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MAGMA: Multiplier-Augmented Geometric Motion Algorithm

2026-10-15 13:30:13
C\'esar E. Ramos Chuquiure, Vansh Thakur, Challen Enninful Adu, Ram Vasudevan
arXiv_RO
 
Abstract

Solving optimal control problems for high-dimensional mechanical systems subject to constraints remains challenging due to nonlinear dynamics and non-convex feasible sets. This paper introduces MAGMA(Multiplier-Augmented Geometric Motion Algorithm), an Affine Geometric Heat Flow (AGHF)-based trajectory optimizer that incorporates an augmented Lagrangian framework solved via a primal-dual flow. A theoretical characterization of the primal-dual AGHF is provided, establishing that MAGMA is a gradient flow on an appropriately defined energy. MAGMA is validated across a variety of challenging trajectory generation problems with obstacles, state limits, and actuation limits. Comparative evaluations against state-of-the-art solvers demonstrate that MAGMA achieves high quality solutions with significantly reduced tuning effort on the hardest problems.

Abstract (translated)

URL

https://arxiv.org/abs/2610.21852

PDF

https://arxiv.org/pdf/2610.21852.pdf

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