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System Design of a Quadrupedal Galloping Machine

Stanford University, 424 Panama Mall, Bldg 560, Stanford, CA 94305, USA, jgnichol{at}stanford.edu

Surya P.N. Singh

Stanford University, 424 Panama Mall, Bldg 560, Stanford, CA 94305, USA

Kenneth J. Waldron

Stanford University, 424 Panama Mall, Bldg 560, Stanford, CA 94305, USA

Luther R. Palmer, III

Ohio State University, Department of Electrical and Computer Engineering, 2015 Neil Avenue, Columbus, OH 43210, USA

David E. Orin

Ohio State University, Department of Electrical and Computer Engineering, 2015 Neil Avenue, Columbus, OH 43210, USA

In this paper we present the system design of a machine that we have constructed to study a quadrupedal gallop gait. The gallop gait is the preferred high-speed gait of most cursorial quadrupeds. To gallop, an animal must generate ballistic trajectories with characteristic strong impacts, coordinate leg movements with asymmetric footfall phasing, and effectively use compliant members, all the while maintaining dynamic stability. In this paper we seek to further understand the primary biological features necessary for galloping by building and testing a robotic quadruped similar in size to a large goat or antelope. These features include high-speed actuation, energy storage, on-line learning control, and high-performance attitude sensing. Because body dynamics are primarily influenced by the impulses delivered by the legs, the successful design and control of single leg energetics is a major focus of this work. The leg stores energy during flight by adding tension to a spring acting across an articulated knee. During stance, the spring energy is quickly released using a novel capstan design. As a precursor to quadruped control, two intelligent strategies have been developed for verification on a one-legged system. The Levenberg-Marquardt on-line learning method is applied to a simple heuristic controller and provides good control over height and forward velocity. Direct adaptive fuzzy control, which requires no system modeling but is more computationally expensive, exhibits better response. Using these techniques we have been successful in operating one leg at speeds necessary for a dynamic gallop of a machine of this scale. Another necessary component of quadruped locomotion is high-resolution and high-bandwidth attitude sensing. The large ground impact accelerations, which cause problems for any single traditional sensor, are overcome through the use of an inertial sensing approach using updates from optical sensors and vehicle kinematics.

Key Words: gallop • intelligent control • quadruped • fuzzy logic

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