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oai:recercat.cat:2117/4464962026-01-21T08:09:13Zcom_2072_1033col_2072_452950

Formulating the unicycle on the sphere path planning problem as a linear time-varying system Thomas, Federico Franch Bullich, Jaume Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. CRG - Grup de Robòtica Computacional Àrees temàtiques de la UPC::Informàtica::Automàtica i control Àrees temàtiques de la UPC::Física::Física de l'estat sòlid Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa Automatic control Dynamics, Rigid System theory Robots Path planning Kinematics Finite element analysis Time-varying systems Standards Automobiles Angular velocity Robot kinematics Quaternions Nonholonomic robots Nonholonomic joints Linear time-varying systems Path planning Control automàtic Dinàmica de cossos rígids Sistemes de control Classificació AMS::70 Mechanics of particles and systems::70E Dynamics of a rigid body and of multibody systems Classificació AMS::70 Mechanics of particles and systems::70Q05 Control of mechanical systems Classificació AMS::93 Systems Theory; Control::93C Control systems, guided systems © 2025 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The kinematics, dynamics, and control of a unicycle moving without slipping on a plane has been extensively studied in the literature of nonholonomic mechanical systems. However, since planar motion can be seen as a limiting case of the motion on a sphere, we focus our analysis on the more general spherical case. This paper introduces a novel approach to path planning for a unicycle rolling on a sphere while satisfying the non-slipping constraint. Our method is based on a simple yet effective idea: first, we model the system as a linear time-varying dynamic system. Then, leveraging the fact that certain such systems can be integrated under specific algebraic conditions, we derive a closed-form expression for the control variables. This formulation includes three free parameters, which can be tuned to generate a path connecting any two configurations of the unicycle. Notably, our approach requires no prior knowledge of nonholonomic system analysis, making it accessible to a broader audience. Peer Reviewed Postprint (author's final draft) 2025-01-01 Article Thomas, F.; Franch, J. Formulating the unicycle on the sphere path planning problem as a linear time-varying system. «IEEE transactions on robotics», 1 Gener 2025, vol. 42, p. 3335-3347. 1552-3098 https://hdl.handle.net/2117/446496 10.1109/TRO.2025.3567525 eng https://ieeexplore.ieee.org/document/10989528 info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-117509GB-I00/ES/SINTESIS DE MOVIMIENTOS ROBOTICOS OPTIMAMENTE AGILES Y GRACILES/ Open Access 13 p. application/pdf Institute of Electrical and Electronics Engineers (IEEE)