This paper addresses the problem of navigation using only relative direction measurements (i.e., relative distances are unknown) under field of view constraints. We present a novel navigation vector field for the bearing-based visual homing problem with respect to static visual landmarks in 2-D and 3-D environments. Our method employs two control fields that are tangent and normal to ellipsoids having landmarks as their foci. The tangent field steers the robot to a set of points where the average of observed bearings is parallel to the average of the desired bearings, and the normal field uses the angle between a pair of bearings as a proxy to adjust the robot's distance from landmarks and to satisfy the field of view constraints. Both fields are blended together to construct an almost globally stable control law. Our method is easy to implement, as it requires only comparisons between average bearings, and between angles of pairs of vectors. We provide simulations that demonstrate the performance of our approach for a double integrator system and unicycles.

中文翻译：

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具有视野约束的仅轴承导航

本文解决了在视场约束下仅使用相对方向测量（即相对距离未知）的导航问题。我们针对 2-D 和 3-D 环境中静态视觉地标的基于方位的视觉归位问题提出了一种新的导航矢量场。我们的方法采用两个控制场，它们与以地标为焦点的椭球相切和垂直。切线场将机器人引导到一组点，其中观察到的轴承的平均值与所需轴承的平均值平行，而法线场使用一对轴承之间的角度作为代理来调整机器人与地标的距离和以满足视野限制。这两个领域融合在一起，构建了一个几乎全局稳定的控制律。我们的方法很容易实现，因为它只需要比较平均方位角和成对向量的角度。我们提供模拟来证明我们的方法对双积分器系统和独轮车的性能。