Gallant: Voxel Grid-based Humanoid Locomotion and Local-navigation across 3D Constrained Terrains (2511.14625v1)

Abstract: Robust humanoid locomotion requires accurate and globally consistent perception of the surrounding 3D environment. However, existing perception modules, mainly based on depth images or elevation maps, offer only partial and locally flattened views of the environment, failing to capture the full 3D structure. This paper presents Gallant, a voxel-grid-based framework for humanoid locomotion and local navigation in 3D constrained terrains. It leverages voxelized LiDAR data as a lightweight and structured perceptual representation, and employs a z-grouped 2D CNN to map this representation to the control policy, enabling fully end-to-end optimization. A high-fidelity LiDAR simulation that dynamically generates realistic observations is developed to support scalable, LiDAR-based training and ensure sim-to-real consistency. Experimental results show that Gallant's broader perceptual coverage facilitates the use of a single policy that goes beyond the limitations of previous methods confined to ground-level obstacles, extending to lateral clutter, overhead constraints, multi-level structures, and narrow passages. Gallant also firstly achieves near 100% success rates in challenging scenarios such as stair climbing and stepping onto elevated platforms through improved end-to-end optimization.

• The paper presents a voxel-grid perception approach that leverages dual LiDAR data and a z-grouped 2D CNN to capture complete 3D structural information.
• It employs curriculum terrain generation and PPO-based policy training to achieve robust humanoid navigation in complex constrained environments.
• Empirical results demonstrate near-100% success rates on challenging tasks, validating simulation-to-real transfer through effective domain randomization.

Gallant: Voxel Grid-Based Humanoid Locomotion and Navigation Across 3D Constrained Terrains

Introduction

The paper "Gallant: Voxel Grid-based Humanoid Locomotion and Local-navigation across 3D Constrained Terrains" (2511.14625) introduces a comprehensive framework for robust humanoid locomotion and local navigation in environments characterized by complex 3D constraints. The approach leverages voxelized LiDAR data as a perceptual backbone, processed via a z-grouped 2D CNN and coupled with curriculum-based training over diverse terrain ensembles. Key differentiators from previous methods include the full preservation of 3D structural information, scalability in both simulation and real-world deployment, and an ability to generalize a single policy across obstacle classes that include ground, lateral, and overhead constraints.

Figure 1: Overview of the Gallant system pipeline, highlighting curriculum learning across terrains, realistic LiDAR simulation with domain randomization, the 2D CNN perception module leveraging voxel grids, and zero-shot sim-to-real transfer across multiple 3D obstacles.

Methodology

Voxel-Grid Perception and LiDAR Simulation

The perceptual foundation of Gallant consists of a robot-centric voxel grid representation derived from dual LiDAR point clouds (front and rear torso mounts). The perception volume $$\Omega = [-0.8, 0.8]\,\mathrm{m} \times [-0.8, 0.8]\,\mathrm{m} \times [-1.0, 1.0]\,\mathrm{m}$$ is discretized at $0.05\,\mathrm{m}$, resulting in a $32 \times 32 \times 40$ tensor encoding occupancy. Unlike 2.5D elevation maps and depth images, this representation is capable of encoding full multi-layer scene geometry, which is critical for reasoning about overhangs, ceilings, and other vertical constraints.

Efficient LiDAR simulation is realized via a GPU-based raycast-voxelization pipeline (NVIDIA Warp), with explicit modeling of both static and dynamic objects—including the robot's own links. The simulation involves domain randomization along four axes: LiDAR pose, scan direction, hit position noise, latency (at 10 Hz with 100–200 ms delay), and point dropout, directly targeting the sim-to-real gap.

Perception Module: Z-Grouped 2D CNN

Due to the strong spatial sparsity and local concentration in the voxel grid, Gallant employs a z-grouped 2D CNN, treating $z$ as the channel dimension over which 2D spatial convolutions operate. This strategy achieves an optimal trade-off between representation capacity and computational efficiency, outperforming standard 3D CNNs and sparse 3D/2D alternatives in both accuracy and inference speed.

Curriculum Terrain Generation

Eight terrain families are constructed for curriculum-based policy training: Plane, Ceiling, Forest, Door, Platform, Pile, Upstair, and Downstair, parameterized by a scalar difficulty coefficient, progressively increasing the complexity of 3D constraints. Terrain generation parameters are interpolated between easier and hardest instantiations, with dynamic task assignment and promotion/demotion protocols based on trial success.

