Publication
Formulating the unicycle on the sphere path planning problem as a linear time-varying system
Journal Article (2025)
Journal
IEEE Transactions on Robotics
Pages
3335-3347
Volume
41
Doc link
https://doi.org/10.1109/TRO.2025.3567525
File
Abstract
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.
Categories
automation, control theory.
Author keywords
Nonholonomic robots, nonholonomic joints, linear time-varying systems, path planning
Scientific reference
F. Thomas and J. Franch. Formulating the unicycle on the sphere path planning problem as a linear time-varying system. IEEE Transactions on Robotics, 41: 3335-3347, 2025.
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