Intelligent motion planning method for spherical multi-retractable legged robots on sloped terrains

Spherical multi-retractable legged robots exhibit excellent omnidirectional mobility and navigation capabilities for complex terrain. Nevertheless, existing algorithms for motion planning are mostly limited to scenarios on flat ground and lack dedicated strategies for slope adaptation, which restricts their engineering deployment in unstructured real world environments. This paper presents a framework for motion planning of spherical multi-retractable legged robots in sloped environments. Based on kinematic and dynamic stability analysis, this work develops a novel gait strategy for traversal along edges of an equilateral triangle, and combines it with optimized constraints from critical angles as well as foot ground contact control to realize autonomous robot locomotion on slopes. Three motion conditions are considered to obtain the maximum traversable slope. Dynamic analysis for slope climbing is also performed to establish an approach for motion planning that adapts to climbing scenarios. Simulations and physical prototype experiments are conducted on 10° and 20° slopes, with further field tests carried out on outdoor grassy slopes. When compared with conventional methods, the proposed framework achieves stable continuous locomotion on a 20° slope. Results verify its improved slope stability and terrain adaptability, and offer a feasible solution for robotic exploration in complex environments.