Controlling chaos in a sagittal plane biped model using the Ott-Grebogi-Yorke method.

Abstract

Controlling a system with chaotic nature provides the ability to control and maintain orbits of different periods which extends the functionality of the system to be flexible. A system with diverse dynamical behaviours can be achieved. Trajectory flows of chaotic systems can be periodically stabilised using only small perturbations from the controlled parameter. The method of chaos control is the Ott-Grebogi-Yorke method. In non-chaotic systems large system parameters changes are required for performance changes. A sagittal plane biped model which is capable of exhibiting periodic and chaotic locomotion was researched and investigated. The locomotion was either periodic or chaotic depending on the design parameters. Nonlinear dynamic tools such as the Bifurcation Diagram, Lyapunov Exponent and Poincaré Map were used to differentiate parameters which generated periodic motion apart from chaotic ones. Numerical analytical tools such as the Closed Return and Linearization of the Poincaré Map were used to detect unstable periodic orbit in chaotic attractors. Chaos control of the model was achieved in simulations. The system dynamic is of the non-smooth continuous type. Differing from other investigated chaotic systems, the biped model has varying phase space dimensions which can range from 3 to 6 dimensions depending on the phase of walking. The design of the biped was such that its features were anthropomorphic with respect to locomotion. The model, consisting of only the lower body (hip to feet), was capable of walking passively or actively and was manufactured with optimal anthropometric parameters based on ground clearance (to avoid foot scuffing) and basin of attraction simulations. During experimentation, the biped successfully walked down an inclined ramp with minimal aid. Real time data acquisitions were performed to capture the results, and the experimental data of the walking trajectories were analysed and verified against simulations. It was verified that the constructed biped exhibits the same walking trend as the derived theoretical model.