Vision-Based Local-Level Frame Mapping and Planning in Spherical Coordinates for Miniature Air Vehicles

This paper presents a vision-based collision avoidance technique for small and miniature air vehicles (MAVs) using local-level frame mapping and planning in spherical coordinates. To explicitly address the obstacle initialization problem, the maps are parameterized using the inverse time-to-collision (TTC). Using bearing-only measurements, an extended Kalman filter is employed to estimate the inverse TTC, azimuth, and elevation to obstacles. Nonlinear observability analysis is used to derive conditions for the observability of the system. Based on these conditions, we design a path planning algorithm that simultaneously minimizes the uncertainties in state estimation while avoiding collisions with obstacles. The behavior of the planning algorithm is analyzed, and the characteristics of the environment in which the planning algorithm is guaranteed to generate collision-free paths for MAVs are described. Numerical results show that the proposed method is successful in solving the path planning problem for MAVs.