# Gradual Collective Upgrade of a Swarm of Autonomous Buoys for Dynamic Ocean
Monitoring

Francesco Vallegra  SUTD-MIT International Design Center
Singapore University of Technology and Design
Singapore
<EMAIL_ADDRESS>David Mateo  Engineering Product Development
Singapore University of Technology and Design
Singapore
<EMAIL_ADDRESS>Grgur Tokić  Dept. of Mechanical Engineering
Massachusetts Institute of Technology
Cambridge, USA
<EMAIL_ADDRESS>Roland Bouffanais  Engineering Product Development
Singapore University of Technology and Design
Singapore
<EMAIL_ADDRESS>Dick K. P. Yue  Dept. of Mechanical Engineering
Massachusetts Institute of Technology
Cambridge, USA
<EMAIL_ADDRESS>
###### Abstract

Swarms of autonomous surface vehicles equipped with environmental sensors and
decentralized communications bring a new wave of attractive possibilities for
the monitoring of dynamic features in oceans and other waterbodies. However, a
key challenge in swarm robotics design is the efficient collective operation
of heterogeneous systems. We present both theoretical analysis and field
experiments on the responsiveness in dynamic area coverage of a collective of
22 autonomous buoys, where 4 units are upgraded to a new design that allows
them to move 80% faster than the rest. This system is able to react on
timescales of the minute to changes in areas on the order of a few thousand
square meters. We have observed that this partial upgrade of the system
significantly increases its average responsiveness, without necessarily
improving the spatial uniformity of the deployment. These experiments show
that the autonomous buoy designs and the cooperative control rule described in
this work provide an efficient, flexible, and scalable solution for the
pervasive and persistent monitoring of water environments.

###### Index Terms:

Distributed Robotics, Collective behavior, Autonomous surface vehicle, Dynamic
area coverage

##  I Introduction

Monitoring the ocean and coastal areas has traditionally been accomplished
using either moored buoys or fixed networks of bulky, partially submerged
platforms. The cost of developing, producing, deploying, and maintaining such
systems has severely limited the range and precision of the sensed data
obtained from monitoring large-scale waterbodies. To overcome these
limitations, the community has started focusing on developing simpler,
smaller, motorized, autonomous surface vehicles [1, 2, 3, 4, 5]. A large group
of such vehicles operating as a collective can be deployed, retrieved, and re-
deployed (partially or completely) at considerably lower cost and operational
complexity than monolithic structures. Following the design paradigm of swarm
robotics, these collectives perform complex tasks cooperatively in a scalable
fashion, with a behavior that is both robust to failures and flexible so as to
operate in dynamic environments [6, 7]. Moreover, a swarm of mobile surface
vehicles forms a dynamic sensor network suitable for high temporal sampling of
waterbodies.

The pressing need for small, low-cost and rapidly deployable autonomous
vehicles has been acknowledged in multiple recent reports [8, 9, 10, 11].
However, using such large distributed systems for ocean monitoring presents as
many possibilities as it does challenges. On the one hand, the system
modularity and the individual cost of production primes them for iterative
design and fast prototyping, in which field tests provide insights enabling a
constant improvement toward future models. On the other hand, this iterative
process is likely to produce an heterogeneous system, in which the agents have
different motor, sensing, communication, or processing capabilities. This
heterogeneous character must be properly handled at the system-level design in
order to benefit from the range of agent capabilities.

We have previously reported on the design, construction, and testing of a
homogeneous swarm of 50 (identical) autonomous buoys performing adaptive
deployment for applications in environmental monitoring [12]. Here, we
investigate and study the nontrivial process of partially upgrading this swarm
robotics system by replacing a small fraction of the original swarming units
(simply denoted v1) with upgraded robotic platforms (v2), based on a fully
redesigned model featuring highly improved motor and processing capabilities
among other things.

Figure 1: Swarm of buoys being deployed in the target area undergoing
monitoring. Note that some units are still being deployed from the shore where
the picture is taken.

