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Abstract—In this paper, we present a strategy of path-planning
for an unmanned aerial vehicle (UAV) to follow a ground vehicle.
The ground vehicle may change its heading and vary its speed
from a standstill up to the velocity of the UAV, while the UAV
will maintain a fixed airspeed and will maneuver itself to track
the ground vehicle. The algorithm also allows the UAV to track
the ground vehicle with an offset vector (i.e. the user may wish
the UAV to stay ahead of the ground vehicle or to its sides). Since
the ground vehicle may operate in a range of velocities, the
algorithm must plan the UAV’s path with the appropriate
schemes for the various ground vehicle speeds. The natural effect
of wind injects a disturbance into the system, and so wind
compensation techniques had to be developed. In order to
maintain the focus of this project on path-planning strategies, the
path-planning algorithm was implemented on top of a system that
already controls the dynamics of the UAV. Simulation of aircraft
and ground vehicles was performed with a hardware-in-the-loop
simulation environment to test for mission feasibility. After
attaining satisfactory simulation results, an experiment was
conducted to confirm the path-planning strategy.
Index Terms—Aircraft navigation, Mobile robot motion-
planning, Surveillance, Tracking, Unmanned aerial vehicles.
I. INTRODUCTION
In order for a UAV to function in a useful manner in any
application, care must be taken to construct a path to ensure
mission success. Current techniques for path planning of
UAVs are often done on a “per-application” basis, and some
even require manual computation of navigation information in
real-time, which severely hinders UAVs from achieving a
more autonomous role [3]. Certainly, different applications of
the UAV call for different path-planning strategies. For,
example the path of a drone conducting border patrol missions
will vary from that of one performing terrain mapping or
planetary exploration [1, 2, 3]. Nevertheless, the high-level
Manuscript received May 5, 2003. (submitted for review on Feb. 24, 2003)
This work was supported in part by the Office of Naval Research (ONR)
under STTR Phase I Grant N00014-02-M-0236
* Authors are with the Department of Mechanical Engineering at the
University of California, Berkeley. (e-mail: {jlee, rosemary, xiao, acvaughn,
khedrick}@vehicle.me.berkeley.edu).
‡ Authors are with the Department of Civil and Environmental
Engineering at the University of California, Berkeley. (e-mail: {zennaro,
raja}@path.berkeley.edu).
navigation needs of many types of applications may be
answered through waypoint navigation [4].
The purpose of this effort in UAV research is to provide
local as well as “over-the-horizon” visual coverage for a
ground vehicle from a UAV that is equipped with a camera.
The constant aerial coverage from the UAV is achieved by
flying the UAV autonomously over a region of interest. This
region of interest may be directly on top of the ground vehicle,
or be as far as a mile ahead of the ground vehicle’s velocity
vector. An additional requirement of maintaining a constant
airspeed for the UAV is also imposed for fuel efficiency
purposes. Not forgetting the human factor, a user-friendly
interface must be generated to ensure maximum functionality
of such UAV system [5].
To fulfill these demands, an algorithm based on waypoint
strategy was created. Under the guidance of this navigation
scheme, the UAV will fly in a sinusoidal manner and change
the amplitude of the sinusoid, all the while maintaining a
constant velocity and tracking the ground vehicle that has
varying speed. Additionally, cases were also taken into
account where the ground vehicle is at a stand still. Finally,
simplicity was maintained when designing the user interface.
This paper focuses on the implementation strategies of
tracking a ground vehicle using a UAV. Special emphasis is
placed on the details of generating the sinuous path. Results
from simulation as well as a real flight test are presented to
demonstrate the effectiveness of this autonomous navigation
scheme.
II. PATH-PLANNING ALGORITHM
The central goal of the path-planning algorithm is to
maneuver the UAV to track the movement of a ground vehicle.
The tracking procedure may be at some offset distance with
respect to the ground. In other words, the UAV could be half
a kilometer to the east of the ground vehicle, and if the ground
vehicle were to move north, the UAV must also fly north but
maintaining the offset to the east of the ground vehicle. The
tracking procedure must also change its strategy when the ratio
of the UAV velocity, vP, to that of the ground vehicle velocity,
vB, goes above a threshold ratio (in this application,
approximately 3:1). This preset ratio is determined by the
limitation of the UAV’s autopilot avionics.
