Distributed Control of Multi-robot Formation Based on Spatially Interconnected Model

This paper addresses the control of multi-robot formation in 2-dimension plane. Dynamic extension is used to linearize the robot's kinematic model. Since the formation models, which use the error of robots' real positions and speeds with respect to their desired values as the controlled valuables, are coupled systems, a spatial shift operator is introduced to model them as spatially interconnected systems. Then distributed controllers which have the same structure as the plants and will simplify the computation compared with centralized controllers are designed. The controllers are dynamic output feedback controllers and can not only stabilize the nominal formation system but also robustly stabilize a perturbed version of the system. The design procedure is presented which involve the application of convex optimization tools, i.e. linear matrix inequalities. The experimental results are simulated in MATLAB software and are confirmed with the formation of Team AmigoBot Mobile Robots.