We have combined a set of 18 v1 buoys with 4 upgraded v2 buoys—hence
constituting a heterogeneous swarm—and performed dynamic area coverage
experiments in fully unstructured environments without the support of any
external infrastructure when it comes to the system’s operations (see Fig. 1).
We measured the collective responsiveness—a proxy to assess the flexible
character of a swarm [13]—by changing the target area at different frequencies
in order to investigate the minimum response time at which the heterogeneous
swarm is able to adapt to changes in the monitored environment. For this
series of experiments on dynamic area coverage, the only practical differences
between the two platforms are the speed of the units, their inertia, and their
hull design. Specifically, design v2 is 80% times faster in open water and 2.3
times lighter than v1, thereby making it considerably more apt to quickly
correct its position to adapt to changes in the target area undergoing
monitoring. The field experiments performed reveal that the partial upgrade of
the system is able to increase the average response of the system, but not
necessarily the uniformity of the deployment.

##  II Robotic Platforms

In [12], we presented a study of dynamic ocean monitoring using a homogeneous
swarm of 50 buoys. Such decentralized and cooperative systems primarily owe
their outstanding effectiveness to the large number of agents put together: a
greater number of agents allows for vaster waterbody coverage and/or refined
multi-point sensing. As technology inexorably moves forward at an increasingly
faster pace, there is a compelling opportunity to expand and upgrade at least
some of the agents of the collective. These new units with improved
capabilities have to be able to fit and operate within the technical framework
of the original system.

The original buoy platform—design v1—is thoroughly described in [12], and we
refer the reader to this report for full technical details. In this section,
we focus on introducing an improved design (v2) and its main differences with
respect to v1. This new design (see Fig 2), re-designed mainly to facilitate
operation and maintenance, can be used to replace some units in the
homogeneous swarm, or expand the original homogeneous system.

.

Figure 2: Exploded view of the upgraded buoy design v2 displaying its modular
design and main components.

The platform has a modular design consisting of (i) a cylindrical hull, (ii) a
top lid hosting the electronics on one side and antennas on the other, and
(iii) a detachable bottom section that can be customized to host a number of
environmental sensors, as shown in Fig. 2. The main hull for v2 is designed to
provide the same omnidirectional vector propulsion apparatus as in v1, while
encapsulating the three thrusters within the cylindrical shape and keeping
them as close as possible to the center of gravity of the platform. This
design choice stands in clear contrast with v1 that has protruding pairs of
propellers, see Fig. 3. On the one hand, this new design minimizes the
wobbling when the thrusters are active and provide a certain level of dynamic
stability to the surface vehicle. On the other hand, the new hull has a larger
packing density, which facilitates stackability and transportation of large
numbers of platforms to remote field areas (see Fig. 1 in [12]). The
mechanical design of v2 and the distribution of components inside the main
hull has been designed and tested to not compromise the hydrostatics of v1,
thereby retaining the critical self-righting feature of the v1 design.

The presence of three lateral aluminum pads allows for heat exchange between
the water and the air inside the hull—a fan ensures adequate air circulation
to homogenize the heat generated mainly by the 3 electronic speed controllers
(ESC in Fig. 2) and the single-board computer Odroid C2. These aluminum pads
can themselves host small sensors or light-emitting devices orientated 45
degrees below the water surface.

The top lid hosts the electronics and related hardware as a modular design
itself. An electronic rack built around the main PCB and battery is screwed on
the inside of this lid, thereby forming one single piece that can easily be
replaced or disassembled for rapid inspection. Following the buoy v1 design,
the outer part of the top lid hosts connectivity hardware such as
communication and GPS antennas, and a charging port. The top lid of v2
includes an LCD screen reporting a range of data and indicators, which greatly
facilitates the basic inspection and troubleshooting of the system’s digital
status. Lastly, a mechanical handle has been incorporated into v2’s top lid
design to aid both manual carrying and latching a stacked platform on top of
it.

The bottom part is designed to securely host the battery, and can be modified
to accommodate any sensor. The latter can be easily and conveniently
interfaced with the electronic stack through a mini-PCI custom PCB that can be
slotted inside the main PCB. This configuration was specifically designed to
support further heterogeneity of the system at the sensing level, with various
units possibly carrying different sensors.

