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Guidance and Control of
Autonomous Fixed Wing Air Vehicles
Randal W. Beard Timothy W. McLain
Brigham Young University
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Contents
Preface vii
1 Introduction 1
1.1 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Coordinate Frames 5
2.1 Rotation Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 MAV Coordinate Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Equation of Coriolis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Kinematics and Dynamics 21
3.1 MAV State Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 MAV Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Rigid Body Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Forces and Moments 29
4.1 Gravitational Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Aerodynamic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 Propulsion Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.5 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Nonlinear Equations of Motion 41
5.1 Six DOF Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Navigation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
iii
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iv CONTENTS
5.3 Wind Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.4 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6 Trim 51
6.1 Turn with a Constant Climb Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.2 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
7 Open Loop Linear Dynamics 59
7.1 Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.2 Linear State Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.3 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
8 Autopilot Design Using Successive Loop Closure 79
8.1 Lateral Autopilot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.2 Longitudinal Autopilot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.3 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
9 Micro UAV Sensors 99
9.1 Rate Gyros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9.2 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.3 Pressure Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
9.4 Magnetometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
9.5 GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
9.6 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
10 State Estimation 109
10.1 Low Pass Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
10.2 State Estimation by Inverting the Sensor Model . . . . . . . . . . . . . . . . . . . 110
10.3 Dynamic Observer Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
10.4 Essentials from Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 116
10.5 Derivation of the Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
10.6 Attitude Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
10.7 GPS Smooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.8 Wind Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.9 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
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CONTENTS v
11 Waypoint and Orbit Following 133
11.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
11.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15011.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
11.4 Another approach to straight line tracking . . . . . . . . . . . . . . . . . . . . . . 153
11.5 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
12 Path Planning 159
12.1 Point-to-Point Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
12.2 Coverage Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
12.3 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
13 Path Manager 169
13.1 Switching Between Waypoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
13.2 Smooth transitions that satisfy kinematic constraints . . . . . . . . . . . . . . . . . 171
13.3 Smooth transitions through the waypoint . . . . . . . . . . . . . . . . . . . . . . . 171
13.4 Smooth transitions that preserve path length . . . . . . . . . . . . . . . . . . . . . 171
13.5 Path Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
13.6 Dubins Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
13.7 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
14 Cameras on Micro UAVs 199
14.1 Gimbal and Camera Frames and Projective Geometry . . . . . . . . . . . . . . . . 200
14.2 Gimbal Pointing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
1 4 . 3 G e o l o c a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 4
