An Overview of Physicomimetics
William M. Spears, Diana F. Spears, Rodney Heil,
Wesley Kerr, and Suranga Hettiarachchi
Computer Science Department,
University of Wyoming, Laramie, WY, 82070, USA
wspears@cs.uwyo.edu
http://www.cs.uwyo.edu/∼wspears
Abstract. This paper provides an overview of our framework, called
physicomimetics, for the distributed control of swarms of robots. We
focus on robotic behaviors that are similar to those shown by solids,
liquids, and gases. Solid formations are useful for distributed sensing
tasks, while liquids are for obstacle avoidance tasks. Gases are handy for
coverage tasks, such as surveillance and sweeping. Theoretical analyses
are provided that allow us to reliably control these behaviors. Finally,
our implementation on seven robots is summarized.
1 Vision
The focus of our research is to design and build rapidly deployable, scalable,
adaptive, cost-effective, and robust swarms of autonomous distributed robots.
Our objective is to provide a scientific, yet practical, approach to the design and
analysis of swarm systems.
The team robots could vary widely in type, as well as size, e.g., from nanobots
to micro-air vehicles (MAVs) and micro-satellites. A robot’s sensors perceive
the world, including other robots, and a robot’s effectors make changes to that
robot and/or the world, including other robots. It is assumed that robots can
only sense and affect nearby robots; thus, a key challenge has been to design
“local” control rules. Not only do we want the desired global behavior to emerge
from the local interaction between robots (self-organization), but we also require
fault-tolerance, that is, the global behavior degrades very gradually if individ-
ual robots are damaged. Self-repair is also desirable, in the event of damage.
Self-organization, fault-tolerance, and self-repair are precisely those principles
exhibited by natural physical systems. Thus, many answers to the problems of
distributed control can be found in the natural laws of physics.
This paper provides an overview of our framework for distributed control,
called “physicomimetics” or “artificial physics” (AP). We use the term “artifi-
cial” (or virtual) because although we are motivated by natural physical forces,
we are not restricted to them [1]. Although the forces are virtual, robots act as if
they were real. Thus the robot’s sensors must see enough to allow it to compute
the force to which it is reacting. The robot’s effectors must allow it to respond
to this perceived force.
E. S¸ahin and W.M. Spears (Eds.): Swarm Robotics WS 2004, LNCS 3342, pp. 84–97, 2005.
c
© Springer-Verlag Berlin Heidelberg 2005

An Overview of Physicomimetics 85
There are two potential advantages to this approach. First, in the real phys-
ical world, collections of small entities yield surprisingly complex behavior from
very simple interactions between the entities. Thus there is a precedent for be-
lieving that complex control is achievable through simple local interactions. This
is required for very small robots, since their sensors and effectors will necessarily
be primitive. Second, since the approach is largely independent of the size and
number of robots, the results scale well to larger robots and larger sets of robots.
2 The Physicomimetics Framework
The basic AP framework is elegantly simple. Virtual physics forces drive a multi-
robot system to a desired configuration or state. The desired configuration (state)
is one that minimizes overall system potential energy. In essence the system acts
as a molecular dynamics (F = ma) simulation.
At an abstract level, AP treats robots as physical particles. This enables the
framework to be embodied in robots ranging in size from nanobots to satellites.
Particles exist in two or three dimensions and are point-masses. Each particle
i has position x and velocity v. We use a discrete-time approximation to the
continuous behavior of the system, with time-step ∆t. At each time step, the
position of each particle undergoes a perturbation ∆x. The perturbation depends
on the current velocity, i.e., ∆x = v∆t. The velocity of each particle at each time
step also changes by ∆v. The change in velocity is controlled by the force on the
particle, i.e., ∆v = F ∆t/m, where m is the mass of that particle and F is the
force on that particle. A frictional force is included, for self-stabilization. This is
modeled as a viscous friction term, i.e., the product of a viscosity coefficient and
the robot’s velocity (independently modeled in the same fashion by Howard et
al. [2]). We have also included a parameter Fmax, which restricts the maximum
force felt by a particle. This provides a necessary restriction on the acceleration a
robot can achieve. Also, a parameter Vmax restricts the velocity of the particles,
which is very important for modeling real robots.
Given a set of initial conditions and some desired global behavior, it is nec-
essary to define what sensors, effectors, and local force laws are required for the
desired behavior to emerge. This is explored, in the next section, for a variety of
simulated static and dynamic multi-robot configurations. Our implementation
with robots is discussed in Section 3.2.
3 Physicomimetic Results
Our research has focused on robotic behaviors that are similar to those shown by
solids, liquids, and gases. Solid crystalline formations are useful for distributed
sensing tasks, to create a virtual antenna or synthetic aperture radar. For such
tasks it is important to maintain connectivity and a lattice geometry. Liquids are
for obstacle avoidance tasks, since fluids easily maneuver around obstacles while
retaining connectivity. Solid and liquid behaviors are formed using a similar force
law, that has attractive and repulsive components. The transition between solids