Particular attention has been placed on identifying a simple way of assembling
parts and components. An example is the thruster attachment, in which a
combination of a laser-cut gaskets and screws allows for servicing all three
thrusters in less than 5 minutes—eight times faster than for the v1 design. In
addition, the structure of the new electronics rack is composed of laser-cut
acrylic sheets and designed using screw-less joineries to facilitate
manufacture, assembly and reduce potential leaks.

Once assembled, platform v2 measures $260\times 260\times 245$ mm and weights
3.2 kg. For comparison, the previous design measures $350\times 350\times 280$
mm and weights 7.4 kg. The reduction in dimensions is primarily achieved by
moving from a spherical form to a cylindrical one, which allows for a compact
embedding of the thrusters. The reduction in weight comes from using plastic
material for the hull as opposed to aluminum alloy in v1. Besides weight
reduction, the usage of 3D printed nylon plastic material inherently prevents
corrosion and safely withstands seawater conditions, while reducing the amount
of biofouling accumulating on the platform during operations as compared to
metal. Due to the low number of v2 prototypes, the plastic hulls have been
3D-printed, making the cost comparable with the aluminum hull of v1. However,
when mass producing the units using plastic injection inside a mold, the cost
per unit is expected to be significantly lowered.

### Performance comparison: buoy v1 vs. v2

Fig. 3 shows a visual comparison between buoy v1 and one of the prototypes of
the improved design v2. By incorporating the thrusters into the main hull,
buoy v2 is much more compact and increases the propellers’ life—the propellers
are protected as compared to v1 in which the protruding pods and open
propellers can easily be damaged during transportation and/or operation.

Figure 3: The two robotic platforms: the new buoy design v2 (left) side by
side with one of the previous buoy model v2 (right).

A series of performance tests were carried out under different environmental
conditions to offer a detailed comparison of the two platforms. The tests were
run over a distance of $100$ m in the direction of the prevailing the wind and
against it. The platforms were initially positioned next to one another so as
to obtain results under the practically identical conditions. The three
BlueRobotics T100 thrusters allow the buoy v2 to move about $80$% faster than
v1 in nominal test operations, although the thrusters are capable of
performing at much higher intensity.

This self-imposed limitation on the thrusters’ intensity is purely related to
the need to develop a more complex vectorial propulsion system than v1’s.
However, since the cooperative control strategy remains the same for v1 and v2
when performing the heterogeneous swarming tests, it was decided to not use
the full power of the thrusters of v2. When testing the two platforms, side by
side, in adverse environmental conditions—strong winds, waves and heavy rains,
the performance of v2 was practically unaffected. On the contrary, buoy v1
drastically underperformed, with instances at which it was fully unable to
reach its target goal.

It is worth noting that buoy v2 is granted a battery 1.5 bigger than the one
in v1 to compensate the need for higher power by the thrusters, and the extra
electronics energy consumption due to fan and LCD.

##  III Dynamic Area Coverage

###  III-A Collective Operations

Our multi-robot system can perform a range of collective behaviors achieved by
means of a cooperative control strategy supported by distributed
communications as described in full details in [12]. For instance, this
distributed robotic system can perform a number of elementary swarming
behaviors, including flocking, navigation, and area coverage. The
effectiveness of the distributed communication setup has been verified and
analyzed in [12].

This large-scale networked array of mobile sensing units is designed to
monitor and characterize waterbodies, which may vary depending on the
application. An example is the deployment of the swarm of buoys in a harbor to
assist in marine operations by monitoring key environmental and flow
parameters. More interestingly, the area to monitor might not be specified
externally or in advance, but instead be defined dynamically by the collective
of agents itself. By local processing of the sensed data, the agents may
determine the shape in which to self-deploy in order to track a particular
temperature profile, oil spill, or a range of biological markers.

###  III-B Cooperative Control for Dynamic Area Coverage

As discussed in the previous section, the distributed robotic systems are
designed to monitor features of interest in waterbodies (e.g. oil spills,
algal blooms, etc.). To do so, we require the agents to spread as uniformly as
possible across a given area that dynamically evolves over time.

