Integrable systems in planar robotics
Tudor S. Ratiu, Nguyen Tien Zung
TL;DR
This paper explores the mathematical structure of planar robotic linkages by studying integrable systems, commuting flows, and topological invariants, introducing new concepts like multi-Nambu systems and volume forms on configuration spaces.
Contribution
It introduces a natural volume form, cross product of integrable systems, and multi-Nambu systems on planar linkage configuration spaces, advancing the mathematical understanding of robotic linkages.
Findings
Defined a natural volume form on configuration spaces
Introduced cross products of integrable systems
Identified Bott-Morse type first integrals
Abstract
The main purpose of this paper is to investigate commuting flows and integrable systems on the configuration spaces of planar linkages. Our study leads to the definition of a natural volume form on each configuration space of planar linkages, the notion of cross products of integrable systems, and also the notion of multi-Nambu integrable systems. The first integrals of our systems are functions of Bott-Morse type, which may be used to study the topology of configuration spaces. Dedicated to Anatoly T. Fomenko on the occasion of his 75th birthday
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Taxonomy
TopicsControl and Dynamics of Mobile Robots · Geometric and Algebraic Topology · Robotic Path Planning Algorithms