Principles for Bipedal Robot Cleat–Foot Interaction on Granular Slopes

Locomotion on soft, flowable slopes remains challenging due to limited understanding of terradynamics. Downward flow and avalanching of flowable surfaces under slight disturbances introduce uncertainty that is difficult to model analytically and computationally. These challenges are amplified for bipedal robots due to their inherent gravitational instability. In prior work, we showed that two cleat inserts emanating from the foot sole (15 cm long) of a 2D-planarized small-scale (40 cm tall) bipedal robot enable quasi-static walking on granular slopes up to 20° [Karsai et. al. 2022]. Here, we systematically investigated locomotor performance by varying cleat depth, cleat spacing (through changes in the number of inserts), intrusion speed, and slope angle. Our experiments revealed that dense cleats cause excessive terrain deformation, while sparse patterns fail to stabilize flow, both reducing performance. An optimal spacing of 4 cm enables robust walking on slopes of 30°. We adapted these principles to an unconstrained 3D bipedal robot (~1 m tall) with 20 cm-long feet and 4 cm cleat spacing, achieving stable dynamic locomotion on granular slopes up to 15°. Feet without cleats resulted in rapid failure, while sparse and densely spaced cleats led to underperformance than optimal cleats. This work provides insight into scaling robophysical principles to a full-scale robot and informs design strategies for reliable legged locomotion in flowable terrain.