86 William M. Spears et al.
and liquids can be performed via a change in only one parameter, which balances
the attractive and repulsive components [3].
Finally, gases are handy for coverage tasks, such as surveillance and sweeping
maneuvers. For these tasks it is imperative that coverage can be maintained,
even in the face of individual robot failures. Gas-like behaviors are created using
purely repulsive forces.
3.1 Simulation Results
Solids: Our initial application required that a swarm of MAVs self-organize into
a hexagonal lattice, creating a distributed sensing grid with spacing R between
MAVs [4]. Potential applications include sensing grids for the mapping or tracing
of chemical/biological plumes [5] or the creation of virtual antennas to improve
the resolution of radar images [1]. To map this into a force law, each robot repels
other robots that are closer than R, while attracting robots that are further than
R in distance. Thus each robot has a circular “potential well” around itself at
radius R – and neighboring robots will be separated by distance R. The inter-
section of these potential wells is a form of constructive interference that creates
“nodes” of low potential energy where the robots are likely to reside. A simple
compass construction illustrates that this intersection of circles of radius R will
form a hexagonal lattice where the robot separation is R. Note that potential
energy (PE) is never actually computed by the robots. Robots compute local
force vectors. PE is only computed for visualization or mathematical analysis.
With this in mind, we defined a force law F = Gmimj/rp, where F ≤ Fmax
is the magnitude of the force between two particles i and j, and r is the distance
between the two particles. The variable p is a user-defined power, which ranges
from -5.0 to 5.0. Unless stated otherwise, we assume p = 2.0 and Fmax = 1 in
this paper. Also, mi = 1.0 for all particles (although the framework does not
require this). The “gravitational constant” G is set at initialization. The force
is repulsive if r < R and attractive if r > R. Each particle has one sensor that
can detect the distance and bearing to nearby particles. The one effector enables
movement with velocity v ≤ Vmax. To ensure that the force laws are local, we
allow particles to sense only their nearest neighbors. Hence, particles have a
visual range of only 1.5R.
A simple generalization of this force law will also create square lattices. If
robots are arbitrarily labeled with one of two colors, then square lattices are
formed if robots that have unlike colors have a separation of R, while robots that
have like colors have separation
√
2R. Furthermore, transformations between
square and hexagonal lattices (and vice versa) are easily accomplished. Figure 1
illustrates formations with 50 robots. The initial deployment configuration (left)
is assumed to be a tight cluster of robots. The robots move outwards into a square
formation (middle). Then they transform to a hexagonal formation (right). Self-
repair in the face of agent failure is also straightforward [6].
The total PE of the initial deployment configuration is an excellent indicator
of the quality of the final formation. High PE predicts high quality formations.

An Overview of Physicomimetics 87
Fig. 1. The initial deployment configuration (left) is assumed to be a fairly tight cluster
of robots. The robots move outwards into a square formation (middle). Then they
transform to a hexagonal formation (right).
This energy is dependent on the value of G, and it can be proven that the optimal
value of G for hexagonal lattices is [7]:
Gopt
 = FmaxRp[2 − 1.51−p]
p/(1−p)
(1)
The value of Gopt does not depend on the number of particles, which is a nice
result. However, for square lattices:
Gopt

= FmaxRp
[
√
2(N − 1)[2 − 1.31−p] + N [2 − 1.71−p]
√
2(N − 1) + N
]p/(1−p)
(2)
Note that in this case Gopt depends on the number of particles N . It occurs
because there are two classes (colors) of robots. However, the dependency on N
is not large and goes to zero as N increases.
Our current research is focused on the movement of formations through
obstacle fields towards some goal. Larger obstacles are created from multiple,
point-sized obstacles; this enables flexible creation of obstacles of arbitrary size
and shape. As a generalization to our standard paradigm, goals are attractive,
whereas obstacles are repulsive (similar to potential field approaches, e.g., [8]).
Figure 2 illustrates how a square formation moves through an obstacle field
via a sequence of rotations and counter-rotations of the whole collective. This
Fig. 2. A solid formation moves through an obstacle field towards a goal (upper left
part of the field). The rotations and counter-rotations of the whole collective are an
emergent property.

