A solvable walking model for a two-legged robot

TL;DR

This paper introduces a mathematically solvable two-legged walking model based on an inverted pendulum, capable of walking on uneven and inclined surfaces with optimized gait speed.

Contribution

The paper presents a new closed-form, reversible biped walking model that can adapt to uneven terrains and optimize gait speed based on robot parameters.

Findings

Model is solvable in closed form.

Capable of walking on uneven surfaces and inclined planes.

Derived optimization results for gait speed.

Abstract

We present a solvable biped walking model based on an inverted pendulum with two massless articulated legs capable of walking on uneven floors and inclined planes. The stride of the two-legged robot results from the pendular motion of a standing leg and the articulated motion of a trailing leg. Gaiting is possible due to the alternating role of the legs, the standing and the trailing leg, and the conservation of energy of the pendular motion. The motion on uneven surfaces and inclined planes is possible by imposing the same maximal opening angle between the two legs in the transition between strides and the adaptability of the time of each stride. This model is solvable in closed form and is reversible in time, modelling the different types of biped motion. Several optimisation results for the speed of gaiting as a function of the robot parameters have been derived.