Routes to tripod gait movement in hexapods

Abstract

The use of hierarchical networks in motor pattern generation in hexapod robots and in insect movement provides ways to understand and control both systems. In this paper we consider the Central Pattern Generator (CPG) of insect movement consisting of six coupled neurons developed by Ghigliazza and Holmes (2004) that produces the global leg coordination pattern. We provide a detailed study of the possible gaits generated by the CPG through different numerical techniques recently developed for the study of small networks, which allow us to consider the complete model without any simplification. We combine the analysis of isolated neurons (using several three dimensional parameter spaces) to give a roadmap of the dynamics of the neurons involved, lateral phase lag plots to show the convergence and transitions towards particular patterns and a quasi-Monte Carlo sweeping method to describe different pattern routes in the parametric phase space. In all of our studies we have found the same final result: most of the observed patterns follow routes that lead to the stable tripod gait. We obtain several routes made of symmetrical patterns, but despite considering mainly a symmetric leg CPG we detect non-symmetrical patterns that provide (minor) routes present in the model. The bifurcations of the main pattern routes detected in the parameter space are studied in detail using continuation techniques. This study reveals the bifurcations that create and destroy the different routes and how for large values of some parameters only the tripod gait is present. Based on the symmetric case, a preliminary study of asymmetric configurations is done revealing the robustness of the already located patterns and routes. Due to the relevance of the tripod gait, and since more parameters are included in this study, we introduce an algorithm to locate the limit of the tripod gait in the parameter space, which shows that there is a large three parametric region where the tripod pattern is ubiquitous and highly dominant in rapidly moving insect regimes.