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.

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