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arXiv · 2309.08871

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

Yanhao Yang·Capprin Bass·Ross L. Hatton
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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.

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Yanhao Yang, Capprin Bass, Ross L. Hatton. 2023-09-16. Towards Geometric Motion Planning for High-Dimensional Systems: Gait-Based Coordinate Optimization and Local Metrics. https://arxiv.org/abs/2309.08871

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