DELTA: Deformable Elevation-Based Local Terrain Attention Encoder for Sparse-Terrain Quadrupedal Locomotion
Authors: Sanghyun Park, Moonkyu Jung, Jemin Hwangbo
Organizations: Robotics and Artificial Intelligence Lab, Korea Advanced Institute of Science and Technology (KAIST), Yuseong-gu, Daejeon 34141, Republic of Korea
Stable quadrupedal locomotion on sparse terrain requires selecting state-relevant terrain evidence for precise foot placement. Model-based foothold planners provide precise foothold selection but rely heavily on explicit model assumptions. Recent attention-based map encoding (AME) studies show that end-to-end reinforcement learning (RL) can learn implicit foothold guidance. However, the computational cost of dense AME encoding grows with map resolution, limiting its scalability to fine-grained sparse terrain. We propose DELTA, a Deformable Elevation-Based Local Terrain Attention encoder. DELTA predicts state-conditioned sampling locations, forms terrain evidence tokens from adaptive local elevation patches, and attends only to a fixed-size token set. With fixed sampling and patch settings, DELTA's encoder cost is independent of map resolution. Experiments show that DELTA achieves final traversal performance comparable to AME at the standard resolution while improving learning efficiency. This fixed encoder cost enables the use of higher-resolution terrain maps, improving traversal on fine-grained sparse terrain. DELTA also demonstrates strong generalization to unseen mixed evaluation courses composed of continuous and discrete terrain elements. Beyond simulation, DELTA demonstrates successful sim-to-real transfer on RAIBO2. Analysis of the learned sampling offsets and attention weights shows that DELTA samples steppable regions and attends to terrain evidence relevant to future touchdowns without foothold labels or attention supervision.
Figures & tables
Fig. 1: Real-robot traversal of an unseen mixed sparse-terrain course using DELTA, requiring precise foot placement on sparse and discontinuous steppable regions without an explicit foothold planner.
Fig. 2: Overall policy architecture and DELTA encoder. (a) DELTA encodes proprioception pt and the robot-centered local elevation map Mt into a terrain representation et , which is fused with proprioception and passed to the actor and critic. (b) DELTA updates the initial query q0 through L deformable terrain attention layers using state-conditioned sampling, scout-guided refinement, adaptive patch encoding, and multi-head cross-attention, yielding qL=et .
Setting
Value
dp/nj
48/12
(H×W×C)std/high
26×16×3 / 41×25×3
Map extent (m)
2.0×1.2
L/D
3/64
Nh/K
4/8
Patch size Ps/P / center
3×3 / 9×9 / 3×3
TABLE I: Main Policy, Control, and DELTA Settings
Fig. 3: Training terrains and mixed evaluation courses. Training includes five continuous terrains (Hills, Slope, Stairs, Steps, Rough Ground) and three discrete terrains (Gaps, Stepping Stones, Grid Stones); the fine-grained stepping stones have half the standard stone radius. The four unseen mixed courses combine: (1) gaps, irregular stepping stones, and ascending stairs; (2) alternating grid stones, a downhill slope, and descending stepping stones; (3) hills, rough tiles, stairs, and terraced platforms with evaluation-only irregular elliptical holes; and (4) rough ground, stairs, and elevated platforms with evaluation-only curved gaps. Blue-highlighted elements in Courses 3 and 4 denote evaluation-only terrain variants.
Policy
Success rate (%) ↑
Iterations to 90% SR ↓
Continuous avg.
Stepping Stones
Gaps
Grid Stones
Overall avg.
MLP
80.8
79.9
85.4
81.2
81.3
N/C
AME
95.4
98.1
99.8
95.7
96.3
8,890±1,475
DELTA
94.6
99.5
99.7
98.5
96.4
2,210±160
TABLE II: Simulation Traversal Performance and Learning Efficiency
Policy
Map size
Stepping-stone SR (%) ↑
Standard
Fine-grained
AME
26×16
97.9
65.7
DELTA
26×16
98.4
84.0
AME
41×25
92.5
68.0
DELTA
41×25
99.1
95.9
TABLE III: Stepping-Stone SR under the Fine-Grained Curriculum
Encoder setting
Map size
Encoder FLOPs (M) ↓
Mean iter. time (s) ↓
Relative training speed ( × ) ↑
AME
26×16
27.570
20.262
1.00
DELTA
26×16
4.496
8.239
2.46
AME
41×25
67.910
46.558
0.44
DELTA
41×25
4.496
10.541
1.92
TABLE IV: Encoder FLOPs and Wall-Clock Training Efficiency
Course
MLP
AME
DELTA
SR (%) ↑
Mean progress (%) ↑
SR (%) ↑
Mean progress (%) ↑
SR (%) ↑
Mean progress (%) ↑
Course 1
0.0
75.3
41.8
62.9
97.6
98.5
Course 2
12.6
65.4
53.8
69.0
99.3
99.6
Course 3
0.0
47.5
6.2
59.9
97.4
98.0
Course 4
1.4
57.2
2.2
58.9
92.0
97.5
Average
3.5
61.4
26.0
62.7
96.6
98.4
TABLE V: Generalization Performance on Four Unseen Mixed Evaluation Courses
Variant
Traversal (%) ↑
Sampling & attention ↑
Stepping-Stone SR
Mixed-Course Avg. SR
GT steppable surface ratio (%)
FT attn. ratio ( × )
DELTA
99.5
96.6
85.4±1.0
2.11±0.16
w/o Scout
95.2
75.0
68.7±1.8
1.33±0.07
w/o Adapt. Patch
97.3
56.1
75.4±2.8
1.84±0.10
Fixed Sampling
96.0
28.2
31.6±6.2
1.18±0.24
TABLE VI: Ablation of DELTA Components
Fig. 4: Final-layer sampling locations and head-averaged attention of DELTA at 41×25 resolution. Attention weights are bilinearly distributed over the elevation map and averaged across heads; black indicates zero weight and blue-to-red indicates increasing attention.
