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arXiv · 2311.14969

Completeness of Riemannian metrics: an application to the control of constrained mechanical systems

José Ángel Acosta·Anthony Bloch·David Martín de Diego
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Abstract

We introduce a mathematical technique based on modifying a given Riemannian metric and we investigate its applicability to controlling and stabilizing constrained mechanical systems. In essence our result is based on the construction of a complete Riemannian metric in the modified space where the constraint is included. In particular this can be applied to the controlled Lagrangians technique Bloch et al. [2000b, 2001] modifying its metric to additionally cover mechanical systems with configuration constraints via control. The technique used consists of approximating incomplete Riemannian metrics by complete ones, modifying the evolution near a boundary and finding a controller satisfying a given design criterion.

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José Ángel Acosta, Anthony Bloch, David Martín de Diego. 2023-11-25. Completeness of Riemannian metrics: an application to the control of constrained mechanical systems. https://doi.org/10.1109/tac.2025.3595000

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