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Bearing-Only Navigation with Field of View Constraints

This paper addresses the problem of navigation using only relative directional measurements (i.e., relative distances are unknown) with field of view constraints. We present a novel navigation vector field for the bearing-based visual homing problem with respect to static 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 bearing vectors is parallel to the average of the desired bearings. The normal field uses the angle between different pairs of bearings as a proxy to adjust the robot's distance from the 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 straightforward to implement, as it requires only comparisons between average bearings, and angles of pairs of vectors. We provide simulations that demonstrate the robustness of our approach on two systems: a double integrator, and a unicycle.