كتاب Robotics and Control - Fundamental Algorithms in MATLAB
منتدى هندسة الإنتاج والتصميم الميكانيكى
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منتدى هندسة الإنتاج والتصميم الميكانيكى
بسم الله الرحمن الرحيم

أهلا وسهلاً بك زائرنا الكريم
نتمنى أن تقضوا معنا أفضل الأوقات
وتسعدونا بالأراء والمساهمات
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أو وإذا كانت هذة زيارتك الأولى للمنتدى فنتشرف بإنضمامك لأسرتنا
وهذا شرح لطريقة التسجيل فى المنتدى بالفيديو :
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 كتاب Robotics and Control - Fundamental Algorithms in MATLAB

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كتاب Robotics and Control - Fundamental Algorithms in MATLAB  Empty
مُساهمةموضوع: كتاب Robotics and Control - Fundamental Algorithms in MATLAB    كتاب Robotics and Control - Fundamental Algorithms in MATLAB  Emptyالثلاثاء 15 فبراير 2022, 2:27 am

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Robotics and Control - Fundamental Algorithms in MATLAB
Peter Corke

كتاب Robotics and Control - Fundamental Algorithms in MATLAB  M_r_a_13
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Contents
1 Introduction 1
1.1 Robots, Jobs and Ethics . 7
1.2 About the Book 8
1.2.1 MATLAB Software and the Toolboxes . 8
1.2.2 Notation, Conventions and Organization 9
1.2.3 Audience and Prerequisites . 10
1.2.4 Learning with the Book 11
1.2.5 Teaching with the Book 11
1.2.6 Outline 11
Further Reading 12
Part I Foundations . 13
2 Representing Position and Orientation 15
2.1 Working in Two Dimensions (2D) . 20
2.1.1 Orientation in 2-Dimensions 21
2.1.2 Pose in 2-Dimensions 24
2.2 Working in Three Dimensions (3D) . 29
2.2.1 Orientation in 3-Dimensions 30
2.2.2 Pose in 3-Dimensions 44
2.3 Advanced Topics . 47
2.3.1 Normalization 47
2.3.2 Understanding the Exponential Mapping . 48
2.3.3 More About Twists 50
2.3.4 Dual Quaternions . 53
2.3.5 Configuration Space . 53
2.4 Using the Toolbox 54
2.5 Wrapping Up 56
Further Reading 58
Exercises 59
3 Time and Motion . 61
3.1 Time-Varying Pose 61
3.1.1 Derivative of Pose . 61
3.1.2 Transforming Spatial Velocities . 62
3.1.3 Incremental Rotation 64
3.1.4 Incremental Rigid-Body Motion . 65
3.2 Accelerating Bodies and Reference Frames . 66
3.2.1 Dynamics of Moving Bodies 66
3.2.2 Transforming Forces and Torques . 67
3.2.3 Inertial Reference Frame . 67
3.3 Creating Time-Varying Pose 68
3.3.1 Smooth One-Dimensional Trajectories . 68
xviiContents
3.3.2 Multi-Dimensional Trajectories . 71
3.3.3 Multi-Segment Trajectories . 72
3.3.4 Interpolation of Orientation in 3D . 73
3.3.5 Cartesian Motion in 3D 75
3.4 Application: Inertial Navigation . 77
3.4.1 Gyroscopes . 77
3.4.2 Accelerometers . 79
3.4.3 Magnetometers . 83
3.4.4 Sensor Fusion 85
3.5 Wrapping Up 88
Further Reading 88
Exercises 89
Part II Mobile Robots 91
4 Mobile Robot Vehicles 97
4.1 Wheeled Mobile Robots . 97
4.1.1 Car-Like Mobile Robots 97
4.1.2 Differentially-Steered Vehicle 107
4.1.3 Omnidirectional Vehicle 110
4.2 Flying Robots . 112
4.3 Advanced Topics 117
4.3.1 Nonholonomic
and Under-Actuated Systems 117
4.4 Wrapping Up . 119
Further Reading . 120
Toolbox and MATLAB Notes 121
Exercises . 121
5 Navigation . 123
5.1 Reactive Navigation 124
5.1.1 Braitenberg Vehicles 124
5.1.2 Simple Automata . 126
5.2 Map-Based Planning . 128
5.2.1 Distance Transform 128
5.2.2 D* . 132
5.2.3 Introduction to Roadmap Methods . 134
5.2.4 Probabilistic Roadmap Method (PRM) 135
5.2.5 Lattice Planner . 138
5.2.6 Rapidly-Exploring Random Tree (RRT) . 142
5.3 Wrapping Up . 144
Further Reading . 145
Resources . 146
MATLAB Notes 146
Exercises . 146
6 Localization 149
