Evolution of a 3D Gallop in a Quadrupedal Model with Biological Characteristics

Abstract

The gallop is the preferred high-speed gait for dynamic locomotion in most cursorial mammals. Due to the lack of good analytical models and proven control strategies, however, the gallop remains an elusive goal in the field of legged robotics. While there have been several attempts at creating a gallop, none have captured all of the important dynamic characteristics of the gait. In this work, we present a practical approach for producing a stable 3D gallop in a quadrupedal model which includes these characteristics. The dynamic model utilizes biologically-based assumptions including articulated legs with nonzero mass, compliance at the knee joints, and a body with an asymmetric mass distribution. Furthermore, the resulting 3D gallop contains the prominent features found in the biological gait: early leg retraction, phase-locked leg motion creating an asymmetric footfall pattern, a significant gathered flight phase, unconstrained spatial dynamics, and a smooth gait. To obtain these results, we employ a multiobjective genetic algorithm with a carefully designed vector fitness function to search for various control parameters. Furthermore, we partition the search space in roughly orthogonal subspaces to find parameters for each sub-controller. A critical component of the controller is an energy control law that ensures a fixed amount of energy in the knee springs during each stride. A characterization of the resulting gait is presented, which highlights biological properties and the visual realism of the solution.