Reduction-based Control of Three-dimensional Bipedal Walking Robots

Author:

Gregg Robert D.1,Spong Mark W.2

Affiliation:

1. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA,

2. Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX 75080, USA,

Abstract

In this paper we develop the concept of reduction-based control, which is founded on a controlled form of geometric reduction known as functional Routhian reduction. We prove a geometric property of general serial-chain robots termed recursive cyclicity, identifying the inherent robot symmetries that we exploit with the Subrobot Theorem. This shows that any serial-chain robot can be decomposed for arbitrarily lower-dimensional analysis and control. We apply this method to construct stable directional three-dimensional walking gaits for a four-degree-of-freedom hipped bipedal robot. The controlled reduction decouples the biped’s sagittal-plane motion from the yaw and lean modes, and on the sagittal subsystem we use passivity-based control to produce known planar limit cycles on flat ground. The unstable yaw and lean modes are separately controlled to 2-periodic orbits through their shaped momenta. We numerically verify the existence of stable 2-periodic straight-walking limit cycles and demonstrate turning capabilities for the controlled biped.

Publisher

SAGE Publications

Subject

Applied Mathematics,Artificial Intelligence,Electrical and Electronic Engineering,Mechanical Engineering,Modeling and Simulation,Software

Reference35 articles.

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