It is paramount for this spreading to happen in a timely and responsive way,
as the shape of the area of interest is in general time-changing with
arbitrary dynamics. For this reason, we choose to define the behavior of the
agents in a purely Markovian fashion with agent’s dynamical rules that
determine the buoys’ movements based solely on the instantaneous state, i.e.
the cooperative control algorithm for agent $i$ can be cast as

$\frac{d\vec{r}_{i}}{dt}=\vec{F}\left(t,\vec{r}_{i}(t),\\{\vec{r}_{j}(t)\\}_{j\sim
i}\right).$ (1)

where $\vec{r}_{i}$ is the position of a given agent $i$, and $j\sim i$ is the
set of agents in the neighborhood of $i$—its “neighbors” according to a
specified interaction distance, be it metric, topological or else [14].

The area of interest is typically determined either by external sources (e.g.
a human operator) or by the sensing capabilities of the agents (e.g.
collective tracking of a temperature gradient, or chemical concentration,
etc.). For the sake of generality, we assume that the area to monitor can be
described mathematically by

$A(\vec{r})<0,$ (2)

where $A$ is a signed distance function (or at least a function that increases
monotonically outside the region). Given (2), the cooperative control rule is
defined as

$\frac{d\vec{r}_{i}}{dt}=v_{0i}\frac{\vec{T}}{\max(1,\|\vec{T}\|)},$ (3)

where $v_{0i}$ is the maximum speed of an agent $i$ and $\vec{T}$ is the “area
coverage target” defined by

$\vec{T}=\frac{1}{1+\exp{(-\beta
A(\vec{r}_{i}))}}\frac{-\vec{\nabla}A}{\|\vec{\nabla}A\|}-\sum_{j\sim
i}\frac{a_{R}^{d}}{r_{ij}^{d}}\frac{\vec{r}_{ij}}{r_{ij}}\,.$ (4)

The first term in (4), proportional to $-\vec{\nabla}A$, attracts the agents
towards the interior of the area and is scaled in such a way that its norm
goes from being practically zero outside the area to cover ($A>0$) to being
unity inside it ($A<0$). The parameter $\beta$ controls how abruptly the
transition between zero and one is, i.e. the steepness of the exponential
decrease. The second term is an inter-agent repulsion term that causes the
agents to spread inside the area. The type of repulsion is controlled by two
parameters, namely the repulsion strength $a_{R}$ and the power of repulsion
$d$. If the power $d$ is large ($d\gtrsim 4$), the repulsion strength is
approximately equal to the nearest-neighbor distance in equilibrium
configurations.

Following numerical optimization run over simulations of the behavior (4), we
set the free parameters to

$\displaystyle d=6,$ $\displaystyle a_{R}=0.38\sqrt{S/N},$
$\displaystyle\beta=40/S,$ (5)

where $S$ is the total surface area to cover and $N$ the number of agents.

###  III-C Target Surface to Monitor

As a testbed for dynamic area exploration, we consider the following surface

$A_{\alpha,\hat{e}}(\vec{r})=r^{2}-R_{\alpha,\hat{e}}^{2}(\hat{r}),$ (6)

where

$R_{\alpha,\hat{e}}(\hat{r})=\frac{R_{0}}{2}\frac{2-\alpha+3\alpha(\hat{r}\cdot\hat{e})^{2}}{\sqrt{1+\alpha/2+11\alpha^{2}/32}}.$
(7)

By changing $\alpha$, the shape of this region goes from a disk of radius
$R_{0}$ ($\alpha=0$), to a two-lobbed area along the principal axis $\hat{e}$
($\alpha=1$), to a “dumbbell-shaped” region with a nodal point at the origin
($\alpha=2$). The normalization factor in (7) is introduced so that the total
surface of the area is kept constant at $S=\pi R_{0}^{2}$ for any
$\alpha\in[0,2]$. The gradient of this surface is

$\nabla A_{\alpha,\hat{e}}(\vec{r})=2\vec{r}-6\alpha
R_{0}\frac{R_{\alpha,\hat{e}}(\hat{r})}{r}(\hat{r}\cdot\hat{e})\hat{e}_{\bot}\,,$
(8)

where $\hat{e}_{\bot}=\hat{e}-(\hat{r}\cdot\hat{e})\hat{r}$ is the orthogonal
projection of the principal axis $\hat{e}$ on the position $\vec{r}$. The
attractive geofencing force field corresponding to this target surface is
presented in Fig. 4. The contours depict the lines of constant
$A_{\alpha,\hat{e}}$ and the arrows show the vector field of the first term of
(4) for three values of $\alpha$.