14.4 Estimating Target Motion in the Image Plane . . . . . . . . . . . . . . . . . . . . 207
14.5 Precision Landing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
14.6 Design Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
A Aviones 223
B Introduction to Modeling in Simulink 225
C Useful Formulas and other Information 227
C.1 Conversion from knots to mph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
D Graphs Theory 229
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vi CONTENTS
Bibliography 238
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Chapter 5
Nonlinear Equations of Motion
5.1 Six DOF Equations of Motion
5.1.1 General Force and Torque Model
If we use the general force and torque models given by
fx
fy
fz
= mg
sin
cos sin
cos cos
+ qS
CX(x, )
CY(x, )
CZ(x, )
l
m
n
= qS
bCl(x,)
cCm(x,)
bCn(x, )
,
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42 5.1 Six DOF Equations of Motion
in the six degree-of-freedom model given by Equations (3.9)-(3.12), we get
pn
pe
h
=
cc ssc cs csc + ss
cs sss + cc css sc
s sc cc
u
v
w
(5.1)
u
v
w
=
rv qw
pw ru
qu pv
+
g sin
g cos sin
g cos cos
+qS
m
CX(x, )
CY(x, )
CZ(x,)
(5.2)
=
1 sin()tan() cos()tan()
0 cos() sin()
0 sin()sec() cos()sec()
p
q
r
(5.3)
p
q
r
=
1pq 2qr
5pr 4(p2 r2)+
6pq 1qr
+ qS
b [Gamma3Cl(x, ) + 4Cn(x, )]cJy
Cm(x, )
b [4Cl(x, ) + 7Cn(x, )]
. (5.4)
5.1.2 Linear Aerodynamic Model
A variety of different models for the aerodynamic forces and moments appear in the literature. In
particular, if we use the linear model described in Chapter 4 we get the following equations of
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Nonlinear Equations of Motion 43
motion:
pn = (cos cos )u + (sin sin cos cos sin )v + (cos sin cos + sin sin )w
(5.5)
pe = (cos sin )u + (sin sin sin + cos cos )v + (cos sin sin sin cos )w
(5.6)
h = u sin v sin cos w cos cos (5.7)
u = rv qw g sin +qS
m
CX0 + CX + CXqcq
Va + CXee
+
Sprop2m Cprop
(kt)
2 V
2a
(5.8)
v = pw ru + g cos sin +qS
m
CY0 + CY+ CYp
bp
2Va+ CYr
br
2VaCYaa + CYr r
(5.9)
w = qu pv + g cos cos +qS
m
CZ0 + CZ + CZq
cq
Va+ CZee
(5.10)
= p + qsin tan + r cos tan (5.11)
= qcos r sin (5.12)
= qsin sec + r cos sec (5.13)
p = 1pq 2qr + qSb
Cp0 + Cp+ Cpp
bp
2Va+ Cpr
br
2Va+ Cpaa + Cpr r
(5.14)
q = 5pr 4(p2 r2) +
qSc
Jy
Cm0 + Cm + Cmq
cq
2Va+ Cmee
(5.15)
r = 6pq 1qr + qSb
Cr0 + Cr+ Crp
bp
2Va+ Crr
br
2Va+ Craa + Crr r
, (5.16)
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44 5.2 Navigation Models
where
Cp0 = 3Cl0 + 4Cn0
Cp = 3Cl + 4Cn
Cpp = 3Clp + 4Cnp
Cpr = 3Clr + 4Cnr
Cpa = 3Cla + 4Cna
Cpr = 3Clr + 4Cnr
Cr0 = 4Cl0 + 7Cn0
Cr = 4Cl + 7Cn
Crp = 4Clp + 7Cnp
Crr = 4Clr + 7Cnr
Cra = 4Cla + 7Cna
Crr = 4Clr + 7Cnr .
5.2 Navigation Models
5.2.1 8 State Navigation Equations
The full 12-state equations of motion given in Equations (5.1)(5.4) are usually not needed to
derive good navigation models. In this section we will show a useful method for reducing these
equations.
The first simplification is to note that the velocity vector in the wind frame, i.e. (Va, 0, 0)T,
where Va is the airspeed, can be related to the inertial coordinates by two angles: the flight path
angle and the heading , as shown in Figure 5.1. The heading is obtained by rotating the inertial
coordinate from by until the x-axis is aligned with the projection of the velocity vector on the
x-y plane. The appropriate transformations are given by
pnpeh
= cos
sin 0sin cos 0
0 0 1
cos 0 sin 0 1 0 sin 0 cos
Va00
= cos cos sin cos sin
Va.
Therefore
pn
pe
h
=
cos cos
sin cos
sin
Va.
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Nonlinear Equations of Motion 45
Flight path
Figure 5.1: The flight path angles and .
Coordinated Turn
The following derivation draws on the discussion [2, p. 224226]. From Equation (5.13) we get
that
= sin cos
q+ cos cos
r.
Figure 5.2 shows a free body diagram of the UAV indicating forces in the x z plane during a
Figure 5.2: Free body diagram indicating forces on the UAV in the y z plane. The nose of the
UAV is out of the page. The UAV is assumed to be pitched at the flight path angle .
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46 5.2 Navigation Models
cork-screw maneuver. Writing the force equations we get
L cos cos = mg cos (5.17)
L sin cos = mVa. (5.18)
Dividing (5.18) by (5.17) and solving for gives
=g
Vatan , (5.19)
which is the equation for a coordinated turn. Given that the turning radius is given by Rt = Va/
we get
Rt =V2a
g tan . (5.20)
From Figure 5.2 we also see that
q = sin (5.21)
r = cos . (5.22)
Plugging Eq. (5.19) into Eq. (5.21) and (5.22) gives
q =g
Va
sin2
cos (5.23)
r =g
Vasin . (5.24)
Plugging into Eq. (??) gives
=g
Va
sin
cos
1
cos .
