Capturability-based Analysis of Legged Robot with Consideration of Swing Legs

TL;DR

This paper extends capturability analysis of legged robots by incorporating swing leg dynamics through a novel time-margin concept and swing leg kernels, revealing how actuation and step length influence capturability.

Contribution

It introduces a swing leg kernel to integrate swing leg dynamics into capturability analysis and analyzes how actuation and step length affect capturability.

Findings

Longer normalized step length improves capturability.

More powerful actuation increases capturability.

Optimal step sequences minimize actuation for given disturbances.

Abstract

Capturability of a robot determines whether it is able to capture a robot within a number of steps. Current capturability analysis is based on stance leg dynamics, without taking adequate consideration on swing leg. In this paper, we combine capturability-based analysis with swing leg dynamics. We first associate original definition of capturability with a time-margin, which encodes a time sequence that can capture the robot. This time-margin capturability requires consideration of swing leg, and we therefore introduce a swing leg kernel that acts as a bridge between step time and step length. We analyze N-step capturability with a combined model of swing leg kernels and a linear inverted pendulum model. By analyzing swing leg kernels with different parameters, we find that more powerful actuation and longer normalized step length result in greater capturability. We also answer the question whether more steps would give greater capturability. For a given disturbance, we find a step sequence that minimizes actuation. This step sequence is whether a step time sequence or a step length sequence, and this classification is based on boundary value problem analysis.