Publication
A tale of two motion problems
Conference Article
Conference
International Workshop on Computational Kinematics (CK)
Edition
2025
Doc link
File
Abstract
This paper establishes a formal equivalence between the disk-on-sphere motion problem and the terrestrial brachistochrone problem by demonstrating that both are governed by the same differential equation. From a geometric perspective, the underlying problem reduces to interpolating a cusp-free arc of a hypocycloid between two points on a circle. This insight not only reveals a deep connection between seemingly unrelated problems but also offers a unifying framework for their analysis.
Categories
automation, control theory, optimisation.
Author keywords
Nonholonomic motion planning, disk-on-sphere motion problem, terrestrial brachistochrone problem, linear time-varying systems.
Scientific reference
F. Thomas and J. Franch. A tale of two motion problems, 2025 International Workshop on Computational Kinematics, 2025, Chennai, India, Springer, to appear.
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