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Stability Analysis of a Clock-Driven Rigid-Body SLIP Model for RHex

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA

Daniel E. Koditschek

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA

Philip Holmes

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA

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 feed forward 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.

Key Words: legged locomotion • return map • spring loaded inverted pendulum • stability

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