6.1 Dead Reckoning . 153
6.1.1 Modeling the Vehicle . 153
6.1.2 Estimating Pose 155
6.2 Localizing with a Map 158
6.3 Creating a Map 163
6.4 Localization and Mapping . 165
6.5 Rao-Blackwellized SLAM . 167
6.6 Pose Graph SLAM . 168
xviiiContents
6.7 Sequential Monte-Carlo Localization . 173
6.8 Application: Scanning Laser Rangefinder 176
Laser Odometry . 177
Laser-Based Map Building 179
Laser-Based Localization 180
6.9 Wrapping Up . 180
Further Reading . 181
Toolbox and MATLAB Notes 183
Exercises . 183
Part III Arm-Type Robots 187
7 Robot Arm Kinematics . 191
7.1 Forward Kinematics 191
7.1.1 2-Dimensional (Planar) Robotic Arms . 192
7.1.2 3-Dimensional Robotic Arms 194
7.2 Inverse Kinematics . 203
7.2.1 2-Dimensional (Planar) Robotic Arms . 203
7.2.2 3-Dimensional Robotic Arms 205
7.3 Trajectories . 209
7.3.1 Joint-Space Motion . 209
7.3.2 Cartesian Motion . 212
7.3.3 Kinematics in Simulink . 212
7.3.4 Motion through a Singularity 213
7.3.5 Configuration Change 214
7.4 Advanced Topics 215
7.4.1 Joint Angle Offsets . 215
7.4.2 Determining Denavit-Hartenberg Parameters 215
7.4.3 Modified Denavit-Hartenberg Parameters . 216
7.5 Applications 218
7.5.1 Writing on a Surface 218
7.5.2 A Simple Walking Robot 219
7.6 Wrapping Up . 223
Further Reading . 224
MATLAB and Toolbox Notes 225
Exercises . 225
8 Manipulator Velocity . 227
8.1 Manipulator Jacobian 227
8.1.1 Jacobian in the World Coordinate Frame 227
8.1.2 Jacobian in the End-Effector Coordinate Frame . 230
8.1.3 Analytical Jacobian . 230
8.2 Jacobian Condition and Manipulability . 232
8.2.1 Jacobian Singularities . 232
8.2.2 Manipulability . 233
8.3 Resolved-Rate Motion Control . 235
8.3.1 Jacobian Singularity 238
8.4 Under- and Over-Actuated Manipulators 238
8.4.1 Jacobian for Under-Actuated Robot . 239
8.4.2 Jacobian for Over-Actuated Robot 240
8.5 Force Relationships 242
8.5.1 Transforming Wrenches to Joint Space 242
8.5.2 Force Ellipsoids 242
8.6 Inverse Kinematics: a General Numerical Approach . 243
8.6.1 Numerical Inverse Kinematics . 243
xixContents
8.7 Advanced Topics 245
8.7.1 Computing the Manipulator Jacobian Using Twists . 245
8.8 Wrapping Up . 245
Further Reading . 246
MATLAB and Toolbox Notes 246
Exercises . 246
9 Dynamics and Control . 249
9.1 Independent Joint Control 249
9.1.1 Actuators . 249
9.1.2 Friction . 250
9.1.3 Effect of the Link Mass 251
9.1.4 Gearbox 252
9.1.5 Modeling the Robot Joint 253
9.1.6 Velocity Control Loop 255
9.1.7 Position Control Loop 259
9.1.8 Independent Joint Control Summary 260
9.2 Rigid-Body Equations of Motion . 261
9.2.1 Gravity Term 262
9.2.2 Inertia Matrix 264
9.2.3 Coriolis Matrix . 265
9.2.4 Friction . 266
9.2.5 Effect of Payload . 266
9.2.6 Base Force 267
9.2.7 Dynamic Manipulability 267
9.3 Forward Dynamics . 269
9.4 Rigid-Body Dynamics Compensation . 270
9.4.1 Feedforward Control . 271
9.4.2 Computed Torque Control 272
9.4.3 Operational Space Control . 273
9.5 Applications 274
9.5.1 Series-Elastic Actuator (SEA) 274
9.6 Wrapping Up . 276
Further Reading . 276
Exercises . 278
Appendices . 281
A Installing the Toolboxes 283
B Linear Algebra Refresher . 287
C Geometry 295
D Lie Groups and Algebras . 307
E Linearization, Jacobians and Hessians 313
F Solving Systems of Equations . 317
G Gaussian Random Variables 327
H Kalman Filter . 331
I Graphs . 337
Bibliography 341
Index 347
Index of People 347
Index of Functions, Classes and Methods 348
General Index . 351
Index
A
Ackermann, Rudolph 99
Asimov, Issac 1
B
Ball, Sir Robert 50, 53
Bayes, Reverend Thomas 155
Black, Harold 4
Bode, Henrik 4
Braitenberg, Valentino 124
Bryan, George 35
C .
