Emergent Mechanism Design via Robot Swarms
Annalisa T. Taylor, Thomas A. Berrueta, Todd D. Murphey

Abstract—Most decentralized robot swarms achieve tasks byspecifying local rules designed to prevent agents from disrupting
one another. In turn, such agents spend a substantial portion of
their computational budget avoiding collisions and unstructuredinteractions. However, recent work has found that task-capable
emergent behaviors can emerge from such messy physical interactions. In this sample from our on-going work we suggestthat instead of designing swarms to avoid physical interactions,tasks can be achieved by harnessing the work generated by adecentralized collective of stochastically colliding agents. We explore the idea of building mechanisms (e.g., ratchets, pulleys, beltdrives) out of the self-organized states of robotic active matter.
Taking advantage of known connections between collision-driven
systems and thermodynamics, we are able to quantify the rate ofwork generation of these emergent system states. Then, we may
design tools and mechanisms that harness the work done by theswarm towards achieving desired tasks. To ensure that desirable
configurations with respect to a given task form consistently, we
propose an algorithm to achieve closed-loop work generation bylocking the system into beneficial self-organized configurations.
Here, we outline plans to produce reliable, emergent mechanisms
from the interactions of colliding agents.

To achieve complex behaviors such as shape formation,
swarms of robots typically follow local and decentralized
rules that deterministically choreograph the movements ofeach agent. The ways in which agents are (dis)allowed tointeract are crucial to task success—if an agent takes anaction out of step from its neighbors, the collective task may
fail entirely. As such, collisions and unstructured interactions
between agents tend to be avoided at all costs, leading tosubstantial computational expenditures for this purpose. In thiswork, rather than wasting time and computational resources oncollision avoidance, we suggest that embracing collisions andphysical interactions can nonetheless lead to nontrivial swarm
task-capability. To this end, we explore useful work generation
in a swarm of colliding robots called smarticles [6].
Each smarticle is comprised of a rectangular body lying ona flat surface and two flapping arms that cannot contact theground. Although an individual smarticle is immotile, a groupof them confined to a small area interacts persistently throughcollisions and produces emergent behaviors [2, 5]. However,controlling such a robot collective and producing useful work
remains an open problem. In this manuscript, we focus oncollectives of three smarticles enclosed in a ring as shownin Fig. 1. This system has been shown to exhibit persistent“dances” that emerge spontaneously from the collisions causedby the movement of each smarticle’s arms [2]. These dances
are self-organized dynamical attractors of the collective andare a function of the pattern of arm movements, also known
as the system’s “drive pattern.”
To develop control and design principles for extracting
useful work from colliding robot collectives, we require aFig. 1.

Mechanism design via rattling-based behavioral annealing.

theoretical framework from which to build as a starting point.
Statistical mechanics from its inception has been concernedwith elucidating the behaviors of colliding elements (i.e.,atoms and particles), as well as their dissipation and work
generation, and its insights extend to macroscopic collisiondriven systems such as billiards [1]. The smarticle system,
whose quasi-random diffusive behavior was characterizedin [5], is an ideal candidate system to explore the potential ofthermodynamics-based swarm control strategies. In particular,
we propose that two key results in nonequilibrium thermodynamics can be applied to ensure robust work generation that
may be harnessed towards task-capability.
The first enabling result is the development of rattling
theory [2]. Rattling theory describes the way in which correlations among disordered degrees of freedom in driven systems
determine the magnitude of system-level fluctuations. The
magnitude of these fluctuations determines the stability ofsystem configurations. Hence, rattling theory predicts which
configurations the system is likely to evolve towards andremain in for long periods of time. Moreover, the theory
predicts that complex systems spontaneously evolve towards
configurations that minimize the magnitude of such fluctuations, also known as the low rattling selection principle.
To quantify the magnitude of these fluctuations at a given
configuration, we can compute rattling R(q)—from which thetheory derives its name—in the following way:R(q) =

1log det C(q),2(1)

