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Consider the unicycle dynamics in 2D plane:

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$$\begin{array}{l} \dot x = v\cos \varphi \\ \dot y = v\sin \varphi \\ \dot \varphi = \omega \end{array}$$

What is the range of the heading angle $\phi$? Some texts say $\varphi \in [ - \pi ,\pi ) $ and other use this convention $\varphi \in [ 0 ,2\pi ) $. What is the reason for this difference?

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No difference at all although φ∈[−π,π) is much more reasonable and intuitive. It is just a matter of system definition.

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