Control of a Group of Mobile Robots Based on Formation Abstraction and Decentralized Locational Optimization

In this paper, we propose a new method of controlling a group of mobile robots based on formation abstraction. The shape of a formation is represented by a deformable polygon, which is constructed by bending a rectangle, to go through narrow spaces without colliding with obstacles. If the trajectory of the front end point, as well as the width and the length of the formation, are given, the formation automatically reshapes itself to fit the area through which the front part of the group has already safely passed. Furthermore, the robots continuously try to optimize their positions to decrease the risk of collisions by integrating a decentralized locational optimization algorithm into the formation control. We show that the objective function, taking into account the distance between robots, does not decrease for fixed and nonconvex polygonal formation shapes if the zero-order hold control is applied for a sufficiently short sampling period. We also analyze the influence of the decentralized locational optimization algorithm on the objective function in the case of variable formations. The effectiveness of the proposed method is demonstrated in both simulations and real robot experiments.