Three-Dimensional Leg Kinematics Enhance Burrowing Performance in Granular Substrates

Locomotion within granular media is prevalent across various animal species, yet accomplished by few robots. While several mechanisms for subsurface robotic locomotion have been studied, excavative burrowing with legs remains comparatively underexplored. Existing legged robotic burrowers thus far have utilized planar leg trajectories. Biological observations have revealed that the appendages of the mole crab Emerita talpoida exhibit non-planar kinematics throughout burrowing, moving laterally during their "power stroke" and medially during their "return stroke". Building upon these observations, this work extends legged burrowing into 3D space. We present a robophysical burrowing appendage, which is capable of generating 3D leg trajectories and controlled leg rotation using a single actuator. Using a 3D Granular Resistive Force Theory model, we estimate leg-substrate interaction forces. We then use this model to quantify burrowing performance via anisotropy, defined as the ratio of mechanical work between the power and return strokes, along the thrust direction. For a given leg configuration, anisotropy is strongly influenced by the leg's rotation: we find that anisotropy increases by <2% with mediolateral motion alone, 65% with leg rotation alone, and 80% when both are combined, relative to the planar case. These findings reveal how 3D leg kinematics modulate resistive forces, providing insights for the design of efficient burrowing robots.