Instability and Chaos in Quadruped Gallop

[+] Author and Article Information
P. Nanua, K. J. Waldron

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210

J. Mech. Des 116(4), 1096-1101 (Dec 01, 1994) (6 pages) doi:10.1115/1.2919492 History: Received July 01, 1993; Revised February 01, 1994; Online June 02, 2008


A dynamic model for the two-dimensional quadruped has been developed. The main body is modelled as a rigid bar and each leg consists of a constant stiffness spring, a viscous damper and a force actuator. Based on symmetry principles, a controller has been devised that will enable the quadruped to gallop at constant speed. The controller consists of two parts: an energy controller which will apply the required amount of force through the legs, and the speed controller that will control the forward speed by appropriately placing the legs. It will be shown that the body pitch need not be explicitly controlled. The stability of this controller will be examined using Poincare maps. Stable systems show either periodic or quasi-periodic response. This system also exhibits chaotic behavior and chaotic response results in instability. The stability of the system with changes in the initial conditions, as well as variations in the system parameters, will also be examined. It will be shown that the system is stable for a range of leg stiffnesses. Outside this range, the system shows chaotic behavior.

Copyright © 1994 by The American Society of Mechanical Engineers
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