Learning Locomotion on Complex Terrain for Quadrupedal Robots with Foot Position Maps and Stability Rewards

Learning-based quadrupedal locomotion typically relies on complex reward formulations that entangle task specification, operational limits, gait preference, and terrain adaptation within a single optimization objective. We instead treat these functions through distinct mechanisms: rewards for task specification, constraints for operational limits, energy minimization for gait preference, and exteroceptive perception for adapting energy use to terrain difficulty. We show that these components jointly enable efficient, terrain-adaptive locomotion, and that removing each component exposes a distinct failure mode. Our formulation removes explicit gait priors (including air-time, contact-count, and foot-clearance targets) in favor of emergent behavior. Compared to a conventional complex-reward baseline, our formulation achieves comparable terrain traversal while reducing cost of transport by 56% and operational-limit violations by 96%. The resulting policies transfer zero-shot to a physical Unitree Go2 using LiDAR-based elevation mapping. Project website with videos: https://tinyurl.com/locomposition.

Quadruped robots deployed for inspection and field missions must cross heterogeneous terrain, from stairs, slopes, and gaps to high platforms, stepping stones, and balance beams, where safe support is sparse or see-through. Existing methods interpose a terrain map or a depth image between sensing and control. Maps are costly to maintain, corrupted by odometry drift and outliers, and misled by see-through gratings, while depth cameras degrade with lighting and surface material. In this paper, we present PointWalker, a mapless framework whose single reinforcement learning policy directly consumes raw point clouds from four light detection and ranging (LiDAR) sensors. Voxelized points are encoded by linear self-attention and fused with proprioception through cross-attention, so terrain geometry reaches the policy without maps or foothold estimation. One proximal policy optimization (PPO) run, with terrain-aware rewards and dual-channel simulation of see-through gratings, yields one policy for all seven terrain classes with a 90.1% mean success rate in simulation. Deployed zero-shot on a Deep Robotics X30 at 50 Hz onboard, it crosses 0.8-m gaps, climbs 0.8-m platforms and 45° steel-grating stairs, carries a 50-kg payload, and completes a 2.5-km mountain route.

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.