Source-linked AI summary
SOLO: Stable Omni-terrain Long-Horizon Perceptive Humanoid Locomotion
Pihai Sun, Gang Han, Jingkai Sun, Jiahao Ma, Zeran Su, Zelin Tao, Peiran Liu, Shuai Shi, Wei Cui, Zifan Wang, Jialin Yu, Wen Zhao, Kangning Yin, Jiaxu Wang, Jiahang Cao, Lingfeng Zhang, Hao Cheng, Jian Tang, Yijie Guo, Qiang Zhang
TL;DR
Perceptive humanoid policies can become fragile over long horizons because dense reconstruction smooths action-critical terrain details and pointwise imitation lacks temporal credit assignment. SOLO combines cell-query reconstruction with trajectory-aware distillation, achieving stronger simulation results and zero-shot completion of continuous indoor and outdoor routes using onboard sensing.
Problem
Long-horizon perceptive locomotion is challenged by smoothed action-critical terrain details and pointwise imitation that lacks temporal credit assignment.
Method
SOLO combines QR, which retrieves cell-specific terrain evidence from depth–proprioception tokens, with TA-MSE, which adds next-state disagreement to the PPO reward for GAE-based credit assignment.
Results
SOLO achieves 97.5% mean stress-test traversal success and 96% stepping-stone success, while completing a continuous 1.5-km outdoor route and an indoor mixed-terrain course zero-shot.
Takeaways & Limitations
Per-cell reconstruction and trajectory-aware distillation together support stable long-horizon perceptive humanoid locomotion across simulated stress tests and real-world routes.
Takeaways & Limitations
The front-facing depth camera leaves a rear blind spot during backward locomotion, while 2.5D mapping assumes one ground surface per cell and depth can be corrupted by transparent or reflective surfaces.
Abstract
from arXiv · showhide
Humans traverse complex terrain over long distances without losing balance, whereas perceptive humanoid policies become fragile as perception and control errors accumulate. We present SOLO, a unified framework addressing two compounding causes of this long-horizon fragility: dense terrain reconstruction smooths action-critical details, and pointwise imitation lacks temporal credit assignment. Its Query Reconstructor (QR) uses Fourier-encoded cell queries to retrieve spatially specific evidence from depth-proprioception tokens, preserving sharp terrain boundaries. Trajectory-Aware MSE (TA-MSE) Distillation adds next-state teacher-student disagreement to the PPO reward, enabling Generalized Advantage Estimation to propagate future disagreement penalties to preceding actions. In simulation, QR reduces height-map L1 error by factors of 3.3-4.0, while TA-MSE surpasses PPO and MSE+PPO in curriculum progression. On stress-test terrains, SOLO achieves 97.5% mean traversal success and 96% stepping-stone success, versus 75.0-75.6% and 0-3% for dense-reconstructor variants. Deployed zero-shot with only a chest-mounted depth camera and proprioception, SOLO completes a continuous 1.5-km outdoor route and an indoor mixed-terrain course. Project page: https://sunpihai-up.github.io/solo/
1 Introduction
SOLO targets long-horizon fragility by preserving action-critical terrain details and assigning credit for future teacher–student disagreement. Its components improve reconstruction, curriculum progression, stress-test success, and zero-shot route deployment.
- Motivation: Long-horizon deployment compounds perception and control errors across repeated terrain transitions and viewpoint changes.Short trials can reset local errors, so isolated-obstacle success does not ensure uninterrupted-route stability.
- Motivation: Dense reconstructors smooth high-frequency foothold boundaries, while pointwise action MSE cannot distinguish actions with different future consequences.These limitations respectively increase foothold errors and leave future teacher matching difficult.
- Method: QR retrieves spatially specific evidence for each height-map cell from depth–proprioception tokens, preserving sharp terrain boundaries.Fourier-encoded cell queries cross-attend to the token memory instead of decoding a shared dense representation.
- Method: TA-MSE adds next-state teacher–student disagreement to the PPO reward, allowing GAE to propagate future penalties to preceding actions.This supplies trajectory-aware credit assignment while retaining current-state teacher–student supervision.
- Results: 3.3–4.0× lower average height-map L1 error is achieved by QR relative to START- and DPL-style reconstructors at the highest curriculum difficulty.TA-MSE also reaches higher curriculum levels than PPO and MSE+PPO after both plateau.
- Results: 97.5% mean stress-test success and 96% stepping-stone success are achieved with QR, versus 75.0–75.6% and 0–3% for dense-reconstructor variants.SOLO also completes a continuous 1.5-km outdoor route and an indoor mixed-terrain course zero-shot using onboard depth and proprioception.
2 Related Work
Related work commonly uses privileged teacher–student learning and explicit terrain reconstruction, while locomotion distillation typically relies on single-step action MSE. SOLO’s TA-MSE extends that practice with next-state disagreement and rollout credit assignment.
