Three-dimensional translational dynamics and stability of multi-legged runners

The spring-loaded inverted pendulum (SLIP) is a simple, passively-elastic two-degree-of-freedom model for legged locomotion that describes the center-of-mass dynamics of many animal species and some legged robots. Conventionally, SLIP models employ a single support leg during stance and, while they can exhibit stable steady gaits when motions are confined to the sagittal plane, three-dimensional gaits are unstable to lateral toppling. In this paper it is shown that multiple stance legs can confer stability. Three SLIP-inspired models are studied: a passive bipedal kangaroo-hopper an actuated insect model, and passive and actuated versions of a hexapedal robot model. The latter models both employ tripod stance phases. The sources of lateral stability are identified and, for the passive systems, analytical estimates of critical parameters are provided. Throughout, rotations are ignored and only center-of-mass translational dynamics are considered.