As a result, the behavior of the UAV is separated into two
Strategies of Path-Planning for a UAV to Track
a Ground Vehicle
Jusuk Lee, Rosemary Huang, Andrew Vaughn, Xiao Xiao, and J. Karl Hedrick*
Marco Zennaro and Raja Sengupta‡
modes (loitering or sinusoidal) depending on the velocity of
the ground vehicle. If the velocity of the ground vehicle is
much slower than that of the UAV (i.e. velocity ratio is above
the threshold), the UAV will be in the loitering mode;
otherwise, the UAV will go into the sinusoidal mode. The
sinusoidal curve in Fig. 1 illustrates the desired path the UAV
will follow using the sinusoidal algorithm. The amplitude of
the sinusoid, A, varies according to the ratio of vP and vB. In
this figure, the UAV has no angular offset but only a distance
offset, which leads the ground vehicle by a distance, d. This
will be the assumption for the rest of the derivations in this
section, as the concept may be extended to the case when a
different angular and/or distance offsets are desired. In the
figure the dashed line is the projected path the ground vehicle
is to follow. It will be referred to as the ground vehicle’s
“travel path” from now on.
D2
D1
y2
A
vB
y1
x2
x1
vP
xP
yP
D1
vB*T
d
Fig. 1. Top view of path-planner algorithm in sinusoidal mode
In Fig. 1, two coordinate systems are shown, one fixed to
the ground vehicle, x1-y1, and the other the beginning of the
sinusoid, x2-y2. Both are oriented in the same direction with
the x-axes pointing the direction of the ground vehicle’s travel.
D2 is the distance in the x direction the UAV will travel in one
time period, T, of the sinusoid. It will equal the distance, D1,
that the ground vehicle will travel in the same direction. Thus,
D1 = vBT, where the period T is arbitrarily chosen. Using this
fact, the equation of a sinusoid can be transformed into an
equation that describes the sinusoidal path in terms of the x2-y2
coordinate system,
=
1
2
sin D
x
Ay P
P
π
. (1)
Here, xP and yP are the desired position of the UAV relative
to the stationary x2-y2 coordinate system. Taking the time
derivative yields
P
P
Px
Dx
Ay ⋅
=
2
2
cos'
π
(2)
where 2
2' DAA
π
=. The magnitude of the UAV velocity, vP,
is related to its x and y components via
222 PPP vyx =+ . (3)
Substituting equation 2 into 3 results in
22
2
222 2
cos'PP
P
Pvx
Dx
Ax =⋅
+
π
, (4)
which after some algebraic manipulation becomes
+
=
2
22 2
cos'1 Dx
A
v
x
P
P
P
π
(5)
Equation 2 and 5 are used in the implementation of this
algorithm to calculate the desired path of the UAV.
Proceeding further, an equation is now derived that will relate
the ratio of the UAV velocity and the ground vehicle velocity
with the amplitude. First, note that dtdxxPP =
, which allows
us to express equation 5 as the following integral,
P
DP
P
Tdx
Dx
A
v
dt ∫∫
+= 2
02
22
0
2
cos'1
1
π
(6)
Now, since
Tdt
T
=
∫0, B
vDT 1
=, and D2 = D1, (7)
Equation 6 becomes
P
DP
PB
dx
D
x
A
vv
D∫
+= 1
01
22
12
cos'1
1
π
, (8)
Let the velocity ratio be BP vv /=
σ
, then
P
DPdx
D
x
A
D∫
+= 1
01
22
1
2
cos'1
1
π
σ
, (9)
This equation is used in the implementation to determine the
A, amplitude of the sinusoid, based on σ. Equation 9 is a
variation of a complete elliptic integral of the second kind,
which means it can be expressed as
))'((
12
1
2
AE −
π
(10)
where E(…) is the aforementioned elliptic integral expressed
in function form. [6].
Fig. 2 is a plot of σ versus the ratio A/D1 based on Equation
9. The plot shows that using this equation, the amplitude of
the sinusoid will increase as the velocity ratio gets larger. This
makes sense because a larger σ corresponds to an increasing vP
or a decreasing vB. In both cases the amplitude needs to be
enlarged to slow the rate at which the plane follows the travel
path.
If the value of σ is above a certain threshold value, h
σ
, the
UAV will exit the sinusoidal mode that generates the
trajectory as discussed above and enter into the loitering
mode. The UAV will then loiter about a specified position, at
the offset angle and distance, relative to the ground vehicle.
The value of h
σ
is set to avoid the large amplitude that would
be caused by the high value of σ. If the value of σ decreases
below h
σ
, then the sinusoidal algorithm will continue.
