MAGMA: Multiplier-Augmented Geometric Motion Algorithm

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.

Robotics (cs.RO)

arXiv:2610.21852 [cs.RO]

(or arXiv:2610.21852v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2610.21852 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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