Noting from Eq. (5.17) that1
cos =
L
mg,
and defining the Load Factoras n= L/mg gives
=g
Va
sin
cos n. (5.25)
Our derivation of the dynamic equation for draws on the discussion in [2, p. 227228]. The
free body diagram of the UAV in the x zplane is shown in Figure 5.3. Since the UAV has a roll
angle of , the projection of the lift vector onto the x z plane is L cos . The centripetal force
due to to the pull-up maneuver is mVa. Therefore, summing the forces in the x zplane gives
L cos = mVa+ mg cos .
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Nonlinear Equations of Motion 47
Figure 5.3: Free body diagram indicating forces on the UAV in the x z plane. The left wing is
out of the page. The UAV is assumed to be in a roll angle of.
Letting n = L/mg and solving for gives
=g
Va(n cos cos ) . (5.26)
We will assume that the mini-UAV is equipped with an autopilot that implements the following
feedback loops: (1) airspeed hold, (2) roll-attitude hold, and (3) load-factor hold. In addition,
we will assume that the autopilot is tuned such that the closed-loop behavior of these loops is
essentially first order. Therefore, the closed loop behavior of the autopilot is given by
Va =1
V(Vca Va)
= 1
(c ) (5.27)
n =1
n(nc n),
where > 0 are positive autopilot time constants, and Vca ,
c, and nc are the inputs to the autopilot.
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48 5.2 Navigation Models
In summary, the equations of motion for the UAV are given by
pn = Va cos cos + wx (5.28)
pe = Va sin cos + wy (5.29)
h = Va sin + wh (5.30)
=g
Va
sin
cos n (5.31)
=g
Va(n cos cos ) (5.32)
Va =1
V(Vca Va) (5.33)
=1
(c ) (5.34)
n =1
n(nc n). (5.35)
An equivalent, but useful alternative to these equations is to assume that the load factor is
selected as
nc = n =cos
cos . (5.36)
In this case equations (5.31) and (5.32) become
=g
Vatan() (5.37)
=
g cos
Va (
1). (5.38)Note that when = 1, the airframe is experiencing a level flight coordinated turn.
5.2.2 6 State Navigation Equations
If we assume that the airspeed is constant and that the load factor is given by Equation (5.36), then
the six state navigation equations become
pn = Va cos cos + wx (5.39)
pe = Va sin cos + wy (5.40)
h = Va sin + wh (5.41)
=g
Vatan() (5.42)
=g cos
Va( 1) (5.43)
=1
(c ), (5.44)
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Nonlinear Equations of Motion 49
where the inputs are and c.
5.2.3 4 State Navigation Equations
There are times when we are interested in 2D path planning. In that case we select = 1 to obtain
pn = Va cos + wx (5.45)
pe = Va sin + wy (5.46)
=g
Vatan (5.47)
=1
(c ), (5.48)
where c is the input.
5.3 Wind Models
5.3.1 Wind Speed Above Ground
According to [9], the wind-speed increases with altitude. Up to an altitude of few hundred meters,
the wind speed profile vw(z) is approximately a logarithmic function of the altitude (z):
vw(z) vo() ln
zz0
, for z > 10z0,
where is the thickness of the surface boundary layer, z0 = 0.1 m in a low density urban zone,
hence
z(vw) = z0evw/v0().
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50 5.4 Design Project
5.4 Design Project
5.1 Homework problem 1.
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Bibliography
[1] R. C. Nelson, Flight Stability and Automatic Control. Boston, Massachusetts: McGraw-Hill,
2nd ed., 1998.
[2] J. Roskam, Airplane Flight Dynamics and Automatic Flight Controls, Parts I & II. Lawrence,Kansas: DARcorporation, 1998.
[3] J. H. Blakelock, Automatic Control of Aircraft and Missiles. John Wiley & Sons, 1965.
[4] J. H. Blakelock, Automatic Control of Aircraft and Missiles. John Wiley & Sons, second
edition ed., 1991.
[5] M. V. Cook, Flight Dynamics Principles. New York: John Wiley & Sons, 1997.
[6] B. Etkin and L. D. Reid, Dynamics of Flight: Stability and Control. John Wiley & Sons,1996.
[7] B. L. Stevens and F. L. Lewis, Aircraft Control and Simulation. Hoboken, New Jersey: John
Wiley & Sons, Inc., 2nd ed., 2003.
[8] W. J. Rugh, Linear System Theory. Englewood Cliffs, New Jersey: Prentice Hall, 2nd ed.,
1996.