apek, Karel 1, 3
Cardano, Gerolamo 35
Chasles, Michel 51
Clifford, William 53
Cook, Captain James 150, 165
Coriolis, Gaspard-Gustave de 67
Coulomb, Charles-Augustin de 251
D
Delaunay, Boris 135
Denavit, Jacques 196
Descartes, René 17
Devol, George C. Jr. 1, 2
Draper, Charles Stark (Doc) 79, 80, 156
E
Einstein, Albert 68
Engelberger, Joseph F. 2
Euclid of Alexandria 16
Euler, Leonhard 34, 66, 263
G
Gauss, Carl Friedrich 59
Goetz, Raymond 7
H
Hall, Edwin 83
Hamilton, Sir William Rowan 42, 53, 58, 59
Harrison, John 150
Hartenberg, Richard 196
Hershey, Allen V. 218
Hesse, Ludwig Otto 314
I
Ilon, Bengt 110
J
Jacobi, Carl Gustav Jacob 230
K
Kálmán, Rudolf 155
L
Lagrange, Joseph-Louis 263
Lazzarini, Mario 172
Leclerc, Georges-Louis 172
Lie, Sophus 307
M
Markov, Andrey 135
McCarthy, John 4
McCulloch, Warren 4
Metropolis, Nicholas 172
Minsky, Marvin 4
Moler, Cleve 9
N
Newell, Allen 4
Newton, Sir Isaac 65–67, 277
Nyquist, Harold 4
P
Pitts, Walter 4
Plücker, Julius 297
Price, Richard 155
R
Rodrigues, Olinde 40, 59
S
Scheinman, Victor 193
Schmidt, Stanley F. 156
Shannon, Claude 4
Simon, Herbert 4
T
Tait, Peter 35, 59
Tesla, Nikola 5
Turing, Alan 4
U
Ulam, Stanislaw 172
V
von Kármán, Theodore 196
von Neumann, John 172
Voronoy, Georgy Feodosevich 135
W
Walter, William Grey 4, 124
Wiener, Norbert 4
Index of Functions, Classes and Methods
Classes are shown in bold, Simulink® models in italics, and methods are prefixed by a dot.
All others are Toolbox functions.
