Optimal Gait Families using Lagrange Multiplier Method

TL;DR

This paper develops a geometric framework and a Lagrange multiplier-based locus generator to efficiently identify families of optimal gaits for robotic locomotion across different step sizes and steering scenarios.

Contribution

It introduces a novel optimal locus generator that captures entire gait families, reducing the need for separate optimization of each gait in robotic motion planning.

Findings

The optimal locus generator effectively models gait families across step sizes.

Application to simplified swimmers demonstrates the generator's validity.

The approach facilitates high-resolution motion planning in robotics.

Abstract

The robotic locomotion community is interested in optimal gaits for control. Based on the optimization criterion, however, there could be a number of possible optimal gaits. For example, the optimal gait for maximizing displacement with respect to cost is quite different from the maximum displacement optimal gait. Beyond these two general optimal gaits, we believe that the optimal gait should deal with various situations for high-resolution of motion planning, e.g., steering the robot or moving in "baby steps." As the step size or steering ratio increases or decreases, the optimal gaits will slightly vary by the geometric relationship and they will form the families of gaits. In this paper, we explored the geometrical framework across these optimal gaits having different step sizes in the family via the Lagrange multiplier method. Based on the structure, we suggest an optimal locus generator that solves all related optimal gaits in the family instead of optimizing each gait respectively. By applying the optimal locus generator to two simplified swimmers in drag-dominated environments, we verify the behavior of the optimal locus generator.