Stability analysis of a clock-driven rigid-body SLIP model for RHex

We apply the stability analysis for hybrid legged locomotion systems, introduced in our companion paper in this issue, to a new simple clock-driven SLIP model inspired by the robot RHex. We adopt in stance phase the three-degrees-of-freedom (3DoF) spring loaded inverted pendulum (SLIP) model introduced in our companion paper to capture RHex's pitching dynamics in the sagittal plane. The coordinating influence of RHex's open-loop clock controller is subsumed into a leg placement strategy derived from a bipedal abstraction of RHex. The "symmetric" factorization analysis introduced in our companion paper yields a necessary condition for gait stability expressed in closed form, which can be imposed directly on the clock parameter space. This represents the first reported analytical insight into how a dynamical runner might be stabilized by a completely feedforward rhythmic limb coordination pattern. Correspondence in steady-state gait location and stability characteristics with an appropriately tuned 24DoF model of RHex provides numerical evidence that the 3DoF SLIP model offers a descriptive explanation for the robot's empirical running behavior.