Hybrid Feedback Control Design for Nonconvex Obstacle Avoidance

Abstract

We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments containing obstacles, with arbitrary non-convex shapes, which can be in close proximity with each other, as long as there exists at least one safe path connecting the initial and the target location. An instrumental transformation that modifies (virtually) the non-convex obstacles, in a non-conservative manner, is introduced to facilitate the design of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">obstacle-avoidance</i> strategy. The proposed navigation approach relies on a hybrid feedback that guarantees global asymptotic stabilization of a target location while ensuring the forward invariance of the modified obstacle-free workspace. The proposed hybrid feedback controller guarantees Zeno-free switching 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 modified obstacle-occupied workspace. Finally, we provide an algorithmic procedure for the sensor-based implementation of the proposed hybrid controller and validate its effectiveness via some numerical simulations.