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Current approaches to distributed control involving many robots generally restrict interactions to pairs of robots within a threshold distance. While this allows for provable stability, there are performance costs associated with the lack of long-distance information. We introduce the acute angle switching algorithm, which allows a small number of long-range interactions in addition to interactions with nearby neighbors. We show that the acute angle switching algorithm provides an improvement in performance while retaining the quality of provable stability. I. INTRODUCTIONWith recent advances in integration and wireless communication, there has been increasing interest in the control problem associated with large numbers of cooperating robots. We are particularly interested in the problem of fully distributed control (commonly referred to as swarming), in which useful formations are created without any centralized coordination. Limitations on communication bandwidth and range make effective swarming algorithms necessary when the number of robots is large.Many robotic swarming algorithms are modeled after phenomena observed in nature, such as the flocking behavior of birds or the schooling behavior of fish. Others are based on simulated physical systems. Common to these approaches are simple local control laws implemented on each robot, and designed in such a way that desirable global behaviors emerge. The control laws are typically based on interactions between a given robot, the environment, and any nearby robots that are within a threshold distance.One key drawback of this approach is that disconnected clusters of robots may never coalesce into a single formation. Disconnected clusters may form as a result of the initial deployment configuration, localized disturbances in the environment, or temporary communication failure, for example.Our work extends the nearby-neighbors approach so that robots interact with selected neighboring robots at larger distances when possible, in addition to interacting with neighbors within a threshold distance. We have developed a nearest neighbor dynamics model paired with an acute angle switching algorithm that uses a small amount of global information to guarantee a planar and connected adjacency graph at all points in time. This allows robots to be deployed in an arbitrary starting configuration and still reach a single connected formation if their sensing is not limited.We show that the underlying system is stable in terms of velocity; that is, all of the robots are guaranteed to come

Current approaches to distributed control involving many robots generally restrict interactions to pairs of robots within a threshold distance. While this allows for provable stability, there are performance costs associated with the lack of long-distance information. We introduce the acute angle switching algorithm, which allows a small number of long-range interactions in addition to interactions with nearby neighbors, without sacrificing provable stability. We prove several formal properties of the acute angle switching algorithm, including system-wide connectivity. Further, we show simulation results demonstrating the efficacy and robustness of multi-robot systems based on the acute angle switching algorithm.

We introduce a novel method for enforcing stability on a decentralized control system. In contrast to previous work, our approach allows for the use of a wide variety of simple control laws, while still providing for a formal proof of stability. Our motivating example uses a simple geometric switching function coupled with PD control that has an intuitive interpretation as a virtual spring mesh. Building on this example, we show a general proof technique that applies to a large class of decentralized control systems. Furthermore, we describe additional cases that illustrate how our technique can be applied to useful systems that are straightforward to implement.

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