An approach to switching control beyond nearest neighbor rules

Abstract

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

Switching Rules for Decentralized Control with Simple Control Laws

“…For any time interval τ j = [t j ...t j+1 ], let V σ(τj ) be a global potential function. It is shown in [8] that a function exists with the following properties:…”

“…It is straightforward to show that such a system is stable in the absence of switching; that is, when springs are neither created nor destroyed (see [8]). However, it is useful to allow the creation and destruction of springs.…”

“…In previous work [8], [9], we analyzed a distributed control system that was essentially a virtual physics model that looked like a spring mesh system. In this example, each agent is treated as a particle in a simulated system, with virtual springs acting between specific pairs of agents.…”

“…Throughout this paper, our motivating example will be the switching function that produces a Gabriel graph, which we describe in more detail in [8] and [9]. This Gabriel graph switching function is described briefly in Section III.…”

Towards a Multi-peclet Number Pollution Monitoring Algorithm

“…As a result of this, researchers in the mobile sensor field have been developing various techniques to monitor the environment. This includes developing algorithms that would enable a swarm of agents form the spatial distribution of a pollutant as in [2] [3]. Also, algorithms have been developed that enable a single agent find a pollution source as in [4][5] [6] [7].…”