Formulating the Unicycle on the Sphere Path Planning Problem as a Linear Time-Varying System
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 s...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:dnet:digitalcsic_::6833e9db24f9825f48e7775227808494 |
| Acceso en línea: | http://hdl.handle.net/10261/427817 https://api.elsevier.com/content/abstract/scopus_id/105004594560 |
| Access Level: | acceso abierto |
| Palabra clave: | Linear time-varying systems Nonholonomic joints Nonholonomic robots Path planning |
| Sumario: | 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 article introduces a novel approach to path planning for a unicycle rolling on a sphere while satisfying the nonslipping 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. |
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