88 William M. Spears et al.
behavior emerges from the interaction of forces and is not a programmed re-
sponse. If this cannot be accomplished, the formation may not be able to make
further progress towards the goal.
Liquids: As stated above, the difference in behavior between solid formations
and liquid formations depends on the balance between the attractive and repul-
sive components of the forces. In fact, the parameter G once again plays a crucial
role. Below a certain value of G ≡ Gt, liquid behavior occurs. Above that value,
solid behavior occurs. The switch between the two behaviors acts very much like
a phase transition. Using a standard balance of forces argument we can show
that the phase transition for hexagonal lattices occurs at [3]:
Gt
 =
FmaxRp
2
√
3
(3)
The phase transition law for square lattices is:
Gt

=
FmaxRp
2
√
2 + 2
(4)
Neither law depends on the number of robots N , and the difference in the
denominators reflects the difference in hexagonal and square geometries. There
are several uses for these equations. Not only can we predict the value of Gt
at which the phase transition will occur, but we can also use Gt to help design
our system. For example, a value of G ≈ 0.9Gt yields the best liquid formation,
while a value of G ≈ 1.8Gt ≈ Gopt yields the best solid formations.
As mentioned before, liquids are especially interesting for their ability to
flow through obstacle fields, while retaining their connectivity. Figure 3 illus-
trates how a “square” liquid formation moves through the same obstacle field as
before. In comparison with the solid formation shown above, far more deforma-
tion occurs as the liquid moves through the obstacles. However, the movement
is quicker, because the liquid does not have to maintain the rigid geometry of
the solid. Despite this, connectivity is maintained. One can easily imagine a sit-
uation where a formation lowers G to move around obstacles, and then raises G
to “re-solidify” the formations after the obstacles have been avoided.
Fig. 3. A liquid formation moves through the same obstacle field towards the goal. Far
more deformation occurs, but connectivity is maintained.

An Overview of Physicomimetics 89
Gases: The primary motivation for gas behavior is regional coverage, e.g., for
surveillance and sweeping. For stealth it is important for individual robots to
have an element of randomness, while the emergent behavior of the collective is
still predictable. Furthermore, any approach must be robust in the face of robot
failures or the addition of new robots. The AP algorithm for surveillance is
simple and elegant – agents repel each other, and are also repelled by perimeter
and obstacle boundaries, providing uniform coverage of the region. If robots
are added/destroyed, they still search the enclosed area, but with more/less
virtual “pressure” [6]. An interesting phase transition for this system depends
on the value of G. When G is high, particles fill the corridor uniformly, providing
excellent on-the-spot coverage. When G is low, particles move toward the corners
of the corridor, providing excellent line-of-sight coverage. Depending on whether
the physical robots are better at motion or sensing, the G parameter can be
tuned appropriately.
Currently we are investigating the more difficult task of “sweeping” a region,
while avoiding obstacles. This task consists of starting a swarm of robots at
one end of a corridor-like region, and allowing them to travel to the opposite
end, providing maximum coverage of the region in minimal time. A goal force
causes the robots to traverse the corridor length. As they move, robots must
not only avoid obstacles, but they must also sweep in behind the obstacles to
minimize holes in the coverage. One obvious tradeoff is the speed at which the
robots move down the corridor. If they move quickly, they traverse the corridor
in minimal time, but may move too quickly to sweep in behind obstacles. On
the other hand, excellent sweeping ability behind obstacles can significantly slow
the swarm. What is required is a Pareto optimal solution that balances sweeping
ability with traversal speed vtraversal.
To address this task we modified our standard AP algorithm to employ a
more realistic gas model that has Brownian motion and expansion properties
[9]. The collective swarm behavior appears as Brownian motion on a small scale,
and as a directed bulk movement of the swarm when viewed from a macroscopic
perspective. The expansion properties provide across-corridor coverage and the
ability to sweep in behind obstacles. An analogy would be the release of a gas
from the ceiling of the room that has an atomic weight slightly higher than the
normal atmosphere. This gas drifts downward, moving around obstacles, and
expanding back to cover the areas under the obstacles.
As mentioned above, speed of movement down the length of the corridor
is governed by vtraversal. However, the expansion properties (across the corri-
dor width) are governed by a temperature parameter T , which determines the
expected kinetic theory speed [9]:
〈vkt〉 =
1
4
√
8πkT
m
(5)
where k is Boltzmann’s constant. Note that 〈vkt〉 is an emergent property of
the system – each robot can continually change its velocity, based on “virtual”
robot/robot, robot/obstacle, and robot/corridor collisions. The net effect is to

