Coordination of legs and body undulation during turning in quadruped locomotion

Sprawled-postured quadrupeds like lizards and salamanders must coordinate limb with body movements to adjust their direction of motion while walking in environments with obstacles. However, their robotics counterpart, the quadrupedal robots, often rely on adjusting their direction of motion by introducing a lateral asymmetry in leg motion amplitude, making the stable transition between forward and turning gaits difficult. We hypothesize that using properly-coordinated body undulation and limb movements will enable effective locomotion and stable transitions between gaits. Using geometric mechanics, we design gaits by prescribing a footfall pattern and optimizing the body undulation which produces a desired motion. We predict that rotations resulting from coordination of body undulation and limb movements can simplify gait transitions in legged robots, and we verify our predictions by measuring displacements and rotations of a robophysical quadruped locomoting through granular media. We find that the amplitude of body undulation controls the steering angle, and thus controls the turning radius. In particular, we find that by increasing the body undulation amplitude from π/12 to π/8, the turning radius decreased from 10.5±0.3 body lengths (BL) to 2.9±0.1 BL.