[9] F. Ruffier and N. Franceschini, Optic flow regulation: the key to aircraft automatic guid-
ance, Robotics and Autonomous Systems, vol. 50, pp. 177194, April 2005.
[10] D. B. Barber, S. R. Griffiths, T. W. McLain, and R. W. Beard, Autonomous landing of
miniature aerial vehicles, in AIAA Infotech@Aerospace, (Arlington, Virginia), American
Institute of Aeronautics and Astronautics, September 2005. AIAA-2005-6949.
[11] http://www.silicondesigns.com/tech.html.
231
http://www.silicondesigns.com/tech.html -
7/30/2019 Uavbook Ch5 Partial[1] Copy
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232 BIBLIOGRAPHY
[12] M. Rauw, FDC 1.2 - A SIMULINK Toolbox for Flight Dynamics and Control Analysis, Feb-
ruary 1998. Available at http://www.mathworks.com/.
[13] R. E. Bicking, Fundamentals of pressure sensor technology. http://www.
sensorsmag.com/articles/1198/fun1198/main.shtml.
[14] T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms. Englewood Cliffs,
New Jersey: Prentice Hall, 2000.
[15] D. B. Barber, J. D. Redding, T. W. McLain, R. W. Beard, and C. N. Taylor, Vision-based tar-
get geo-location using a fixed-wing miniature air vehicle, Journal of Intelligent and Robotic
Systems, vol. 47, pp. 361382, December 2006.
[16] S. Park, J. Deyst, and J. How, A new nonlinear guidance logic for trajectory tracking,
in Proceedings of the AIAA Guidance, Navigation and Control Conference, August 2004.
AIAA-2004-4900.
[17] I. Kaminer, A. Pascoal, E. Hallberg, and C. Silvestre, Trajectory tracking for autonomous
vehicles: An integrated approach to guidance and control, AIAA Journal of Guidance, Con-
trol and Dynamics, vol. 21, no. 1, pp. 2938, 1998.
[18] P. Aguiar, D. Dacic, J. Hespanha, and P. Kokotivic, Path-following or reference-tracking?
An answer relaxing the limits to performance, in Proceedings of IAV2004, 5th IFAC/EURONSymposium on Intelligent Autonomous Vehicles, (Lisbon, Portugal), 2004.
[19] A. P. Aguiar, J. P. Hespanha, and P. V. Kokotovic, Path-following for nonminimum phase
systems removes performance limitations, IEEE Transactions on Automatic Control, vol. 50,
pp. 234238, February 2005.
[20] J. Hauser and R. Hindman, Maneuver regulation from trajectory tracking: Feedback lin-
earizable systems, in Proceedings of the IFAC Symposium on Nonlinear Control Systems
Design, (Tahoe City, CA), pp. 595600, June 1995.
[21] P. Encarnacao and A. Pascoal, Combined trajectory tracking and path following: An appli-
cation to the coordinated control of marine craft, in Proceedings of the IEEE Conference on
Decision and Control, (Orlando, FL), pp. 964969, 2001.
[22] R. Skjetne, T. Fossen, and P. Kokotovic, Robust output maneuvering for a class of nonlinear
systems, Automatica, vol. 40, pp. 373383, 2004.
http://www.sensorsmag.com/articles/1198/fun1198/main.shtmlhttp://www.sensorsmag.com/articles/1198/fun1198/main.shtmlhttp://www.mathworks.com/ -
7/30/2019 Uavbook Ch5 Partial[1] Copy
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BIBLIOGRAPHY 233
[23] R. Rysdyk, UAV path following for constant line-of-sight, in Proceedings of the AIAA 2nd
Unmanned Unlimited Conference, AIAA, September 2003. Paper no. AIAA-2003-6626.
[24] O. Khatib, Real-time obstacle avoidance for manipulators and mobile robots, in Proceed-
ings of the IEEE International Conference on Robotics and Automation, vol. 2, pp. 500505,
1985.
[25] K. Sigurd and J. P. How, UAV trajectory design using total field collision avoidance, in
Proceedings of the AIAA Guidance, Navigation and Control Conference, August 2003.
[26] H. K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice Hall, 3rd ed., 2002.
[27] E. P. Anderson, R. W. Beard, and T. W. McLain, Real time dynamic trajectory smoothing
for uninhabited aerial vehicles, IEEE Transactions on Control Systems Technology, vol. 13,
pp. 471477, May 2005.
