Impulsive actuation enables robots to perform agile
manoeuvres 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 impulse
effectiveness (impulse used per travelled distance) and locomotion
speed by facilitating periodicity and stability. To test this premise,
we introduce a theoretical two-dimensional model based on rigidbody
mechanics to prove stability. We then implement a more
elaborate model in simulation to study transient behaviour 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 disc with off-centred mass. In keeping with our
theory, stable limit cycles of the off-centred disc 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