Figure 4: Effect of the geofencing term for the area given by (6). The arrows
show the vector field of the first term in (4), and the color gradient maps
its norm. The contour lines mark isolines $A_{\alpha,\hat{e}}$.

##  IV Theoretical analysis

We can study the performance of the cooperative rule (4) in _dynamic_ area
coverage by imposing a cyclic temporal evolution of the shape of the
monitoring area at different frequencies.

To quantify the response of the system, we consider two metrics for the
dynamic coverage performance that were previously used when testing with a
homogeneous swarm [12]. The first one is the “tessellation performance”
$P_{T}$, defined as the inverse of the relative size of the largest cell
assigned to any agent after segmenting the target area with a Voronoi
tessellation, or

$P_{T}=\frac{A}{A_{LVC}N},$ (9)

where $A$ is the total area of the target surface, $A_{LVC}$ is the area of
the largest Voronoi cell (dark cell in the inset of the top panel in Fig. 5),
and $N$ is the number of agents.

The second metric is the so-called “coverage performance” $P_{C}$, defined as
the percentage of the target area covered by the agents (assuming each agent
covers a disk of a certain radius $R_{s}$ around its position), or

$P_{C}=\frac{\bigcup_{i=1}^{N}{c_{i}}\cap A}{A},$ (10)

where $c_{i}$ is a disk of radius $R_{s}$ centered at the position of agent
$i$ (see inset at the bottom of Fig. 5).

The tessellation performance is meant to capture the expected accuracy of the
least accurate mobile sensing unit, since it only involves the largest Voronoi
cell. The coverage performance, on the other hand, is a measure of the average
quality of the deployment, i.e. a good proxy for system-level performance.
Both metrics take only positive values lower than unity, and where the unity
corresponds to an ideal coverage.

###  IV-A Ideal Homogeneous Swarm

We first consider a swarm of $N=20$ agents following the dynamics given by Eq.
(4) with a certain speed $v_{0}$ identical for all the agents. We then study
the responsiveness—a proxy to assess the flexible character of a swarm [13]—of
the system when covering the surface (2) changing at a frequency $\omega$ such
that $\alpha(t)=1-\cos\omega t$. The particular values of $R_{0}$ and $v_{0}$
are arbitrary, as the behavior of the system only depends on the normalized
frequency $\bar{\omega}=\omega R_{0}/v_{0}$.

The collective response of a system following (4) is shown in Fig. 5. The
obtained response, measured either with the tessellation or coverage metrics,
can be fit to the form

$P(\bar{\omega})=\frac{P_{0}\bar{\omega}_{c}^{\lambda}+P_{\infty}\bar{\omega}^{\lambda}}{\bar{\omega}_{c}^{\lambda}+\bar{\omega}^{\lambda}},$
(11)

where $P_{0}$ and $P_{\infty}$ are the limit performances for
$\omega\rightarrow 0$ and $\omega\rightarrow\infty$ respectively,
$\bar{\omega}_{c}$ is the “cutoff frequency” of the system, and the exponent
$\lambda$ measures how steep the transition from $P_{0}$ to $P_{\infty}$ is.
The values for these parameters obtained by fitting (11) to the results in
Fig. 5 are given in Table I.

Figure 5: Frequency response of a swarm of $N=20$ agents in dynamic area coverage according to its Tessellation performance $P_{T}$ (top) and its Coverage performance $P_{C}$(bottom). The different markers correspond to calculations with different agent speeds $v_{0}$. The dashed line corresponds to the ideal performance of (11).  TABLE I: Parameters of the ideal performance (11) obtained by fitting the theoretical response of an ideal homogeneous system, measured both as $P_{T}$ and $P_{C}$. | Tessellation ($P_{T}$) | Coverage ($P_{C}$)
---|---|---
$P_{0}$ | $0.758$ | $0.700$
$P_{\infty}$ | $0.530$ | $0.526$
$\bar{\omega}_{c}$ | $1.03$ | $300.44$
$\lambda$ | $1.37$ | $0.48$