[28] D. Hsu, R. Kindel, J.-C. Latombe, and S. Rock, Randomized kinodynamic motion plan-
ning with moving obstacles, in Algorithmic and Computational Robotics: New Directions,
pp. 247264f, A. K. Peters, 2001.
[29] F. Lamiraux, S. Sekhavat, and J.-P. Laumond, Motion planning and control for Hilare pulling
a trailer, IEEE Transactions on Robotics and Automation, vol. 15, pp. 640652, August
1999.
[30] R. M. Murray and S. S. Sastry, Nonholonomic motion planning: Steering using sinusoids,
IEEE Transactions on Automatic Control, vol. 38, pp. 700716, May 1993.
[31] T. Balch and R. C. Arkin, Behavior-based formation control for multirobot teams, IEEE
Transactions on Robotics and Automation, vol. 14, pp. 926939, December 1998.
[32] R. C. Arkin, Behavior-based Robotics. MIT Press, 1998.
[33] L. E. Dubins, On curves of minimal length with a constraint on average curvature, and with
prescribed initial and terminal positions and tangents, American Journal of Mathematics,
vol. 79, pp. 497516, 1957.
[34] E. P. Anderson and R. W. Beard, An algorithmic implementation of constrained extremal
control for UAVs, in Proceedings of the AIAA Guidance, Navigation and Control Confer-
ence, (Monterey, CA), August 2002. AIAA Paper No. 2002-4470.
-
7/30/2019 Uavbook Ch5 Partial[1] Copy
21/25
234 BIBLIOGRAPHY
[35] D. R. Nelson, D. B. Barber, T. W. McLain, and R. W. Beard, Vector field path following for
miniature air vehicles, IEEE Transactions on Robotics, vol. 37, pp. 519529, June 2007.
[36] D. R. Nelson, D. B. Barber, T. W. McLain, and R. W. Beard, Vector field path following for
small unmanned air vehicles, in American Control Conference, (Minneapolis, Minnesota),
pp. 57885794, June 2006.
[37] R. Sedgewick, Algorithms. Addison-Wesley, 2nd ed., 1988.
[38] F. Aurenhammer, Voronoi diagrams - a survey of fundamental geometric data struct, ACM
Computing Surveys, vol. 23, pp. 345405, September 1991.
[39] T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms. McGraw-Hill,
1993.
[40] M. Pachter and P. R. Chandler, Challenges of autonomous control, IEEE Control Systems
Magazine, vol. 18, pp. 9297, August 1998.
[41] P. Chandler, S. Rasumussen, and M. Pachter, UAV cooperative path planning, in Proceed-
ings of the AIAA Guidance, Navigation, and Control Conference, (Denver, CO), August 2000.
AIAA Paper No. AIAA-2000-4370.
[42] T. McLain and R. Beard, Cooperative rendezvous of multiple unmanned air vehicles, in
Proceedings of the AIAA Guidance, Navigation and Control Conference, (Denver, CO), Au-
gust 2000. Paper no. AIAA-2000-4369.
[43] R. W. Beard, T. W. McLain, and M. Goodrich, Coordinated target assignment and intercept
for unmanned air vehicles, in Proceedings of the IEEE International Conference on Robotics
and Automation, (Washington DC), pp. 25812586, May 2002.
[44] P. R. Chandler, M. Pachter, D. Swaroop, J. M. Fowler, J. K. Howlett, S. Rasmussen, C. Schu-
macher, and K. Nygard, Complexity in UAV cooperative control, in Proceedings of the
American Control Conference, (Anchorage, AK), pp. 18311836, May 2002.
[45] G. Yang and V. Kapila, Optimal path planning for unmanned air vehicles with kinematic and
tactical constraints, in Proceedings of the IEEE Conference on Decision and Control, (Las
Vegas, NV), pp. 13011306, 2002.
[46] E. Frazzoli, M. A. Dahleh, and E. Feron, Real-time motion planning for agile autonomous
vehicles, Journal of Guidance, Control, and Dynamics, vol. 25, pp. 116129, January-
February 2002.
