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arXiv · 2209.10824

The collision avoidance and the controllability for $n$ bodies in dimension one

Chong-Kyu Han·Donghoon Park
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Abstract

We present a method of design of control systems for $n$ bodies in the real line $\Bbb R^1$ and on the unit circle $ S^1$, to be collision-free and controllable. The problem reduces to designing a control-affine system in $\Bbb R^n$ and in $n$-torus $T^n, $ respectively, that avoids certain obstacles. We prove the controllability of the system by showing that the vector fields that define the control-affine system, together with their brackets of first order, span the whole tangent space of the state space, and then by applying the Rashevsky-Chow theorem.

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Chong-Kyu Han, Donghoon Park. 2022-09-22. The collision avoidance and the controllability for $n$ bodies in dimension one. https://arxiv.org/abs/2209.10824

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