Efficient and Stable Locomotion for Impulse-Actuated Robots Using Strictly Convex Foot Shapes

Impulsive actuation enables robots to perform agile maneuvers and surpass difficult terrain, yet its capacity to induce continuous and stable locomotion have not been explored. We claim that strictly convex foot shapes can improve the impulse effectiveness (impulse used per travelled distance) and locomotion speed by facilitating periodicity and stability. To test this premise, we introduce a theoretical 2-D model based on rigid-body mechanics to prove stability. We then implement a more elaborate model in simulation to study transient behavior and impulse effectiveness. Finally, we test our findings on a robot platform to prove their physical validity. Our results prove that continuous and stable locomotion can be achieved in the strictly convex case of a disk with an off-centered mass. In keeping with our theory, stable limit cycles of the off-centered disk outperform the theoretical performance of a cube in simulation and experiment, using up to 10 times less impulse per distance to travel at the same locomotion speed.