90 William M. Spears et al.
Fig. 4. These three figures depict a sweep of a swarm of robots from the top of a
corridor to the bottom.
provide a stochastic component to each robot, while maintaining predictable col-
lective behavior. The resultant velocity of each robot depends on both vtraversal
and 〈vkt〉. In other words, although the speed of the swarm is predictable, the
individual robot velocities are not. This is especially valuable for stealthy surveil-
lance.
Figure 4 illustrates the compromise between traversal speed and the quality of
the sweep, providing effective coverage in reasonable time, with the exception of
small gaps behind the obstacles. Numerous experiments with different corridors
confirm this effectiveness in simulation [10].
3.2 Results with Robots
The current focus of this project is the physical embodiment of AP on a team
of robots.
For our experiments, we built seven robots. The “head” of each robot is a
sensor platform used to detect other robots in the vicinity. For distance infor-
mation we use Sharp GP2D12 IR sensors. The head is mounted horizontally on
a servo motor. With 180◦ of servo motion, and two Sharp sensors mounted on
opposite sides, the head provides a simple “vision” system with a 360◦ view.
After a 360◦ scan, object detection is performed. A first derivative filter detects
object boundaries, even under conditions of partial occlusion. Width filters are
used to ignore narrow and wide objects. This algorithm detects nearby robots,
producing a “robot” list that gives the bearing/distance of neighboring robots.
Once sensing and object detection are complete, the AP algorithm computes
the virtual force felt by that robot. In response, the robot turns and moves to
some position. This “cycle” of sensing, computation and motion continues until
we shut down the robots or they run out of power. Figure 5 shows the AP code.

An Overview of Physicomimetics 91
void ap() {
int theta, index = 0;
float r, F, fx, fy, sum_fx = 0.0, sum_fy = 0.0;
float vx, vy, delta_vx, delta_vy, delta_x, delta_y;
vx = vy = 0.0; // Full friction.
// Row i of robots[][] is for the ith robot located.
// Column 0/1 has the bearing/range to that robot.
while ((robots[index][0] != -1)) { // For all neighboring robots do:
theta = robots[index][0]; // get the robot bearing
r = robots[index][1]; // and distance.
if (r > 1.5 * R) F = 0.0; // If robot too far, ignore it.
else {
F = G / (r * r); // Force law, with p = 2.
if (F > F_MAX) F = F_MAX;
if (r < R) F = -F; // Has effect of negating force vector.
}
fx = F * cos(theta); // Compute x component of force.
fy = F * sin(theta); // Compute y component of force.
sum_fx += fx; // Sum x components of force.
sum_fy += fy; // Sum y components of force.
index++;
}
delta_vx = delta_T*sum_fx; // Change in x component of velocity.
delta_vy = delta_T*sum_fy; // Change in y component of velocity.
vx = vx + delta_vx; // New x component of velocity.
vy = vy + delta_vy; // New y component of velocity.
delta_x = delta_T*vx; // Change in x component of position.
delta_y = delta_T*vy; // Change in y component of position.
// Distance to move.
distance = (int)sqrt(delta_x*delta_x + delta_y*delta_y);
// Bearing of movement.
turn = (int)(atan2(delta_y, delta_x));
// Turn robot in minimal direction.
if (delta_x < 0.0) turn += 180; }
Fig. 5. The main AP code, which takes as input a robot neighbor list (with distance
and bearing information) and outputs a vector of motion.
It takes a robot neighbor list as input, and outputs the vector of motion in terms
of a turn and distance to move.
To evaluate performance we ran two experiments. The objective of the first
experiment was to form a hexagon. The desired distance R between robots was
23 inches. Using the theory, we chose a G of 270 (p = 2 and Fmax = 1). The
beginning configuration was random. The results were very consistent, producing
a good quality hexagon ten times in a row and taking approximately seven cycles
on average. A cycle takes about 25 seconds to perform, almost all of which is
devoted to the scan of the environment. The AP algorithm itself is extremely fast.
A new localization technology that we are developing will be much faster and

