Design and Control of Swarm Dynamics

Complexity science has shown that collective behaviors in animal groups, that is swarms, emerge from repeated local interactions between neighboring individuals. It has also revealed that a set of simple local interaction rules applied to very simple artificial agents gives rise to complex patterns possessing long-range and long-lasting dynamic order. These swarming systems, be them natural or artificial, are all characterized by somehow similar features: (i) lack of central controller or leader overseeing the collective dynamics, instead the latter emerges through self-organization, (ii) local perception of the environment leading to a certain level of global knowledge by means of effective distributed information sharing, and (iii) a high degree of adaptation to rapidly changing circumstances. These features afford swarms unique distributed problem solving capabilities—a.k.a. swarm intelligence—such that collectively they perform tasks far exceeding each individual agent’s ability.

Animal groups provide paradigmatic examples of collective phenomena in which repeated interactions among individuals produce dynamic patterns and responses on a scale larger than individuals themselves. Some of the examples around us include the coordinated movements of fish and birds in a school or a flock, respectively, the chemotactic aggregation of amoebae, the formation of lanes in densely packed human crowds, the generation of vortices in bacterial colonies, the synchronized march of wingless locusts, and the synchronized flashing of fireflies. Many more examples can also be found inside all of us: the firing of neurons in our brains, the clustering of differentiated cells to construct our organs both during embryonic development and wound healing, and the targeted response of neutrophils as part of the initial immune response to a bacterial infection. This nonexhaustive list of collective behaviors of unicellular and multicellular organisms is revealing of the pervasiveness of swarming in the natural world.

The previous chapter was centered on awe-inspiring collective behaviors observed in the animal kingdom, and how this inspirational bounty can be harnessed to develop innovative swarm designs. We stressed two important points related to some very common collective behaviors: (1) they occur across vastly different spatial scales—from the microscale world to our macroscale world, and (2) they emerge across immensely different taxa—from bacteria to quadrupeds. When faced with such empirical evidences, the physicist will immediately suggest the existence of universal mechanisms at the root of collective phenomena that would justify and explain such commonalities in dynamic behaviors. This may appear counterintuitive at first since the fundamental laws of physics yield forces and energies of very different magnitudes across a wide range of scales. For instance, swimming at the micrometer scale requires aggregating microorganisms—e.g. bacteria or amoebae—to power themselves by harnessing viscous forces which form the main source of drag for macroscale schooling fish. The undeniable successes of physics in the past centuries certainly come from an uninterrupted search for universality across seemingly unrelated phenomena—e.g. dispersion in optical waves and dispersion in mechanical waves. It comes therefore with no surprise that physicists have been extremely active, and successful, in the past two decades uncovering the prominent universal mechanisms at play in collective phenomena at large. This chapter will present a brief overview of those while stressing their importance for the designer of swarming systems.

Characterizing the dynamics of a swarm as we did in the previous two chapters is only one step toward understanding it. We also need to understand how local interactions influence the overall system’s dynamics. The modern science of networks provides a very elegant and powerful framework—essentially grounded in graph theory—to bridge the gap between local dynamics and interactions at the agents level and global response at the swarm level. Indeed, network models offer a natural way of describing how self-organization arises in complex systems, which in turn helps us gain insight into dynamical processes occurring on them. Moreover, network science has a lot in common with statistical physics: percolation, scaling, order parameters, renormalization, self-similarity, phase transitions, and critical exponents were introduced in Chap. 3 in the context of swarm dynamics, and they remain highly relevant for a network analysis (Albert and Barabási, Rev. Mod. Phys., 74:47–97, 2002). As was noticed with our analysis of correlations of fluctuations in Chap. 3, it can be really challenging to identify emerging patterns and their properties, especially for swarms lacking apparent order. Network theory provides yet another invaluable toolbox to uncover “hidden” structures emerging through self-organization.

Swarming agents are interconnected organisms or agents. As is well known in our information age, a key benefit of being connected is access to information. We have discovered and observed this interconnectivity from the biological standpoint in Chap. 2, then analyzed it from the physical viewpoint in Chap. 3, and thoroughly studied its network structure and dynamics in Chap. 4. Such dynamic interconnectivity serves the purpose of channeling information exchanges, which are critical to the effectiveness in swarming. Indeed, it is well known that collective animal behavior is dependent on the existence of communication channels enabling information exchange between individuals (Krause, Ruxton, Living in Groups, Oxford Series in Ecology and Evolution, 2002). For instance, the collective surveillance against oncoming threats of a flock of birds provides a higher level of vigilance only if the information obtained by each pair of eyes is shared among the flock. However, up to now our discussion about information was limited to generalities and we have not detailed the following: (i) the role of information in collective behaviors, (ii) how information is communicated throughout a swarm, and (iii) how information is processed or computed in a decentralized way by the swarm. This chapter is concerned with (i) and (ii), while the next one will deal with distributed information processing from the perspective of decision-making or collective computation.

In her book “Information Theory and the Living System,” Gatlin (Gatlin, Information Theory and the Living System, 1972) states that “Life may be defined operationally as an information processing system—a structural hierarchy of functioning units—that has acquired through evolution the ability to store and process the information necessary for its own accurate reproduction.” Somehow this statement can readily be adapted to define swarms from the information processing viewpoint: a swarm can be defined operationally as a single distributed information processing system—a dynamic and decentralized structure of functioning units—that has the ability to process information and adapt to changing environments. This definition echoes the general role of computation in complex systems given by Mitchell (Mitchell, Complexity: A Guided Tour, 2009): “computation is what a complex system does with information in order to succeed or adapt in its environment.”

Swarm intelligence offers a unique alternative way of designing “intelligent” systems, in which the combination of autonomy, emergence (through self-organization), and distributed problem solving replaces embedded centralized control. In these concluding words, it is no longer necessary to discuss the power and distinctive capabilities of swarms in collectively solving complex tasks and problems. The ultimate goal is therefore to leverage the power, robustness, flexibility, and scalability of swarms while still being able to design, direct, and control the collective task to be performed. In the face of changing circumstances, possibly adverse external factors or internal element failures, a robust artificial swarm should continue to operate if properly designed. Furthermore, a flexible artificial swarm should, in principle, be able to maintain its distributed operation through graceful degradation. In other words, if properly designed, an artificial swarm should avoid catastrophic collapses in collective action. The property of scalability should not be understated given the recent explosion in low-cost, miniaturized, and highly reliable sensors, communication devices, and microcomputers (Rubenstein, Cornejo, Nagpal, Science, 345, 795–799, 2014).