Slope-constrained global path planning for quadruped robots

Abstract Legged robots are increasingly deployed on natural terrain, yet most global planners either ignore slope and directional traversability, encode terrain steepness only as a simple cost term that often assumes symmetric traversal, or depend on computationally expensive dense 3D maps that limit real-time use on embedded CPUs. These limitations reduce safety (e.g., unexpected rollovers); neglect the fact that a surface patch may be traversable uphill but unsafe downhill, or vice versa; and constrain operational range when only a local elevation map is available. We present a slope-constrained global path planning method for quadruped robots that factors pitch and roll limits directly into state and motion validity instead of the optimization objective. It samples 2D positions and attaches paired opposite headings to exploit forward/backward locomotion while minimizing in-place rotation on steep ground, and it validates inter-node motions with distance, slope, and heading change thresholds using an adapted LazyPRM* road map. Nodes violating slope thresholds are pruned early, shrinking the search space. We implement the proposed approach in a ROS framework with a CPU-efficient 2.5D elevation map and validate it in both simulation and real-world scenarios. Results show that tightening pitch/roll bounds induces characteristic zigzag or circumferential paths and that omitting roll limits can cause catastrophic failures in simulation. Limitations include no online global replanning as new map data arrive, reliance on a bounded initial elevation map, an assumption of quasi-uniform slope between closely spaced ( $$&lt;10$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> cm) waypoints, and limited testing on extremely challenging natural terrain. These constraints outline clear directions for extending slope-informed global planning in legged autonomy.