92 William M. Spears et al.
Fig. 6. Seven robots self-organize into a hexagonal formation, which then successfully
moves towards a light source (a window, not the reflection of the window). Pictures
taken at the initial conditions, at two minutes, fifteen minutes, and thirty minutes.
will replace the current scan technique. For all runs the robots were separated
by 20.5 to 26 inches in the final formation, which is only slightly more error than
the sensor error.
The objective of the second experiment was to form a hexagon and then move
in formation to a goal. For this experiment, we placed four photo-diode light
sensors on each robot, one per side. These produced an additional force vector,
moving the robots towards a light source (a window). The magnitude of the goal
force must be less than
√
3G/Rp for cohesion of the formation to be maintained
[11]. The results, shown in Figure 6, were consistent over ten runs, achieving
an accuracy comparable to the formation experiment above. The robots moved
about one foot in 13 cycles of the AP algorithm.
In conclusion, the ability to set system parameters from theory greatly en-
hances our ability to generate correct robotic swarm behavior.
4 Discussion and Outlook
This paper has summarized our framework for distributed control of swarms of
robots in sensor networks, based on laws of artificial physics (AP). The moti-
vation for this approach is that natural laws of physics satisfy the requirements
of distributed control, namely, self-organization, fault-tolerance, and self-repair.
The results have been quite encouraging. We illustrated how AP can self-organize
hexagonal and square lattices. Results showing fault-tolerance and self-repair are
in [1]. We have also summarized simulation results with dynamic multi-agent be-
haviors such as obstacle avoidance, surveillance, and sweeping. This paper also
outlines several physics-based analyses of AP, focusing on potential energy, force

An Overview of Physicomimetics 93
balance equations, and kinetic theory. These analyses provide a predictive tech-
nique for setting parameters in the robotic systems. Finally, we have shown AP
on a team of seven mobile robots.
We consider AP to be one level of a more complex control architecture.
The lowest level controls the movement of the robots. AP is at the next higher
level, providing “way points” for the robots, as well as providing simple repair
mechanisms. Our goal is to put as much behavior as possible into this level, in
order to provide the ability to generate laws governing important parameters.
However, levels above AP are needed to solve more complex tasks requiring
planning, learning, and global information [12].
5 Future Work
Currently, we are improving our mechanism for robot localization. This work is
an extension of Navarro-Serment et. al. [13], using a combination of RF with
acoustic pulses to perform trilateration. This will distinguish robots from ob-
stacles in a straightforward fashion, and will be much faster than our current
“scan” technique.
We also plan to address the topic of optimality, if needed. It is well understood
that potential field (PF) approaches can yield sub-optimal solutions. Since AP is
similar to PF, similar problems arise with AP. Our experience thus far indicates
that this is not a crucial concern, especially for the tasks that we have examined.
However, if optimality is required we can apply new results from control theory
to design force laws that guarantee optimality [14, 15]. Although oscillations of
the formations do not occur, excess movement of the robots can occur due the
fact that the force law F = Gmimj/rp is not zero at the desired separation
distance R. Current work using an alternative force law based on the Lennard-
Jones potential, where the magnitude of the force is negligible at the desired
separation, greatly minimizes this motion.
From a theoretical standpoint, we plan to formally analyze other important
aspects of AP systems. This analysis will be more dynamic (e.g., kinetic theory)
than the analysis presented here. We also intend to expand the repertoire of
formations, both static and dynamic. For example, initial progress has been
made on developing static and dynamic linear formations. Many other formations
are possible within the AP framework. Using evolutionary algorithms to create
desired force laws is one intriguing possibility that we are currently investigating.
We summarize one preliminary experiment here.
5.1 Evolving Force Laws for Surveillance
This task consists of an environment with areas of forest and non-forest. The goal
is for a swarm of MAVs to locate tanks on the ground. Tanks are hidden from the
MAVs if they are in the forest. Each MAV has a target sensor with a small field
of view for locating the tanks (with probability of detection Pd), and a foliage
sensor with a larger field of view for detecting forest below it. The environment

