Similarity-Based Rigidity Formation Maneuver Control of Underactuated Surface Vehicles Over Directed Graphs

This article develops a formation maneuver control strategy for a group of underactuated unmanned surface vehicles (USVs) under similarity rigidity framework over directed graphs. The control objective is to achieve similar formation transformations (translation, rotation, and scaling) while maintaining the desired formation shape. The desired formation shape is determined by a set of similarity constraints on the signed angle and the distance ratio of a pair of edges joining a common vertex. Instead of the error variables with respect to the angle or distance ratio usually used in traditional similarity-rigidity control methods, the relative position errors are obtained by the constant rigidity matrix. Once the position of each USV overlaps with the configuration of the target formation, the desired formation maneuver can be achieved. The proposed control strategy can be implemented in a local coordinate system and directed graphs without intervehicle communication. Simulation results demonstrate the effectiveness of the proposed control strategy.