Figure 2: Terrain types adopted during curriculum training, covering ground-level, lateral, and overhead challenges.

PPO Policy Structure

Actions are optimized with PPO, receiving concatenated inputs from the CNN-based voxel feature encoding and proprioceptive channels, augmented with a height map (privileged for the critic only) for improved credit assignment. The reward combines target-reaching with geometry-aware shaping components (directional velocity, head height, foot clearance), imparting structure-aware behavioral bias.

Experimental Results

Simulation Evaluation

Empirical results demonstrate Gallant's dominance over ablations across all terrain types, with near-100% success rates in ceiling, stair, and platform scenarios—tasks that previously exhibited high failure rates. Ablations reveal critical dependencies:

• Dynamic Object Simulation: Omitting dynamic geometry in LiDAR scans (w/o-Self-Scan) induced severe out-of-distribution failures, particularly under ceiling and platform constraints where the robot's links occlude sensor returns.
• Network Architecture: Sparse 2D/3D and full 3D CNNs provided inferior accuracy-to-compute ratios compared to the z-grouped 2D CNN. The latter achieved significant reduction in training time per iteration with equal or improved task performance.
• Perceptual Representation: Using only a height map failed on overhead/lateral constraints; combining voxel grid (actor) and height map (critic) established a synergy, yielding robust training signals and real-world transfer resilience.
• Voxel Grid Resolution: A $5\,\mathrm{cm}$ discretization balanced FoV and geometric fidelity, outperforming coarser ($10\,\mathrm{cm}$) and finer ($2.5\,\mathrm{cm}$) resolutions.

  Figure 3: Visualization of ablation analyses—dynamic object simulation is critical for accurate voxel representation and overall task success.

Real-World Deployment

Zero-shot transfer of Gallant's policy to a Unitree G1 humanoid in unconstrained real-world settings consistently achieved high success rates across all terrain types, outperforming both elevation map-based controllers and Gallant variants without LiDAR domain randomization. The pipeline handled overhead, lateral, platform, pile, and stair constraints without terrain-specific adaptation or fine-tuning. Sensory latency and motion-induced point cloud jitter remained the principal bottlenecks; platform and pile constraints showed reduced success when latency exceeded 100 ms.

Figure 4: Humanoid robot traversing complex real-world and simulated terrains with a single Gallant policy, demonstrating robustness across diverse constraint classes.

Figure 5: Quantitative comparison of real-world traversal times for Height Map, NoDR (no domain randomization), and full Gallant pipeline across 15 trials per terrain.

Figure 6: Correlation of Gallant simulation and real-world success rates across tasks, validating simulated evaluation fidelity.

Implications and Future Directions

Gallant establishes voxel grids as a superior perceptual representation for embodied control in 3D-constrained environments, overcoming limitations of flattened or partial views intrinsic to depth/elevation approaches. The z-grouped 2D CNN configuration is computationally efficient and inductively well-suited for robot-centric egocentric perception. The full-stack integration—from sensor simulation, perception, control, to curriculum training—enables robust sim-to-real generalization of a single locomotion/navigation policy.

Practical deployments now have access to full-space obstacle negotiation, including overhangs and lateral clutter, on a real humanoid platform without domain-specific customization. The approach is extensible to higher-level navigation frameworks, reactive collision avoidance, and multi-modal sensor integration (e.g., fusion with vision). The persistent bottleneck remains sensor-induced latency, where policy preemption and higher refresh-rate sensors could eliminate remaining performance ceilings.

Figure 7: Failure modes induced by insufficient domain randomization, illustrating the consequences of neglecting sensor latency and noise during training.

Conclusion

Gallant delivers a technically rigorous and practically effective pipeline for humanoid navigation and locomotion in highly constrained 3D terrains. Its core innovations—voxel grid perception, high-fidelity LiDAR simulation with domain randomization, and z-grouped 2D CNN processing—translate directly to strong numerical results and policy generalization. Limitations due to sensor latency persist, but foundational advances in perceptual representation and symbiotic simulation-training paradigms provide a robust template for further research in embodied AI and robot autonomy.