论文标题
避免碰撞和$ n $尸体的可控性。
The collision avoidance and the controllability for $n$ bodies in dimension one
论文作者
论文摘要
我们提出了一种用于$ n $物体的控制系统的方法，用于实际行$ \ bbb r^1 $，在单位圆圈$ s^1 $上，无碰撞且可控。该问题减少了在$ \ bbb r^n $和$ n $ -torus $ t^n（分别避免避免某些障碍物）中设计控制膜系统。我们通过证明定义控制疗法系统的矢量字段以及其一阶的括号，跨越状态空间的整个切线空间，然后应用Rashevsky-Chow定理来证明系统的可控性。
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.