-
7/30/2019 Uavbook Ch5 Partial[1] Copy
22/25
BIBLIOGRAPHY 235
[47] N. Faiz, S. K. Agrawal, and R. M. Murray, Trajectory planning of differentially flat systems
with dynamics and inequalities, AIAA Journal of Guidance, Control and Dynamics, vol. 24,
pp. 219227, MarchApril 2001.
[48] R. K. Prasanth, J. D. Boskovic, S.-M. Li, and R. K. Mehra, Initial study of autonomous
trajectory generation for unmanned aerial vehicles, in Proceedings of the IEEE Conference
on Decision and Control, (Orlando, FL), pp. 640645, December 2001.
[49] O. A. Yakimenko, Direct method for rapid prototyping of near-optimal aircraft trajectories,
AIAA Journal of Guidance, Control and Dynamics, vol. 23, pp. 865875, September-October
2000.
[50] S. Sun, M. B. Egerstedt, and C. F. Martin, Control theoretic smoothing splines, IEEE Trans-actions on Automatic Control, vol. 45, pp. 22712279, December 2000.
[51] A. W. Proud, M. Pachter, and J. J. DAzzo, Close formation flight control, in Proceedings
of the AIAA Guidance, Navigation, and Control Conference and Exhibit, (Portland, OR),
pp. 12311246, American Institute of Aeronautics and Astronautics, August 1999. Paper no.
AIAA-99-4207.
[52] R. L. Burden and J. D. Faires, Numerical Analysis. Boston: PWS-KENT Publishing Com-
pany, fourth ed., 1988.
[53] T. L. Vincent and W. J. Grantham, Nonlinear and Optimal Control Systems. John Wiley &
Sons, Inc., 1997.
[54] E. P. Anderson, Constrained extremal trajectories and unmanned air vehicle trajec-
tory generation, Masters thesis, Brigham Young University, Provo, Utah 84602, April
2002. Available at http://www.ee.byu.edu/magicc/publications/thesis/
ErikAnderson.ps.
[55] E. P. Anderson, R. W. Beard, and T. W. McLain, Dynamic trajectory smoothing for UAVs,
Tech. Rep. MAGICC-2003-01, Brigham Young University, February 2003. Available at
http://www.ee.byu.edu/magicc/tr/2003-01.pdf.
[56] J. H. Evers, Biological inspiration for agile autonomous air vehicles, in Symposium on
Platform Innovations and System Integration for Unmanned Air, Land, and Sea Vehicles ,
(Florence, Italy), NATO Research and Technology Organization AVT-146, May 2007. Paper
no. 15.
http://www.ee.byu.edu/magicc/tr/2003-01.pdfhttp://www.ee.byu.edu/magicc/publications/thesis/ErikAnderson.pshttp://www.ee.byu.edu/magicc/publications/thesis/ErikAnderson.ps -
7/30/2019 Uavbook Ch5 Partial[1] Copy
23/25
236 BIBLIOGRAPHY
[57] S. Ettinger, M. Nechyba, P. Ifju, and M. Waszak, Vision-guided flight stability and control
for micro air vehicles, Advanced Robotics, vol. 17, no. 3, pp. 617640, 2003.
[58] E. Frew and S. Rock, Trajectory generation for monocular-vision based tracking of a
constant-velocity target, in Proceedings of the 2003 IEEE International Conference on Ro-
botics and Automation, 2003.
[59] R. Kumar, S. Samarasekera, S. Hsu, and K. Hanna, Registration of highly-oblique and
zoomed in aerial video to reference imagery, in Proceedings of the IEEE Computer Soci-
ety Computer Vision and Pattern Recognition Conference, Barcelona, Spain , 2000.
[60] D. Lee, K. Lillywhite, S. Fowers, B. Nelson, and J. Archibald, An embedded vision system
for an unmanned four-rotor helicopter, in SPIE Optics East, Intelligent Robots and ComputerVision XXIV: Algorithms, Techniques, and Active Vision, vol. vol. 6382-24, 63840G, (Boston,
MA, USA), October 2006.
[61] J. Lopez, M. Markel, N. Siddiqi, G. Gebert, and J. Evers, Performance of passive ranging
from image flow, in Proceedings of the IEEE International Conference on Image Processing,
vol. 1, pp. I929I932, September 2003.
[62] M. Pachter, N. Ceccarelli, and P. R. Chandler, Vision-based target geo-location using camera
equipped mavs, in Proceedings of the IEEE Conference on Decision and Control, (New
Orleans, LA), December 2007. (to appear).
