Hybrid Feedback for Autonomous Navigation in Planar Environments With Convex Obstacles

Abstract

We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments cluttered with obstacles having arbitrary convex shapes. The proposed navigation approach relies on a hybrid feedback to guarantee global asymptotic stabilization of the robot toward a predefined target location while ensuring the forward invariance of the obstacle-free workspace. The main idea consists in designing an appropriate switching strategy between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">move-to-target</i> mode and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">obstacle-avoidance</i> mode based on the proximity of the robot with respect to the nearest obstacle. The proposed hybrid controller generates continuous velocity input trajectories when the robot is initialized away from the boundaries of the unsafe regions. Finally, we provide an algorithmic procedure for the sensor-based implementation of the proposed hybrid controller and validate its effectiveness through some simulation results.