A comparative look at two formation control approaches based on optimization and algebraic graph theory

Abstract This paper takes a novel look at formation control by comparing control setups based on two very different frameworks. These are applied to the distributed control of communicating omnidirectional mobile robots. One framework, which is possibly the most common approach to formation control, is based on algebraic graph theory, whereas the other, namely distributed model predictive control (DMPC), is based on distributed optimization, representing a rather uncommon view on the task. In this study, formation control is understood as the task of attaining and maintaining a specific relative positioning between robotic agents while moving the formation through the environment. While interesting on its own, formation control can serve as the basis for superordinate tasks like cooperative transportation. For an encompassing treatment of the task, two different control goals are considered, resulting in different setups for each control framework. One goal consists of moving the formation’s geometric center to a specific position, whereas the other aims at letting the whole formation move with the desired velocity. In both cases, the involved robots are subject to input constraints. Already during control design, some qualitative differences between the two frameworks become apparent, with the DMPC controller exhibiting characteristic beneficial qualities in exchange for its higher computational demand. Results from various simulation scenarios confirm these observations. Considerations on the practical implementation of the two schemes, as well as hardware experiments with tailor-made mobile robots, provide valuable insight for robotics practitioners, and highlight the applicability of the two frameworks.