A
about 75, 116, 143, 202, 211, 262, 316
angdiff 101
angles 46
angvec2r 40
angvec2tr 59
animate 74, 75
AprilTag 162
apriltags 162, 182
atan2 301
B
Bicycle 98, 99, 107, 109
Bicycle 161, 164, 166, 174, 183
BinaryOccupancyGrid 146
bug 127
bug.plot 127
bug2 127
–, .path 127, 129
BundleAdjust 337
C
ccode 316
ctraj 8, 76, 212, 213
D
delta2tr 65
DHFactor 216, 220
–, .dh.command 220
dim 161
Dstar 132
–, .costmap 132
–, .modify_cost 133
–, .niter 133
–, .plan 132, 133
–, .query 133
DXform 129
–, .plan 129, 130
–, .query 129
–, .visualize 129
–, .visualize3d 130
E
e2h 27
eig 39
EKF 156, 158, 161, 164–166
eps 48
ETS2 192, 225
–, .fkine 192
–, .plot 193
–, .Rz 192, 194
–, .structure 193, 194
–, .teach 192
–, .Tx 192, 194
ETS3 225
–, .fkine 194
–, .Ry 194
–, .Rz 194
–, .Tx 194
–, .Ty 194
–, .Tz 194
eul2jac 231
eul2r 34, 35
eul2tr 46
eval 216, 220
ExampleHelperRobot Simulator 121
exp 24, 41
expm 24, 41, 45, 50, 52, 59
eye 27, 216
F
fcode 316
fkine 212
fminsearch 205349
G
gait 223
gaussfunc 327, 328
GeometricJacobian 246
Graph 212
H
h2e 27
I
icp 178
InitFcn 273
interp 75, 76
InverseKinematics 225
ithin 134
J
jacobian 170, 228, 316
Jacobian 235
jsingu 232
jtraj 202, 210, 212, 214, 261,
272, 273
L
LandmarkMap 158, 161
Lattice 139, 337
Link 196, 198, 215, 254, 266
–, .A 197
–, .a 197
–, .offset 197
–, .RP 197
log 23, 40
logm 23, 40, 52
lscov 246
lspb 70, 71, 76, 210
M
makemap 129, 146
matlabFunction 316
mdl_puma560 199, 205, 261, 263,
272
mdl_quadrotor 116
mdl_twolink 251
meshgrid 263, 264
model 101
models 198
MonteCarloLocalization 183
mplot 236
mstraj 218, 222
mtraj 71, 74, 210
N
Navigation 128
null 318
numcols 79, 87, 88, 137, 218, 263,
264
numrows 129, 218
O
oa2r 38
P
ParticleFilter 175, 183
pcregrigid 181
PGraph 337
–, .add_edge 337, 338
–, .add_node 337
–, .closest 338
–, .cost 338
–, .edges 338
–, .neighbours 338
–, .plot 338
pinv 238, 239, 241
ploop 259, 278
ploop_test 259
plot 177
plot_homline 304
plot_point 26
Plucker 52, 304
–, .L 304
–, .side 297
pol2cart 177
Polygon 147
PoseGraph 170, 171, 177, 337
–, .optimize 171
–, .plot 170, 171
–, .plotoccgrid 179
–, .scan 177
–, .scanmap 179
–, .scanxy 177
–, .time 178
PRM 136, 146, 337
–, .plan 136
–, .query 137
–, .visualize 137
Q
q.animate 74
qplot 211
Quaternion 42
R
rand 137
randinit 136, 137
randn 137, 327
RandomPath 155, 164, 174
RangeBearingSensor 159, 160, 162, 164–166,
175, 184
–, .h 160
–, .H_w 160
–, .H_x 160
–, .reading 159
Revolute 196
RevoluteMDH 217
RigidBodyTree 225, 246
RNE 272, 278
roblocks 101, 109
Robot 269
Index of Functions, Classes and Methods350 Index
rotx 32, 33, 40, 41, 64
roty 32–34
rotz 32, 34
rpy2r 39, 60
rpy2tr 43
RRT 142, 337
–, .path 143
–, .plan 142
–, .visualize 142
running 101
S
SE2 55, 170, 199
–, .Rx 209
SE3 55, 201, 202, 206, 208, 209, 212–214, 219, 222, 231
–, .Rx 214
–, .Ry 213
–, .Rz 222
–, .torotvec 231
Sensor 159, 164
–, .H_xf 164
sensorfield 125, 146
SerialLink 198, 204, 210, 222, 225, 247, 263
–, .accel 269
–, .base 201, 202, 263
–, .coriolis 261
–, .edit 198
–, .fdyn 270
–, .fellipse 243
–, .fkine 198, 201, 202, 205, 207, 211, 228, 236
–, .gravity 263
–, .gravload 262, 263, 267
–, .ikcon 225
–, .ikine 206, 208, 213, 214, 222, 225, 244
–, .ikine6s 205–209, 212–214, 219, 225
–, .ikinesym 204
–, .inertia 261, 264, 266, 268
–, .jacob0 229–234, 242, 268
–, .jacobn 230
–, .jtraj 210
–, .links 267
–, .maniplty 213, 234, 269
–, .motordynamics 254
