Design and analysis of a potential-based controller for safe robot navigation in unknown GPS-denied environments with strictly convex obstacles

In this paper, we propose an obstacle avoidance controller for a disk-shaped holonomic robot with double-integrator dynamics and local sensing. The control objective is for the robot to converge to a target velocity while avoiding collisions with strictly convex obstacles in an unbounded environment. We assume that the robot has no information about the location and geometry of the obstacles, has no localization capabilities, and can only measure its own velocity and its relative position vector to the closest point on any obstacles in its sensing range. We first propose a potential-based controller for the case with a single obstacle, and we prove that the robot safely navigates past the obstacle and attains the desired velocity. For the case with multiple obstacles, we propose a switching control scheme in which the robot applies the single-obstacle controller for the closest obstacle at each instant. We investigate the correctness of this switching control law and demonstrate the absence of local stable equilibrium points that would trap the robot. We validate our analytical results through simulations of a robot that uses the proposed controllers to successfully navigate through an environment with strictly convex obstacles of various shapes and sizes.