Closed-Form Trajectories of the Unicycle

Details Closed-Form Trajectories of the Unicycle Closed-Form Trajectories of the Unicycle

2009-06-08

arxiv.org/abs/0906.1588v1

Mathematics

Optimization and Control

This is part of a paper accepted for publication in a local conference (JAR08) in Argentina

Scientific paper

This paper presents a methodology to stabilize some kind of Nonlinear Control system known as Driftless, utilizing the concept of \textit{Pseudo-Kinetic Energy} introduced in this work. Once this controller is applied to the Unicycle-type robot, stability is guaranteed with the salient property that the structure of the controller allows to solve in closed-form the trajectories of the vehicle. While the proposed controller only ensures stability (not asymptotic stability) the obtained closed-form solutions will show a path to obtain in closed form the solutions for the general control problem of the unicycle. Some conclusions and future directions for research are also depicted.

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