Guaranteed Obstacle Avoidance of Convex Objects in 2-D Without Object Tracking, Environment Mapping, or Stopping

This letter proves that a simple range-based end-to-end feedback controller avoids convex obstacles when its heading is sufficiently far away from a head-on collision. Sufficient is as small as nearly, but not exactly, 0 degrees for a wall or circular object and at least 45 degrees for any convex obstacle. The guarantees use a new modeling and analysis framework for sensor-object interaction combined with a new barrier function that are the main contributions. The controller avoids state estimation, mapping, object tracking, and learning from data. This guaranteed behavior is useful for navigating safely around arbitrary convex obstacles. We demonstrate the behavior of the controller in a simulated navigation scenario.