Fig. 2. Speed ratio, σ, vs amplitude/distance, A/D1, ratio of path-
planning algorithm (all D1 values overlap)
In the loitering mode, the UAV enters into a circle or rose
curve trajectory (this is a user-defined option). In the circle
trajectory, the plane circles about a set point and essentially
maintains a constant bank angle. The rose curve is beneficial
because it will allow a camera on the bottom of the plane to
face the ground for a greater amount of time than when
circling. The rose curve is created by giving the plane
waypoints in a line and then after the plane has gone through
those points the line is rotated about a fixed center at the
desired offset from the ground vehicle. Once the line is
rotated, waypoints are given along the new line. This pattern
continues, until σ decreases below h
σ
. In either of the path-
planning modes, the UAV’s offset is centered at the ground
vehicle and defined by a cardinal direction, θ, and a distance,
L, as seen in Fig. 3.
Fig. 3. Top view of path-planning algorithm in loitering mode
III. WIND COMPENSATION
The ground velocity of the UAV is used for the path-
planning algorithm. However, when wind is present the
UAV’s ground velocity changes, while the true air speed of the
UAV is kept constant. Therefore, not only will the UAV have
difficulty following the sinusoidal path, but also the path-
generation algorithm will also generate paths with undesirable
features. Fortunately, the UAV has the capability to estimate
the wind velocity, which can be used by the path-generation
algorithm. This new path is offset at a ratio of the wind
velocity vector; therefore adding or subtracting to the distance
of the next waypoint for the UAV to go to. Additionally, a
hysteresis was added to eliminate frequent switching between
the loitering and sinusoidal modes that is caused by the
fluctuation of the UAV’s ground speed.
IV. SOFTWARE PLATFORM
In order to most efficiently develop, test, and debug the
system, a “controller development platform” (CDP) was
developed on top of the low-level UAV controller software,
which is provided by CloudCap Technology Incorporated [7].
The CDP facilitates the development process by taking care of
the tasks of data collection, unit conversion, and
communication. It simplifies the testing and debugging of any
controller algorithm by offering a hardware-in-the-loop
simulation environment and a real-time feedback of the
controller behaviors through the CDP GUI. The hardware-in-
the-loop strategy reduced development time, especially
because the simulation software differs from the actual
software merely by a few compiler flags.
The software architecture of the CDP is illustrated in Fig. 4.
The control developer is only required to implement one of the
modules, the controller module, while everything else is ready
for test flight.
Fig. 4. CDP software architecture
The bottom layer of the CDP is the CloudCap
Communication SDK, which is a library that provides
communication primitives between the controller and the
ground station through a serial port. The library comes with a
simple packet dispatcher. Inside this module we nested our
routines to forward the packets that we receive from the
ground station to one of the two modules: the real ground
vehicle status module or the UAV status module. In turn, these
modules keep track of the status of their respective vehicles.
CONTROLLER
Packet Dispatcher
Cloudcap SDK
Ground Vehicle
Model
MUX
LLA/LOCA CONVERSION
GUI
Real Ground
Vehicle Status UAV Status
The MUX module is a set of switches that route the ground
vehicle information appropriately.
The LLA / LOCA conversion module is used for coordinate
transformations between the ground vehicle’s local coordinate
system (LOCA) and GPS Longitude Latitude Altitude format
used by the UAV autopilot.
The interaction between the user and the software is
managed through a GUI module. The user can observe the
state of the UAV, the ground station, and the controller
algorithm, and also command and alter the behavior of the
path-planning controller. In addition, the GUI is used to
“drive” the simulated ground vehicle during the development
phase.
V. SIMULATION IMPLEMENTATION AND RESULTS
We have successfully simulated the path-planning algorithm
using the CDP and simulation hardware and software provided
by CloudCap [7]. A ground vehicle simulation was also
developed in order to aid in the simulation and send its status
to the ground vehicle model module of the CDP. The discrete
time equations for the position of the ground vehicle are given
by Equations 11 and 12:
xLat(k+1) = xLat(k)+ vN∆T (11)
xLong(k+1) = xLong(k) + vE∆T (12)
where the position of the ground vehicle model is reported in
degrees of latitude, xLat, and longitude, xLong. The velocity
magnitude in the north direction is vN and the velocity in the
east direction is vE. Since the algorithm is run once every
second, an update of the ground vehicle model’s position
occurs at 1Hz, and so the ∆T in Equations 11 and 12 is set to
one.
The velocity vector of the ground vehicle is determined
through the heading and the speed. Equations 13 and 14
calculate the velocity in terms of radius of the earth and in
units of degrees.
π
ψ
180
)cos( ⋅=
Lat
B
Nr
v
v (13)
π
ψ
180
)sin( ⋅=
Long
B
Er
v
v (14)
where rLat and rLon are the radius of the earth in latitude and
longitude direction, respectively; vB is the magnitude of the
ground vehicle’s velocity vector whereas ψ and heading.