94 William M. Spears et al.
is shown in Figure 7 with three MAVs. The smallest circle represents the target
sensor. The next largest circle represents the foliage field of view. Each MAV
acts as if it were contained in a “bubble” that has a certain radius (depicted as
the outer circle). If the bubbles of two MAVs are separated from each other, the
MAVs are attracted to one another. If the bubbles overlap, they are repelled.
The optimum MAV separation occurs when the bubbles touch.
Fig. 7. The surveillance environment, showing areas of forest, three MAVs, and 100
tanks. The triangle represents a tank that has not yet been seen but is visible, the +
represents a tank that has been seen and is visible, the × represents a hidden tank
that has not been seen, and the | represents a tank that is currently hidden but has
been previously seen.
A genetic algorithm is used to find the optimum bubble radius, as well as the
G, p, and Fmax parameters of the force law. We generated one environment with
100 tanks, 25% forest coverage, 20 MAVs, and Pd = 1. The GA fitness function
was the percentage of tanks seen within 3000 time steps. In this “training” phase
the GA was used to evolve a force law, that when used by all MAVs, created
perfect coverage (all tanks were seen).
Testing consisted of generating other environments and performing ablation
studies. First, nine other environments were created with the same parameter
settings. The MAVs had no difficulty finding all tanks. Next, the percentage of

An Overview of Physicomimetics 95
foliage was systematically changed from 0% to 90% in increments of 10%. In all
cases the MAVs found all tanks. Finally, two ablation studies were performed.
First, the number of MAVs was reduced from 20, to 15, to 10, and then to 5.
The results were quite robust; performance only suffered when the number of
agents was reduced to 5. Second, we also lowered the probability of detection Pd
from 1.0, to 0.75, to 0.5, and then to 0.25. Again, the results were quite robust,
showing negligible performance drops (see Figure 8).
In summary, the results are extremely promising. Using only one training
environment, the GA evolved a force law that showed surprising generality over
changes in the environment, the number of MAVs, and the quality of the target
detection sensor.
0
10
20
30
40
50
60
70
80
0 1000 2000 3000 4000 5000
Ta
nk
s
Fo
un
d
Time
20 MAVs
10 MAVs
5 MAVs
0
10
20
30
40
50
60
70
80
0 1000 2000 3000 4000 5000
Ta
nk
s
Fo
un
d
Time
Pd = 1.0
Pd = 0.25
Fig. 8. The number of tanks found as the number of MAVs is reduced (left graph).
The number of tanks found as the probability of detection (Pd) of the target sensor is
reduced (right graph). The number of visible tanks is 73.
6 Related Work
Most of the swarm literature can be subdivided into swarm intelligence, behavior-
based, rule-based, control-theoretic and physics-based techniques. Swarm intelli-
gence techniques are ethologically motivated and have had excellent success with
foraging, task allocation, and division of labor problems [16]. In Beni et. al. [17,
18], a swarm distribution is determined via a system of linear equations de-
scribing difference equations with periodic boundary conditions. Behavior-based
approaches [19–22] are also very popular. They derive vector information in a
fashion similar to AP. Furthermore, particular behaviors such as “aggregation”
and “dispersion” are similar to the attractive and repulsive forces in AP. Both
behavior-based and rule-based (e.g., [23]) systems have proved quite successful
in demonstrating a variety of behaviors in a heuristic manner. Behavior-based
and rule-based techniques do not make use of potential fields or forces. Instead,
they deal directly with velocity vectors and heuristics for changing those vectors
(although the term “potential field” is often used in the behavior-based litera-
ture, it generally refers to a field that differs from the strict Newtonian physics
definition). Control-theoretic approaches have also been applied effectively [14].
Our approach does not make the assumption of having leaders and followers [24].

96 William M. Spears et al.
One of the earliest physics-based techniques is the potential fields (PF) ap-
proach (e.g., [8]). Most of the PF literature deals with a small number of robots
(typically just one) that navigate through a field of obstacles to get to a target
location. The environment, rather than the agents, exert forces. Obstacles exert
repulsive forces, while goals exert attractive forces. Recently, Howard et al. [2]
and Vail and Veloso [25] extended PF to include inter-agent repulsive forces –
for the purpose of achieving coverage. Although this work was developed inde-
pendently of AP, it affirms the feasibility of a physics force-based approach. The
social potential fields [26] framework by Reif and Wang is highly related to AP,
in that they rely on a force-law simulation similar to our own. We plan to merge
their approach with ours.
Acknowledgments
The surveillance task mentioned in this paper is supported by DARPA grant
#DODARMY41700. Thanks to Vaibhav Mutha for an early version of the ob-
stacle avoidance code.
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