–, .nofriction 270
–, .plot 201, 207, 211, 214, 219, 225, 269
–, .plot3d 225
–, .rne 261, 262, 267
–, .teach 225, 233, 243, 246
–, .tool 201
–, .vellipse 233
shortest 74
sigma 327
simplify 23, 60, 170
skew 309
sl_bicycle 99
sl_braitenberg 124, 125
sl_ctorque 271, 272
sl_driveline 102, 103
sl_drivepoint 101, 102
sl_drivepose 106, 107
sl_fforward 271, 272
sl_jspace 212, 213
sl_lanechange 99, 100
sl_opspace 273
sl_pursuit 104
sl_quadcopter 116
sl_quadrotor 115, 116
sl_rrmc 235, 236
sl_rrmc2 236, 237
sl_sea 275
sl_ztorque 269
SO2 55, 72
SO3 55, 74
spy 325
sqrt 157, 268
sqrtm 302
T
T1.torpy 71
t2r 45
T2xyz 212
tags 162
tau-d 257
tau_ff 258
torpy 75
tpoly 69, 70, 76, 89, 90, 210
tr2angvec 39
tr2delta 65
tr2eul 34, 35
tr2rotvec 231
tr2rpy 36
Tracking Controller 109
traj 218
tranimate 32, 33, 59, 60
transl 8, 45, 201, 202, 206, 208, 211, 213, 221, 222, 236
transl2 25, 26
trexp 41, 50, 52, 59
trinterp 76
tripleangle 36, 60
triplepoint 134
trlog 41, 52, 231
trot2 25
trotx 45, 46, 202, 220, 263
troty 213
trotz 220
trplot 25, 33, 45, 59
trplot2 26, 59
Ts
–, .t 212
–, .torpy 212
Twist 28, 52, 199
–, .expm 52
–, .line 52
–, .S 52
–, .T 28, 52, 199
U
Unicycle 109, 121, 183
UnitQuaternion 43, 44, 48, 66, 74, 79
–, .animate 79
–, .dot 62
–, .dotb 62
–, .omega 79
–, .plot 66
–, .torpy 79351
V
Vehicle 154, 156, 158, 183
–, .Fv 156
–, .Fx 156
–, .step 155
vex 23, 24, 40, 41, 309
vloop 255, 278
vloop_test 256
VREP_class 185
X, Y, Z
xv 316
General Index
General Index
Symbols
\-operator 69, 317, 319
A
A* search 132, 137, 140, 339
absorption shock 275
acceleration 79, 80, 85, 118, 249, 273
–, angular 66
–, centripetal 68
–, Coriolis 68, 89
–, discontinuity 76
–, Euler 68
–, gravitational 68, 81
–, inertial 81
–, proper 81
–, sensor 81, 85
–, specific 81
accelerometer 37, 39, 79–81, 85
–, triaxial 81, 85
Ackermann steering 99
actuation 118
–, electric 254
–, electro-hydraulic 249
actuator 118, 249
–, joint 250
–, saturation 116
–, series-elastic (SEA) 274, 275
addition, vector 287
adjoint
–, logarithm of 311
–, matrix 63, 67, 199, 245, 297, 311
adjugate 289
adjustment, bundle 182
AHRS (see attitude and heading reference system)
aircraft 117, 119
algebra 307
algebraic group 308
algorithm
–, Bresenham 179
–, bug 126–128
–, D* 132
–, FastSLAM (see also Rao-Blackwellized SLAM) 181
–, ICP (iterated closest point) 181
–, Levenberg-Marquardt 244, 320, 321
–, Newton-Euler 261
–, rapidly exploring 143
–, resolved-rate motion control 235
–, RRT (rapidly-exploring random tree) 143
–, skeletonization 134, 135
–, thinning 134, 135
–, velocity loop control 255
ampullae 81
anaglyph, stereo glasses 33
analysis, root-locus 278
analytical Jacobian 231
angle
–, Cardan 30, 36
–, declination 83
–, elevation 150
–, Euler 34–36, 38, 57, 73, 194, 230, 231, 245
–, singularity 37
–, heading 85
–, inclination 83
–, joint 5, 12, 196
–, nautical 36
–, representation 34
–, roll-pitch-yaw 35, 36, 76, 210–212, 230
–, rate 74
–, singularity 36
–, rotation 23, 24, 29, 33, 35, 37, 41
–, steering 99, 100, 139, 143
–, Tait-Bryan 36
–, trajectory
–, joint 270
–, LSPB (linear segment with parabolic blend) 70, 259,
260
–, XYZ sequence 36
angle-axis representation 39, 43
angular
–, acceleration 66
–, momentum 66, 77, 78
–, rate 86
–, uncertainty 157
–, velocity 48, 50, 62, 66, 68, 77, 78, 153, 231, 332
anthropomorphic 145, 200, 201
anti-symmetric matrix 289
Apollo 13 36, 38