The ground vehicle’s position and velocity are used with the
path-planning algorithm in order for a simulated UAV to
follow a simulated ground vehicle before implementation with
the actual plane and ground vehicle. The simulated plane was
previously developed by CloudCap Technology.
Simulations were conducted to assist in the development of
the path-planning strategies and to confirm that the software
would work with an actual plane. The speed of the UAV is
held constant at approximately 20-23 m/s throughout all of the
simulations and experiments. The results of a simulation test
with the ground vehicle heading south at a constant 10 m/s are
shown in Fig. 5. The value of σ is approximately 2, which is
lower than the threshold value of hσ = 3; thus, the path is a sine
wave. There is no wind in this simulation.
-122.34 -122.335 -122.33 -122.325 -122.32 -122.315 -122.31
37.74
37.745
37.75
37.755
37.76
Longitude
L
a
t
i
t
u
d
e
Car Path
Desired Pat h
Plane Pat h
Fig. 5. Simulation of UAV and ground vehicle with no wind and the
ground vehicle traveling south at a constant velocity
The next step in the simulation process is to test the wind
compensation algorithm. The simulated plane estimates the
simulated wind velocity, which is used in the wind
compensation algorithm. The wind is simulated at 10 m/s
coming from the south. First, a simulation was conducted
without any wind compensation in the path-planning
algorithm. The resulting path is shown in Fig. 6. The ground
vehicle is traveling at 10 m/s to the north and then turns and
heads at 10 m/s to the east. The UAV has difficulty following
the sine wave with tail wind; the UAV goes too far and then
has to cut back. When the UAV has a crosswind it stays too
far away from the ground vehicle (to the side).
-122.3 -122.29 -122.28 -122.27 -122.26 -122.25 -122.24
37.59
37.595
37.6
37.605
37.61
37.615
37.62
37.625
37.63
37.635
Longitude
L
a
t
i
t
u
d
e
Car Path
Plane Pat h
Fig. 6. Simulation with 10 m/s south wind, constant speed in the
ground vehicle, and no wind compensation
Next, a simulation is shown with the wind compensation
added (Fig. 7). The wind and vehicle conditions are the same
as the previous experiment. Notice that the sine wave paths
are much better and the path is centered over the ground
vehicle. In the simulations and algorithms that we derived, we
only worked with constant wind; gusts have not yet been
considered.
-122.39 -122.385 -122.38 -122.375 -122.37 -122.365 -122.36 -122.355 -122.35 -122.345 -122.34
37.535
37.54
37.545
37.55
37.555
37.56
37.565
37.57
Longitude
L
a
t
i
t
u
d
e
Car Pat h
Plane Path
Fig. 7. Simulation with 10 m/s south wind, constant speed in the
ground vehicle, and wind compensation added
Fig. 8 demonstrates the viability of the loitering and
sinusoidal modes and the switch between the two modes. The
ground vehicle is heading approximately north at 8 m/s and
then comes to a halt. At that point the UAV enters into a
loitering mode and starts circling the ground vehicle. After a
couple of seconds, the offset distance is slowly increased so
that the plane will loiter over a region ahead of the ground
vehicle. (This can be seen by the circles that continue after the
car path ends.)
-122.31 -122.305 -122.3 -122.295 -122.29 -122.285 -122.28
37.735
37.74
37.745
37.75
37.755
37.76
Longitude
L
a
t
i
t
u
d
e
Car Path
Desired P ath
Plane Path
Fig. 8. Simulation with no wind and changing speed in the ground
vehicle (switch from sinusoidal to loitering mode)
As demonstrated above, reassuring simulation results were
attained, which increased the confidence for an experiment to
verify the path-planning strategy.
VI. EXPERIMENTAL RESULTS
A UAV furnished by Advanced Ceramics Research (ACR)
was outfitted with CloudCap Technology’s Piccolo® system
for low-level control. The path-planning algorithm was
incorporated into the CloudCap’s ground station software, and
the ground station was loaded in the bed of a truck.
The truck was driven at speeds varying from 0 to 45 mph
throughout the test. At all times the UAV followed the
motions of the truck by traveling either in a sine wave
trajectory or loitering. There was no angular offset for the test.
The UAV was set to be 40m in front of the truck at all times
and then loiter directly above the truck. There were low wind
conditions for the day of the test.
Fig. 9 shows the entire data from the experiment. The truck
mainly made 90° turns, per constraint of the desolate desert
highways in Tucson, Arizona. The truck first began to travel
towards the west with a high value of σ (i.e. slow moving
truck); therefore the UAV was in loitering mode. The truck
then returned to the starting point and then began to travel
south. At this point the σ-value is at around 2:1. Following,
the truck headed toward the east with the same sigma value.
