OUP accepted manuscript
IMA Journal of Mathematical Control and Information
This paper proposes a distributed algorithm for the compact deployment of robots, using both distanceand angular-based arguments in the controllers' design. Our objective is to achieve a configuration maximizing the coverage of the environment while increasing the graph's connectivity. First, we provide: (i) a dispersion protocol guaranteeing connectivity maintenance; and (ii) a compactness controller with static and variable control gains that minimizes the inter-agent angles. Second, we
... t a sequential, multi-stage strategy and analyse its stability. Finally, we validate our theoretical results with simulations, where a group of robots are deployed to carry out sensing or communication tasks. Distributed control of compact formations for multi-robot swarms 3 of 31 algorithms allow robots to adapt their motion profiles so to preserve connectivity. More recently, [Bezzo et al. (2010 [Bezzo et al. ( , 2011a] tackled the deployment of mobile routers in accident areas problem, using an appropriated routing and position optimization algorithm. 1.1.2 Formation shape control A fundamental task for robot reconfiguration is formation shape control. The reader can refer to [Oh et al. (2015) ] for a recent survey on multi-agent formation control. By definition, the formation shape control problem involves a group of agents tasked with forming and maintaining a given geometric shape, described in terms of relative geometrical constraints. Among many others, [Bishop et al. (2015); Mou et al. (2015)] have recently proposed distributed control strategies guaranteeing the convergence to a prescribed formation shape, while [Martínez et al. (2006)] proposed different approaches to deal with location and trajectory following of a moving target. Formation control based on virtual structure methods was also introduced in [Chen et al. (2010); Consolinia et al. (2008); Beard et al. (2001)] and strategies especially tailored to submarine/oceanic applications were studied in, e.g., [Sepulchre et al. (2008); Brinon-Arranz, et al. (2014); Ghabcheloo et al. (2005)], with an emphasis on circular formations. Recently, [Eren (2012)] also exploited rigid graph theory for bearing-based formation control. Closer to the topic of this paper, some other works focused on the formation shape control of triangular formations. In ], a "positively-oriented" triangular formation is maintained by having each agent locally controlling its own position so that the distance to the next agent in the triangle is constant. This approach was later extended in [Cao et al. (2011) ] to a multi-level procedure, where each agent cyclically switches between periods of localization, position control and standby. A distance based approach was also considered in [Summers et al. (2009); Anderson et al. (2010)], where authors analyse equilibrium formation shapes with incorrect interagent distances. In a different way, [Basiri et al. (2010); Bishop (2011a); Bishop et al. (2011b, 2010)] consider an angle-based (rather than inter-distance based) perspective. Here, each agent measures the bearing to the other two agents in a local coordinate system, and control its motion according to prescribed geometric constraints.