Stability Analysis of the Walking Robots Motion

The theme of walking robots stability is analyzed in the paper as a particular case of stability for dynamic systems that depend on parameters, deduced, in the mathematical model, by specifying the parameters, not specified numerically, that define the dynamic system. Another aspect of the walking robots' stability assurance is the necessity of sequentially using parameter time, in evolving a dynamic system that permits the local constant selection of the dynamic system's remaining parameters, assuring its stable evolution. In opposition is the stability of rocket flight, which presupposes asymptotic stability. The optimization of the walking robot's dynamic system evolution is possible by identifying the mathematical conditions of separation between the stable and unstable zone in the range of free parameters, inspired from the mathematical conditions already analysed by us for the general case of the dynamic systems, in some of our previous papers. The theoretical considerations are exemplified on walking robot's mathematical model. The possible chaotic evolution of the dynamic systems, with possible application on walking robots evolution is also analysed. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).