- Teacher–student perceptive locomotion: Privileged simulator teachers are commonly distilled into students using onboard sensing for challenging humanoid locomotion.Prior systems cover parkour, stairs, sparse footholds, and other difficult terrains.
- Terrain reconstruction for locomotion: Explicit terrain reconstruction bridges the sensing gap between privileged teachers and onboard-sensing students through dense maps, cross-attention reconstructors, or alternative memory representations.START and DPL exemplify dense recurrent and cross-attention terrain reconstruction approaches.
- Policy distillation and trajectory-aware imitation: Locomotion distillation typically adds action MSE to PPO, but this single-step objective does not model future states induced by the student.TA-MSE retains current-state MSE and inserts next-state teacher–student MSE into the PPO reward.
- Policy distillation and trajectory-aware imitation: GAE propagates later disagreement penalties to earlier actions without requiring another critic, dynamics model, or teacher rollout.This makes the temporal alignment operate across the full sampled rollout horizon.
3 Method
SOLO combines Query Reconstructor terrain estimation with Trajectory-Aware MSE distillation to improve deployable humanoid locomotion under partial observation and long-horizon error accumulation.
- System overview: The student combines QR estimates with proprioception to produce an action distribution, while teacher, critic, and privileged observations are removed for deployment.The deployment pipeline retains onboard sensing, QR, and the student policy.
- Query Reconstructor: QR reconstructs a local height map and base velocity from depth–proprioception histories, using spatially specific cell queries rather than dense decoding.Fourier-encoded cell queries cross-attend to shared sensor memory, while a separate velocity query predicts base velocity.
- Trajectory-Aware MSE Distillation: TA-MSE supplements current-state teacher matching with next-state disagreement evaluated on student-visited states.This targets actions whose induced next states are harder for the student to match.
- Trajectory-Aware MSE Distillation: GAE propagates later disagreement penalties to preceding actions without requiring another critic, dynamics model, or teacher rollout.The disagreement is attached to the preceding transition and incorporated into PPO credit assignment over sampled trajectories.
- Training procedure: Training proceeds from privileged teacher learning, through privileged-input student distillation, to joint QR-conditioned student fine-tuning.Stage III updates QR from the QR-conditioned student’s on-policy buffer while policy updates consume detached QR predictions.
- Deployment: Deployment runs QR and the student at 50 Hz using only chest-mounted depth and proprioception after removing training-only components.This configuration supports onboard hardware trials without the teacher, critic, AMP discriminator, or privileged labels.
4 Experiments
SOLO is evaluated through matched component ablations, simulated stress tests, and zero-shot hardware deployments. QR improves reconstruction and locomotion outcomes, while TA-MSE improves curriculum progression.
- Real-Robot Deployment: A continuous 1.5 km outdoor route was completed without policy resets or physical assistance.
- Real-Robot Deployment: One indoor run traversed ascending and descending stairs, stepping stones, a gap, and a movable obstacle without resets or intervention.
- Real-Robot Deployment: 69/70 isolated-terrain trials succeeded, with the only failure occurring on stepping stones.
- Reconstruction Accuracy: QR reduced average height-map L1 error from 7.59/9.26 cm for START/DPL to 2.29 cm, a 3.3–4.0× reduction.The largest absolute reduction occurred on stepping stones, where local height discontinuities require per-cell fidelity.
- Distillation Curriculum Progress: TA-MSE reached the curriculum ceiling near 5.5, while MSE+PPO plateaued around 5.1 and PPO remained below 5.0 with larger oscillations.The comparison used the same teacher, privileged map input, curriculum, initialization, and training budget.
- Locomotion on Highest-Difficulty Terrain: QR raised mean stress-test success from 75.0–75.6% to 97.5% and stepping-stone success from 0–3% to 96%.QR also had the lowest Foot Stumble and Foothold-Grad penalty magnitudes across the four stair settings.
5 Conclusion
SOLO combines per-cell terrain reconstruction with trajectory-aware distillation for stable long-horizon perceptive humanoid locomotion. QR improves reconstruction and stress-test success, while TA-MSE improves curriculum progression and the system transfers to extended hardware routes.
- SOLO combines per-cell terrain reconstruction and trajectory-aware distillation for stable long-horizon perceptive humanoid locomotion.
- QR reduces highest-difficulty height-map L1 error by 3.3–4.0× relative to START and DPL.
- TA-MSE reaches the curriculum ceiling after PPO and MSE+PPO plateau.
- With TA-MSE fixed, QR raises mean stress-test success from 75.0–75.6% to 97.5% and stepping-stone success from 0–3% to 96%.
- The same depth-proprioception-QR-student stack supports continuous outdoor and indoor deployments, including a 1.5-km route.