Fig. 5: Representative real-world courses: (a) Gaps, (b) Stepping Stones, (c) Gaps–Stepping Stones–Gaps, and (d) Stairs–Gaps–Stairs. Gap distances are 10–20 cm, with 15-cm stepping-stone spacing.
Although reinforcement learning has significantly advanced humanoid locomotion, perceptive policies still struggle on sparse-foothold terrain and constrained environments. Success in these scenarios requires both broad terrain awareness and precise foothold selection, two perceptual roles that conventional encoders often entangle. To address this challenge, we propose Global-Local Attention Decomposition (GLAD) for terrain encoding in humanoid locomotion. Realized by a coarse-to-fine encoder over a robot-centric elevation map, GLAD explicitly separates these objectives: a global attention branch utilizes attention pooling to summarize the surrounding terrain context, while a state-conditioned local attention branch sparsifies and encodes precise foothold-relevant geometry. This explicit attention decomposition prevents the dilution of fine-grained spatial cues while reducing training overhead. Experiments demonstrate that GLAD enables reliable locomotion over challenging gaps, stepping stones, and stairs. Furthermore, the learned policy exhibits emergent terrain-responsive behaviors, autonomously following narrow paths and avoiding obstacles under simple velocity commands without explicit navigation planners. In real-world deployment on a Unitree G1 humanoid robot using onboard LiDAR, the proposed method achieves robust zero-shot sim-to-real transfer across diverse sparse-foothold and obstacle-rich domains.
Shengcheng Fu, Yang Zhang, Zhanxiang Cao +4
Tongji University, Shanghai, China · Shanghai Jiao Tong University, Shanghai, China · Shanghai Innovation Institute, Shanghai, China +1
Achieving agile and generalized legged locomotion across terrains requires tight integration of perception and control, especially under occlusions and sparse footholds. Existing methods have demonstrated agility on parkour courses but often rely on end-to-end sensorimotor models with limited generalization and interpretability. By contrast, methods targeting generalized locomotion typically exhibit limited agility and struggle with visual occlusions. We introduce a unified reinforcement learning (RL) framework for agile and generalized locomotion that incorporates a novel attention-based map encoder in the control policy. This encoder extracts local and global mapping features and uses attention mechanisms to focus on salient regions, producing an interpretable and generalized embedding for RL-based control. We further propose a learning-based mapping pipeline that provides fast, uncertainty-aware terrain representations robust to noise and occlusions, serving as policy inputs. It uses neural networks to convert depth observations into local elevations with uncertainties, and fuses them with odometry. The pipeline also integrates with parallel simulation so that we can train controllers with online mapping, aiding sim-to-real transfer. We validate our framework with the proposed mapping pipeline on a quadruped and a biped robot, and the resulting controllers demonstrate strong agility and generalization to unseen terrains in simulation and in real-world experiments.
Chong Zhang, Victor Klemm, Fan Yang +1
1Robotic Systems Lab, ETH Zurich, Switzerland · 2Secure, Reliable, and Intelligent Systems Lab, ETH Zurich, Switzerland · 3ETH AI Center, Switzerland
Quadrupedal locomotion over complex terrain has been a long-standing research topic in robotics. While recent reinforcement learning-based locomotion methods improve generalizability and foot-placement precision, they rely on implicit inference of foot positions from joint angles, lacking the explicit precision and stability guarantees of optimization-based approaches. To address this, we introduce a foot position map integrated into the heightmap, and a dynamic locomotion-stability reward within an attention-based framework to achieve locomotion on complex terrain. We validate our method extensively on terrains seen during training as well as out-of-domain (OOD) terrains. Our results demonstrate that the proposed method enables precise and stable movement, resulting in improved locomotion success rates on both in-domain and OOD terrains.