The cutoff frequency for tessellation performance is $\omega_{c}\simeq
v_{0}/R_{0}$. This is revealing that the capacity of the system to maintain a
uniform configuration goes down as the boundaries of the target area move too
fast for a single agent to follow them. In contrast, the cutoff frequency for
the coverage performance is two orders of magnitude larger, $\omega_{c}\simeq
300v_{0}/R_{0}$, thus showing that the collective maintains the capacity to
cover an area well beyond the individual agents’ limitations, an expected and
sought feature of swarming systems.

###  IV-B Ideal Heterogeneous Swarm

Next, we consider the case where the agents are not identical, and a fraction
$\rho_{F}$ of agents move at speed $v_{F}=2v_{0}$ while the rest move at
$v_{0}$. The performance of the system could in principle have a complicated
dependency on $\rho_{F}$, $v_{0}$, and $v_{F}$. However, we observe that as
long as the two speeds differ in approximately less than one order of
magnitude, the performance only depends on these parameters through the mean
speed of the collective,

$\langle v\rangle=(1-\rho_{F})v_{0}+\rho_{F}v_{F}.$ (12)

The results are identical to the homogeneous case if one makes the
substitution $v_{0}\rightarrow\langle v\rangle$, see Fig. 6. Therefore, a
heterogeneous swarm with a fraction $\rho_{F}$ of agents moving twice as fast
as the rest will have a cutoff frequency of the form

$\omega_{c}(\rho_{F})=(1+\rho_{F})\omega_{c}(\rho_{F}=0)\,.$ (13)

Figure 6: Frequency response of a heterogeneous swarm of $N=20$ agents where a
fraction $\rho_{F}$ of them move twice as fast as the rest, measured by its
Tessellation performance (top) and Coverage performance (bottom). The
different markers correspond to calculations with different fractions of fast
agents. Note that the frequency is normalized using the average speed, which
depends on $\rho_{F}$.

##  V Experimental Results

We have performed a series of field tests of dynamic area coverage using
$N=22$ buoys deployed in an uncontrolled environment with no supporting
infrastructure (Bedok Reservoir in Singapore). For each test, the collective
is tasked with covering the dynamic area defined by (2) with an $\alpha(t)$
oscillating at a certain frequency $\omega$. Given the parameters of the test
($R_{0}=25$ m and $v_{0}\simeq 0.5$ m/s), the system is expected to have a
collective cutoff frequency of approximately $\omega_{c}=0.02~{}s^{-1}$. This
means that, in general, one expects the swarm of buoys to be able to respond
to changes in coverage at a time scale of approximately 1 minute when covering
areas of the order of $1000~{}m^{2}$. The evolution of the Coverage
performance $P_{C}$, and Tessellation performance $P_{T}$ for one of these
experiments is presented in Fig. 7.

Figure 7: Evolution of the two metrics for collective response $P_{T}$ and
$P_{C}$ during a field experiment. The top panels show the distribution of the
18 v1 buoys (black dots) and 4 v2 ones (red triangles), along with the post-
processed tessellation (top) and coverage (bottom). The frequency of the
target area oscillations is $\omega=0.02$ s-1, close to the theoretically
predicted cutoff frequency of the collective.

As the core of this study is about heterogeneous swarming, we have also
carried out a series of tests to study the effect of replacing a small portion
($\rho_{F}=4/22$) of the ${v1}{}$ buoys by the faster and improved
model—design v2 presented in Sec. II. The theoretical prediction (see Fig. 6)
using an idealized model is that this heterogeneous system would display a
similar performance to the homogeneous case but with the frequencies shifted
by $\omega\rightarrow(1+\rho_{F})\omega=1.18\omega$. The experimental results
for a total of 7 field tests are presented in Fig. 8. The overall performance
of the homogeneous system, measured either by the tessellation or coverage
metrics, is about $25\%$ lower than the ideal case. This is a consequence of
(i) the real dynamics and controllability of the buoys, (ii) the precision and
accuracy of the GPS-based localization, and (iii) the finite communication
rate between buoys as part of the distributed communication network. All these
factors contribute to some extent, to the fact that the spatial distribution
of the buoys is not as uniform as the cooperative control algorithm allows
for.