6 Limitations
SOLO’s deployment scope is constrained by its command-conditioned interface, front-facing depth sensing, 2.5D terrain representation, and depth failures on transparent or reflective surfaces.
- The front-facing depth camera leaves a rear blind spot during backward locomotion on changing terrain.
- The 2.5D height map represents only one ground surface per cell, while transparent or reflective surfaces can corrupt depth.
- Longer-lived memory, complementary sensing, and volumetric terrain representations are identified as extensions for these challenging settings.
A Evaluation Protocols
The evaluation uses matched fixed-terrain protocols with 100 highest-difficulty rollouts, and success is defined by passing a fixed distance before termination.
- Each reported terrain is evaluated in a separate job at one fixed curriculum difficulty, avoiding cross-terrain interference.
- Highest-difficulty evaluations fix difficulty at 0.99 and use N = 100 rollouts, with observation noise and external pushes disabled.
- A rollout succeeds when root translation exceeds dpass = 5.0 m along positive x; resets and time limits terminate evaluation.
A.2 Terrain-Reconstructor Evaluation
The evaluation measures terrain reconstruction error during closed-loop long-horizon rollouts, using each reconstructor with its corresponding deployable student policy.
- Reconstruction error is measured on states visited by each student under its closed-loop visitation distribution.The teacher, controller, terrain, commands, training budget, and distillation objective remain fixed across methods.
- At each active control step, the evaluation records simulator ground-truth and estimated height maps for each rollout.Per-rollout error is computed across active steps and averaged over N rollouts.
A.3 Matched Offline Reconstructor Comparison
The matched offline comparison isolates reconstructor architecture by using one fixed sampler, common data, and identical optimization, while evaluating aggregate and level-9 reconstruction quality.
- A fixed teacher sampler collects approximately 249k labeled frames over four terrain seeds for the matched offline comparison.The comparison isolates architecture from sampling policy using one fixed sampler, common data, and identical optimization.
- 30.9% lower overall height-map L1 versus START and 31.6% versus DPL is reported for QR.The matched comparison reports aggregate and level-9 L1 in centimeters and Edge F1@1-cell as a higher-is-better metric.
- QR preserves sharper discontinuities, with separated and ground-truth-aligned footholds on stepping stones.The qualitative comparison includes Step Stones, High Plane, Random Grid, and Stairs Up/Down, with separate color scales for each row.
A.4 Seed-Paired Reduced-Compute TA-MSE Ablation
The seed-paired reduced-compute ablation compares MSE+PPO and TA-MSE across matched training seeds, terrain levels, and continuation settings.
- Three seed-matched D-PPO checkpoints continue training for 3,000 iterations with either MSE+PPO or TA-MSE.The protocol uses half-resolution depth and 2×2048 environments, evaluating ten terrain levels with 64 episodes per method–seed–terrain–level cell.
- 79.43% level-9 stepping-stone success with TA-MSE exceeds 72.66% with the comparison objective by 6.77 percentage points.Easy and medium terrain remain near saturation for both objectives.
- The policy architecture includes a shared height-map and proprioceptive pathway plus a student-only LSTM proprioceptive bypass.The expanded architecture also specifies action-head, LSTM-bypass, and QR dimensions for deployment.
- PPO and QR use optimizer settings from the three-stage curriculum, with GAE λ following Schulman et al.
C.2 Training Budget and Onboard Runtime
The appendix specifies the training budget, procedural terrain and randomization setup, hardware configuration, and onboard runtime for SOLO deployments.
- Training Budget: Training uses four H800 GPUs, with the three-stage pipeline budget summarized by environments per GPU, updates, and wall-clock time.
- Onboard Runtime: 1.15 ± 0.23 ms average end-to-end pipeline latency fits within the 20-ms budget of the 50-Hz controller.TensorRT inference alone takes 1.03 ± 0.21 ms on Jetson AGX Thor, and the deployed engine occupies 7.56 MB.
- Training Budget: Procedural training terrain uses a 10×17 curriculum grid of 8.0×8.0 m patches, with difficulty increasing across ten rows.The 17 active variants have equal sampling weight, and Table A9 groups them by terrain family and difficulty range.
- Onboard Runtime: The Omni humanoid policy directly controls 25 joints and receives egocentric depth from a chest-mounted Intel RealSense D455.The hardware configuration includes the runtime input and policy-execution setup used in real-robot deployments.
- Onboard Runtime: One uninterrupted hardware run traverses 15 cm stairs, 20 cm and 30 cm stepping stones, a 45 cm gap, and a movable obstacle.
- Training Budget: Synthetic depth corruptions include value and edge noise, missing pixels, blind regions, and blur approximating chest-mounted D455 artifacts.Physical and sensory randomization parameters are summarized in Table A10.