Swarm multi-robot systems consist of groups of robots with simple interaction rules that exploit local information to collectively perform task-directed activities. Behavioral prediction of such systems is challenging; consequently, most existing methods for programming swarms lack principled design criteria. In this work we consider a particular class of swarm robot systems with hundreds of robots. The systems in this class are significantly larger than currently deployed systems. We show that the large size of such swarms makes them amenable to statistical analysis.
This work makes use of a mathematical framework based on equilibrium thermodynamic and statistical mechanical methods to enable a principled controller synthesis methodology for homogeneous robot swarms. This involves a two-step procedure. The first step is the construction of a toolbox, a set of distributed processes and their associated macroscopic characterizations. Analytical or numerical statistical mechanics and thermodynamics methods are used to determine these characterizations. The second step consists of construction of the robots' controllers by combining distributed processes while, simultaneously, coupling the processes associated macroscopic characterization. This approach aims to allow system designers to think about controller synthesis as the problem of combining macroscopic templates rather than as manipulation of low-level controllers which are often sensitive to changes. Thus, this work is a step toward elevation of the level of description used while programming swarm behaviors.
General prediction of distributed behavior remains a difficult problem, though this research makes explicit a dynamical systems property, termed ergodicity, that makes behavioral prediction tractable. The toolbox is constructed from ergodic processes because they admit qualitative descriptions of performance, provide time-invariant equilibrium states, foster an understanding of behavioral regimes, and permit stability analysis. This work outlines several constructive principles and guidelines that aid in establishing a link between these formal properties and the realities of task directed robot system design. Examples of such guidelines include exploiting distinct timescales, and seeking conservation properties within task behavior.
We show that, taken together, these tools enable principled design of multi-robot systems. Controllers based on ergodic processes are produced for a number of classic coordination and collective decision making problems in the multi-robot literature. The synthesized controllers are validated with a special simulation tool designed for experiments with large-scale systems. The results show that, despite the simplicity of the individual processes, non-trivial collective behavior can be successfully synthesized. Moreover, the focus on ergodic dynamics and topological characteristics rather than algorithmic properties leads to novel solutions for these and related tasks.
More broadly, the research shows that macroscopic models provide an appropriate abstraction for synthesizing useful behavior in large-scale loosely-coupled distributed systems. For example, we demonstrate that by manipulating conditions in a colony of Temnothorax rugatulus, commonly studied social ants, a directed transport behavior can be induced. We also demonstrate how models of crowd behavior can be used in the design and validation of a coordinated multi-robot system to minimize egress path length and collective evacuation times.