Figure 8: Experimental frequency response of a swarm of buoys tasked with
dynamic area coverage. The homogeneous system is composed of 22 v1 buoys while
the heterogeneous case has 18 v1 and 4 v2.

Introducing heterogeneity in the real swarming system yields interesting
results regarding its collective response (see Fig. 8). Instead of slightly
improving both performance metrics as in the ideal case (see Sec. IV), what we
observe is that a small proportion ($\rho_{F}=4/22\simeq 18\%$) of faster
buoys dramatically improves the coverage performance of the system while
having a negligible effect on the tessellation performance.

As discussed before, the tessellation metric measures the performance of the
system at the location where the deployment is the least uniform, and it is
therefore primarily sensitive to the worst-performing section of the system.
The coverage metric, in contrast, takes into account the deployment of all
buoys and thus measures the system-level performance of this swarming system.
These experimental observations reveal how the heterogeneity affects the
operations of the system. Since the agents form a regular lattice in the
target area and have a relatively small mobility within that lattice, the
faster buoys (v2) can only use their higher speed to improve the deployment in
the vicinity of their location in the lattice. This improvement always
translates into an improved average performance, and thus an improved
coverage. However, if the worst-performing agent happens to be far from the v2
buoys—e.g. in the snapshots of Fig. 7, these cannot affect its performance,
and thus the tessellation performance remains virtually the same as in the
heterogeneous case.

##  VI Discussion

The efficient collective operation of heterogeneous swarms has been identified
as one of the key challenges in robotics [15]. In general, such a swarm can be
composed of a large number of different classes of agents where some may be
specialized in specific tasks such as sensing, communications, or (sensed)
data processing. However, with complex systems yielding emergent behaviors, it
is not obvious that such individual enhancements of a fraction of the agents
automatically translate into an increased collective performance. In this
work, we study the effect of increasing the motor capabilities of 18% of the
agents on the responsiveness of the group when performing a dynamic area
monitoring in real-world and unstructured water environments.

Experimentally, we observe that the timescale at which the system is able to
respond is in good agreement with the theoretical prediction, confirming that
this distributed smart sensor array of buoys is capable of responding to
changing environments on the order of the minute, which is well beyond what is
needed to track morphological changes in oil spills, algal blooms, or other
surface contaminants.

We also present empirical evidence that the partial upgrade of the system
improves the responsiveness of the system when using a cooperative control
algorithm designed for homogeneous systems and that does not explicitly take
into account the different motor capabilities of the heterogeneous set of
agents. We measure the performance of the system with two metrics, the
tessellation $P_{T}$ and the coverage $P_{C}$ performances. Since $P_{T}$ only
takes into account the agent with the largest area to cover, it is an
individual measure of the “weakest link” in the system. As such, it is
indicative of the robustness of the collective. $P_{C}$, on the other hand,
measures an average collective performance that is less sensitive to any
individual agent’s behavior. While the partial upgrade makes the system more
capable of dynamically covering a target area on average ($P_{C}$), it does
not improve the coverage of the least-covered regions ($P_{T}$).

In order to magnify the effect of the new and improved agents, the system
would need to operate taking into account the specific properties of the
different agents. For instance, a further improvement in the collective
responsiveness of this heterogeneous swarm could be achieved by developing a
new cooperative control strategy that positions the faster agents in the most
critical areas, or that implements an optimization procedure constrained by
the motor capabilities of the different agents. Such a procedure, however,
could prove difficult to maintain as it is not robust to hardware design
changes: as more kinds of agents are added during the life-cycle of the
collective, the control algorithm should grow in complexity to accommodate
these changes.

## Acknowledgments

This work was supported by Grants from the SUTD-MIT International Design
Center (IDC) and the Singapore Ministry of Education (MOE-Tier 1 Grant
#T1MOE1701). We are grateful for the assistance of B. Patel, H. Shekhar, S.
Jain, and P. Rastogi in preparing and performing the field tests described in
this work.

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