Two miles later, the truck made a U-turn and reversed its route
to return to the starting point. Throughout the return trip the σ
–value was roughly 2:3. The long stretch throughout most of
the plot had a low enough σ-value for the UAV to stay in
sinusoidal mode.
Fig. 10 exhibits a close-up of the loitering mode. Notice the
path is circular instead of a rose curve. This was the loitering
pattern chosen for the day of the experiment. Fig. 11 separates
the long east to west stretch of the experiment from the rest of
the experimental data. The experimental results shown here
verify the simulation results.
-109.76 -109.75 -109. 74 -109.73 -109.72 -109. 71 -109.7 -109.69 -109.68
32.08
32.09
32.1
32.11
32.12
32.13
32.14
Longitude
L
a
t
i
t
u
d
e
Car Path
Desired Path
Plane Path
Fig. 9. Data from the entire experiment, with the UAV following a
truck. The truck started on the west side of the plot and drove east at
varying speeds, then turned back and retraced its path.
-109.7605 -109.76 -109.7595 -109.759 -109.7585 -109.758 -109.7575 -109.757
32.1145
32.115
32.1155
32.116
32.1165
32.117
Longitude
L
a
t
i
t
u
d
e
Car Pat h
Plane Path
Fig. 10. Close up of experimental data highlighting loitering mode
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32.085
32.09
32.095
32.1
32.105
32.11
32.115
32.12
32.125
32.13
32.135
Longitude
L
a
t
i
t
u
d
e
Car Path
Desired Path
Plane Path
Fig. 11. Close up of experimental data highlighting loitering mode.
The truck was traveling from the east to the west.
The real time video feed provided situational awareness
coverage at nearly all times during the test. The picture in Fig.
12 was captured from the video footage provided from
onboard the plane. The picture displays the plane’s view as it
passes over the truck. The points at which the plane path and
truck path cross are essentially the zero-point of the plane’s
sine wave trajectory.
VII. CONCLUSIONS AND FUTURE WORK
We have presented a path-planning strategy for an
unmanned aerial vehicle (UAV) to follow a ground vehicle,
which can change its headings and velocity. If the ground
vehicle is not moving, or its speed is under a selected
threshold, the UAV starts to loiter, following a circular or rose
curve trajectory. When the vehicle is moving above the
threshold, the UAV follows it along a sinusoidal trajectory
with dynamically adjusting amplitude to compensate for
vehicle speed changes.
Fig. 12. Picture of video taken from a camera on the bottom of the
UAV.
The wind introduces a disturbance in the system that has
been addressed by using the calculated wind velocity and
offsetting the planned UAV trajectory accordingly.
The path-planning algorithm has been developed, tested and
debugged using the “controller development platform” we
have implemented on top of the simulation software and
hardware provided by CloudCap Technology.
The system has been successfully tested on a real UAV. The
experimental results reflect the results obtained in the
simulation phase. The ground vehicle was successfully tracked
even under ground vehicle speed and heading changes.
The authors are currently working on extending the
strategies presented in this paper to incorporate multiple
vehicles. In order to do so, the CDP has to be extended to be
able to support multiple vehicles simulations, and the control
has to be expanded to avoid collisions and coordinate the
motion of the UAVs.
REFERENCES
[1] D.A. Schoenwald, “AUVs: In space, air, water, and on the
ground”, IEEE Control Systems Magazine, 20(6):15-18,
December 2000.
[2] K. C. Wong, C. Bil, G. Gordon, P.W. Gibbens, “Study of the
Unmanned Aerial Vehicle (UAV) market in Australia”,
Aerospace Technology Forum Report, August 1997.
[3] Unmanned Aerial Vehicles Roadmap: 2002-2027, Office of the
Secretary of Defense, December 2002.
[4] M. Niculescu. Lateral track control law for Aerosonde UAV.
39th AIAA Aerospace Sciences Meeting and Exhibit, Paper
2001-0016, January 2001.
[5] S. Banda, J. Doyle, R. Murray, J. Paduano, J. Speyer, and G.
Stein, “Research needs in dynamics and control for uninhabited
aerial vehicles,” http://www.cds.caltech.edu/murray/notes/uav-
nov97.html, November 1997, Panel Report.
[6] M. Abramowitz and I.A. Stegun, Handbook of Mathematical
Functions, Dover Publications, 1965, 17.6.
[7] CloudCap Technology – Piccolo avionics system for small
Unmanned Aerial Vehicles.
http://www.cloudcaptech.com/piccolo.htm, 2001-2003.
