Towards Geometric Motion Planning for High-Dimensional Systems: Gait-Based Coordinate Optimization and Local Metrics

TL;DR

This paper introduces a gait-based coordinate optimization method and a unified local metric representation to enable geometric motion planning in high-dimensional systems, demonstrated on systems with up to 11 shape variables.

Contribution

It presents a novel approach combining gait-based optimization and local metrics to overcome the curse of dimensionality in geometric motion planning for high-dimensional systems.

Findings

Optimal gait shows improved efficiency over reduced-order models.

Method successfully applied to systems with up to 11 shape variables.

Provides a geometric interpretation of gait optimality.

Abstract

Geometric motion planning offers effective and interpretable gait analysis and optimization tools for locomoting systems. However, due to the curse of dimensionality in coordinate optimization, a key component of geometric motion planning, it is almost infeasible to apply current geometric motion planning to high-dimensional systems. In this paper, we propose a gait-based coordinate optimization method that overcomes the curse of dimensionality. We also identify a unified geometric representation of locomotion by generalizing various nonholonomic constraints into local metrics. By combining these two approaches, we take a step towards geometric motion planning for high-dimensional systems. We test our method in two classes of high-dimensional systems - low Reynolds number swimmers and free-falling Cassie - with up to 11-dimensional shape variables. The resulting optimal gait in the high-dimensional system shows better efficiency compared to that of the reduced-order model. Furthermore, we provide a geometric optimality interpretation of the optimal gait.