[63] R. J. Prazenica, A. J. Kurdila, R. C. Sharpley, P. Binev, M. H. Hielsberg, J. Lane, and J. Evers,
Vision-based receding horizon control for micro air vehicles in urban environments, AIAA
Journal of Guidance, Dynamics, and Control, (in review).
[64] I. Wang, V. Dobrokhodov, I. Kaminer, and K. Jones, On vision-based target tracking and
range estimation for small UAVs, in 2005 AIAA Guidance, Navigation, and Control Confer-
ence and Exhibit, pp. 111, 2005.
[65] Y. Watanabe, A. J. Calise, E. N. Johnson, and J. H. Evers, Minimum-effort guidance for
vision-based collision avoidance, in Proceedings of the AIAA Atmospheric Flight Mechan-
ics Conference and Exhibit, (Keystone, Colorado), American Institute of Aeronautics and
Astronautics, August 2006. Paper no. AIAA-2006-6608.
[66] Y. Watanabe, E. N. Johnson, and A. J. Calise, Optimal 3-D guidance from a 2-D vision
sensor, in Proceedings of the AIAA Guidance, Navigation, and Control Conference, (Prov-
-
7/30/2019 Uavbook Ch5 Partial[1] Copy
24/25
BIBLIOGRAPHY 237
idence, Rhode Island), American Institute of Aeronautics and Astronautics, August 2004.
Paper no. AIAA-2004-4779.
[67] I. H. Whang, V. N. Dobrokhodov, I. I. Kaminer, and K. D. Jones, On vision-based tracking
and range estimation for small uavs, in Proceedings of the AIAA Guidance, Navigation, and
Control Conference and Exhibit, (San Francisco, CA), August 2005.
[68] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University, 1985.
[69] Y. Ma, S. Soatto, J. Kosecka, and S. Sastry, An Invitation to 3-D Vision: From Images to
Geometric Models. Springer-Verlag, 2003.
[70] R. W. Beard, J. W. Curtis, M. Eilders, J. Evers, and J. R. Cloutier, Vision aided proportional
navigation for micro air vehicles, in Proceedings of the AIAA Guidance, Navigation andControl Conference, (Hilton Head, North Carolina), American Institute of Aeronautics and
Astronautics, August 2007. Paper number AIAA-2007-****.
[71] P. Zarchan, Tactical and Strategic Missile Guidance, vol. 124 ofProgress in Astronautics and
Aeronautics. Washington DC: American Institute of Aeronautics and Astronautics, 1990.
[72] A. E. Bryson and Y. C. Ho, Applied Optimal Control. Waltham, MA: Blaisdell Publishing
Company, 1969.
[73] M. Guelman, Proportional navigation with a maneuvering target, IEEE Transactions on
Aerospace and Electronic Systems, vol. 8, pp. 364371, May 1972.
[74] C. F. Lin, Modern Navigation, Guidance, and Control Processing. Englewood Cliffs, New
Jersey: Prentice Hall, 1991.
[75] M. Guelman, M. Idan, and O. M. Golan, Three-dimensional minimum energy guidance,
IEEE Transactions on Aerospace and Electronic Systems, vol. 31, pp. 835841, April 1995.
[76] R. Beard, D. Kingston, M. Quigley, D. Snyder, R. Christiansen, W. Johnson, T. McLain, and
M. Goodrich, Autonomous vehicle technologies for small fixed wing UAVs, AIAA Journal
of Aerospace, Computing, Information, and Communication, vol. 2, pp. 92108, January
2005.
[77] P. G. Ifju, D. A. Jenkins, S. Ettinger, Y. Lian, W. Shyy, and M. R. Waszak, Flexible wing
based micro air vehicles, in AIAA Aerospace Sciences Meeting and Exhibit, (Reno, NV),
American Institute of Aeronautics and Astronautics, January 2002. Paper no. AIAA-2002-
0705.
-
7/30/2019 Uavbook Ch5 Partial[1] Copy
25/25
238 BIBLIOGRAPHY
[78] J. G. Lee, H. S. Han, and Y. J. Kim, Guidance performance analysis of bank-to-turn (BTT)
missiles, in Proceedings of the IEEE International Conference on Control Applications,
(Kohala, Hawaii), pp. 991996, August 1999.