where q is a configuration variable (e.g., coordinates [x, y, θ]of all smarticles), and C(q) is the system’s configuration-spacecovariance matrix sampled over short trajectories initialized atq. Using R(q) the low rattling selection principle ispss (q) ∝ e−γR(q) ,(2)with γ as a system-specific constant of order 1. This closed
form relationship between the nonequilibrium steady-state
and rattling allows one to quantify the likelihood of system
configurations and thus characterize the emergence of selforganized system configurations. It is important to note thatfor a given drive pattern, a complex system may produce avariety of self-organized states, which themselves are subject
to change if a different drive pattern is applied.
Equipped with a way to numerically identify emergent
nonequilibrium system configurations (e.g., the dances shownin [2]), the second thermodynamic result needed to enablerobust collision-driven swarm work generation is the Crooks
Fluctuation Theorem (CFT) [3]. The CFT provides a closedform relationship between the irreversibility of transitions
between system configurations and the work that must be donein order for that transition to be possible. This theorem has
been greatly extended since its introduction. Notably, workin [4] provides a lower bound on the amount of work thatmust be generated for a nonequilibrium system to remain
at a given state. Then, by combining the CFT (and itsextensions) with rattling theory we arrive at the following
conclusion: complex nonequilibrium systems spontaneously
evolve towards self-organized states, which themselves must
persistently do work on their environments in order to bemaintained. Put plainly in terms of our smarticle system,
we are simultaneously guaranteed that the swarm will evolve
to self-organized configurations and that those configurations
will generate a net amount of work—precisely the conditions
we require to enable collision-driven task-capable behaviors.
Given a guaranteed source of work generation in our swarmof colliding agents, our final task is to harness this energy
towards desirable outcomes. However, while the CFT andrattling theory guarantee that our systems will be able toproduce work, they say nothing about the character of thework generated. Moreover, both the amount and the type ofwork generated may vary from low-rattling configuration tolow-rattling configuration. For example, in our three-smarticle
system certain self-organized states lead to work generation via
linear displacements whereas others produce a net angular momentum. While both of these configurations produce work, themechanisms needed to harness said work into task-capability
may have to be designed differently. Momentarily sidestepping
the issue of the configuration-dependent character of the work
generated by the system, we may consider designing a toolthat harnesses the net angular momentum of the smarticle
swarm to actuate simple mechanisms such as a belt drive
transmission or a pulley. One minimal design that leverages therotational energy of this spontaneously arising configuration
is a planetary gear, as shown in Fig. 1. By harnessing thisrotational energy, a smarticle-actuated planetary gear system
could potentially power a mechanical or electrical device.

Algorithm 1 Rattling-Based Behavioral Annealing
1: Run smarticle system with desired drive pattern
2: Allow it to settle into a low-rattling configuration
3: Determine if type of work generation matches desired
mechanism
4: while Work is not of correct type do
5:Increase drive entropy for some duration
6:
Decrease drive entropy7:
if Work is of correct type then
8:
Break
9:
end if
10: end while
11: Exploit mechanical work in current configuration

Although the three smarticle system has been shown toreliably self-organize into low-rattling configurations, due tointrinsic nondeterminism we cannot a priori specify which
configuration that will be. Some of the states the system mayfind itself in will be irrelevant to a candidate mechanism,as was mentioned above, and thus have no relative value inachieving a chosen task or goal. Hence, it is necessary to beable to not only observe the prevalence and persistence of lowrattling configurations, but also to influence their stability inorder to guide the system towards beneficial configurations. As
shown in [2], one way to do this is by raising drive entropy—
or, in other words, move the smarticle arms completely randomly when the system is in an undesirable configuration.
Raising drive entropy leads to a direct increase in the rattling ofa configuration, which effectively destabilizes it by increasing
the likelihood of leaving it. Thus, by increasing drive entropy
we may not be able to specify desirable states, but we may
specify the undesirable ones and leave them.
Using this knowledge, we may construct an algorithm thatwould guarantee desirable work generation with respect to a
specified task. In Algorithm 1 we propose such an algorithm,
which we term rattling-based behavioral annealing. Remarkably, the proposed algorithm is very similar to an annealingschedule with drive entropy playing the role of temperature,and indeed at a high-level it operates on similar principles.
The crucial insight, as is the case in annealing processes, isthat when we raise drive entropy the system explores a greater
diversity of configurations in which to settle, whereas without
raising drive entropy the system may remain stuck in a (taskirrelevant) low-rattling state. By executing this rattling-basedannealing process multiple times, we can iteratively explore
the system’s low-rattling states until we eventually find thedesired state.
Robots and swarms have for long been design to avoid
unstructured and unpredictable interactions. While this has
produced demonstrable progress, designing systems to explicitly avoid the emergence of self-organized behaviors is a
missed opportunity for the development of future autonomy.
By exploiting thermodynamics, future swarms may becometask-capable despite appearing disorderly.

R EFERENCES[1] Timothy Chumley, Scott Cook, and Renato Feres. Frombilliards to thermodynamics. Computers & Mathematics
with Applications, 65(10):1596–1613, 2013.
[2] Pavel Chvykov, Thomas A Berrueta, Akash Vardhan,William Savoie, Alexander Samland, Todd D Murphey,
Kurt Wiesenfeld, Daniel I Goldman, and Jeremy L England. Low rattling: A predictive principle for selforganization in active collectives. Science, 371(6524):90–
95, 2021.
[3] Gavin E Crooks. Entropy production fluctuation theorem
and the nonequilibrium work relation for free energy
differences. Physical Review E, 60(3):2721, 1999.
[4] Jordan M. Horowitz, Kevin Zhou, and Jeremy L. England.
Minimum energetic cost to maintain a target nonequilibrium state. Phys. Rev. E, 95:042102, Apr 2017. doi:
10.1103/PhysRevE.95.042102. URL https://link.aps.org/
doi/10.1103/PhysRevE.95.042102.
[5] W. Savoie, T. A. Berrueta, Z. Jackson, A. Pervan,R. Warkentin, S. Li, T. D. Murphey, K. Wiesenfeld, andD. I. Goldman. A robot made of robots: Emergent
transport and control of a smarticle ensemble. Science
Robotics, 4(34), 2019. doi: 10.1126/scirobotics.aax4316.
[6] William Carey Savoie. Effect of shape and particle
coordination on collective dynamics of granular matter.
PhD thesis, Georgia Institute of Technology, 2019.