On the dynamics of a quadruped robot model with impedance control: Self-stabilizing high speed trot-running and period-doubling bifurcations

TitleOn the dynamics of a quadruped robot model with impedance control: Self-stabilizing high speed trot-running and period-doubling bifurcations
Publication TypeConference Paper
Year of Publication2014
AuthorsLee, J., D. Jin Hyun, J. Ahn, S. Kim, and N.. Hogan
Conference NameIntelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on
Date PublishedSept
KeywordsAcceleration, Bifurcation, chaos, chaotic dynamics, command speed upper limit, Convergence, gait analysis, gradual acceleration, impedance control, legged locomotion, Limit-cycles, Mathematical model, numerical analysis, period-doubling bifurcations, periodic trot gaits, Poincare map analysis, Poincare mapping, quadruped robot model dynamics, robot dynamics, Robot kinematics, Robots, self-stabilizing high speed trot-running, stability, Stability analysis, trajectory control, trajectory orbital stability, trot gait stability, velocity control
Abstract

The MIT Cheetah demonstrated a stable 6 m/s trot gait in the sagittal plane utilizing the self-stable characteristics of locomotion. This paper presents a numerical analysis of the behavior of a quadruped robot model with the proposed controller. We first demonstrate the existence of periodic trot gaits at various speeds and examine local orbital stability of each trajectory using Poincar`e map analysis. Beyond the local stability, we additionally demonstrate the stability of the model against large initial perturbations. Stability of trot gaits at a wide range of speed enables gradual acceleration demonstrated in this paper and a real machine. This simulation study also suggests the upper limit of the command speed that ensures stable steady-state running. As we increase the command speed, we observe series of period-doubling bifurcations, which suggests presence of chaotic dynamics beyond a certain level of command speed. Extension of this simulation analysis will provide useful guidelines for searching control parameters to further improve the system performance.

DOI10.1109/IROS.2014.6943260