Three-dimensional bipedal model with zero-energy-cost walking

TL;DR

This paper introduces a simple 3D bipedal robot model capable of zero-energy-cost walking by eliminating foot-ground collisions through coordinated oscillations, with analytical and numerical analysis of its collisionless gaits.

Contribution

The paper presents a novel 3D biped model that achieves collisionless, energy-efficient walking without relying on complex mechanisms or springs, and provides analytical solutions for its gait modes.

Findings

Collisionless gaits exist with finite speed and foot clearance.

Analytical solutions are derived for minimal oscillation modes.

Model parameters can tune collisionless walking modes.

Abstract

We study a three-dimensional articulated rigid-body biped model that possesses zero cost of transport walking gaits. Energy losses are avoided due to the complete elimination of the foot-ground collisions by the concerted oscillatory motion of the model's parts. The model consists of two parts connected via a universal joint. It does not rely on any geometry altering mechanisms, massless parts or springs. Despite the model's simplicity, its collisionless gaits feature walking with finite speed, foot clearance and ground friction. The collisionless spectrum can be studied analytically in the small movement limit, revealing infinitely many periodic modes. The modes differ in the number of sagittal and coronal plane oscillations at different stages of the walking cycle. We focus on the mode with the minimal number of such oscillations, presenting its complete analytical solution. We then numerically evolve it toward a general non-small movement solution. A general collisionless mode can be tuned by adjusting a single model parameter. Some of the presented results display a surprising degree of generality and universality.