  We study the problem of target stabilization with robust obstacle avoidance
in robots and vehicles that have access only to vision-based sensors for the
purpose of realtime localization. This problem is particularly challenging due
to the topological obstructions induced by the obstacle, which preclude the
existence of smooth feedback controllers able to achieve simultaneous
stabilization and robust obstacle avoidance. To overcome this issue, we develop
a vision-based hybrid controller that switches between two different feedback
laws depending on the current position of the vehicle using a hysteresis
mechanism and a data-assisted supervisor. The main innovation of the paper is
the incorporation of suitable perception maps into the hybrid controller. These
maps can be learned from data obtained from cameras in the vehicles and trained
via convolutional neural networks (CNN). Under suitable assumptions on this
perception map, we establish theoretical guarantees for the trajectories of the
vehicle in terms of convergence and obstacle avoidance. Moreover, the proposed
vision-based hybrid controller is numerically tested under different scenarios,
including noisy data, sensors with failures, and cameras with occlusions.
