Linear(2176, 1024)

TABLE XIII: Navigation networks: encoder

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Sep 3, 2026J/K move · Enter open · S save

MulDP: Multimodal Diffusion Policy for Autonomous Quadruped Parkour Navigation across Complex Terrains

Kangmai Hu, Yueqi Zhang, Peng Zhai, Xiaoyi Wei+4

College of Intelligent Robotics and Advanced Manufacturing, Fudan University, Shanghai 200433, China

Robot Policy Learning Robot Navigation Diffusion Policy Terrain-Aware Robot Locomotion Quadruped Robot Navigation

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Quadruped robots have demonstrated impressive agility in parkour locomotion across complex terrains. However, most systems still rely on human intervention for high-level planning, and autonomous parkour navigation remains underexplored. The key challenges include fine-grained velocity regulation, long-horizon anticipatory behaviors, and tight coupling between perception and embodied execution. To address these challenges, we propose a Multimodal Diffusion Policy (MulDP) that integrates visual perception with robot proprioception and goal information to generate temporally coherent and anticipatory navigation velocity commands, tightly coupling perception with embodied control to enable robust autonomous navigation. To support the training of MulDP, we construct the first Quadruped Parkour Navigation Dataset (QPND), a multimodal dataset that encompasses diverse navigation behaviors and complex terrains. Extensive simulation and real-world experiments demonstrate that MulDP enables robust long-horizon autonomous navigation and effective traversal across complex terrains.

Abstract

Quadruped Robot Navigation

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