–, Lunar Module 37, 79
approach vector 38, 39, 208, 209
April tag 162
architecture, subsumption 125
ArduCopter (software project) 120
artificial intelligence 4
Asimo humanoid robot 6
ASV (see autonomous surface vehicle)
attitude and heading reference system (AHRS) 85
automata 126
automated guided vehicle 94
autonomous surface vehicle (ASV) 94
autonomous underwater vehicle (AUV) 94, 118, 119
axis
–, instantaneous 62
–, of motion 71
–, optical 38352 Index
–, rotation 30, 37, 39, 41, 46, 48, 61, 66
–, Earth 83
–, screw 45, 50
B
back
–, EMF (electromotive force) 250, 258
–, end 168
ballbot 110
base
–, force 267
–, transform 197
Baxter robot 209, 275
behavior-based robot 125
Beidou (satellite navigation system) 151
bi-quaternion (see dual quaternion)
bias 86
bicycle model 98, 105, 142, 143
bifilar pendulum 277
blade flapping 113
blend 70
–, parabolic 70
body
–, acceleration estimation 81
–, moving 66
body-fixed frame 37, 53, 68, 77, 113
Braitenberg vehicle 124
breaking, stiction 250
Bresenham algorithm 179
Buffon’s needle problem 172
bug algorithm 126
bundle adjustment 182
C
C-space 54
calibration
–, camera 9
–, sensor 86
camera 168
–, pose 173
car 117–119
Cardan angle sequence 34
Cartesian
–, coordinate system 20
–, geometry 17
–, motion 75, 209, 212, 236
–, plane 17
–, point 177
–, trajectory 89, 212, 222
celestial navigation 150
center of mass 62, 66, 113, 251, 262
centripetal
–, acceleration 68
–, force 262
Chasles theorem 50
chi-squared distribution 158, 329
Cholesky decomposition 290
circle 74
city block distance 128
closed-form solution 203
clothoid 99
CML (see concurrent mapping and localization)
coefficient
–, Coulomb 270
–, viscous friction 250, 270
column space 291
compass 39, 83, 106, 149, 151, 153, 162
compensation, gravity 116
computed torque control 272
concurrent mapping and localization (CML) 165
condition number (see matrix condition number)
confidence test 162
configuration
–, change 214, 215
–, kinematic 196, 206, 207, 213, 214, 236
–, of a system 53
–, space 53, 54, 112, 117, 119, 143, 196, 199, 208, 209
–, zero-angle 195
connected component, graph 137, 338
constraint
–, nonholonomic 99, 109
–, rolling 119
control
–, feedback 260
–, feedforward 116, 258, 260, 270, 271
–, flexible transmission 12
–, force 273
–, independent joint 249
–, integral
–, action 257
–, windup 278
–, joint 249, 260
–, loop, nested 249
–, mobile robot 100–107
–, model-based 190
–, proportional 101, 102, 104, 255
–, derivative 114–116
–, integral 116, 258, 259
–, resolved-rate motion 235, 246
–, shared 7
–, space, operational space 273, 274
–, torque 270
–, computed 272
–, feedforward 271
–, traded 6
–, velocity 100, 255, 259
coordinate
–, frame 15, 16, 20
–, 2-dimensional 17
–, 3-dimensional 17
–, end-effector 192
–, global 179
–, moving 66
–, right-handed 29
–, velocity 66
–, generalized 53, 98, 107, 111, 117, 118, 192, 261
–, homogeneous 302
–, joint 196, 216, 227, 261
–, Plücker 50, 52, 296
–, point 20, 24, 45, 49
–, random 337
–, system 17
–, vector 15–17, 287, 295, 302
Coriolis
–, acceleration 68, 89
–, force 261, 262, 265, 273353
distortion, iron 85
distribution
–, chi-squared 329
–, von Mises 154
DOF (see degree of freedom)
down hill 319
drag, aerodynamic 113
dual
–, number 53
–, quaternion 53
Dubbins path 99
dynamics 249
–, error 272
–, forward 114, 116, 249, 269, 270
–, inverse 261, 271, 272
–, quadrotor 113, 114
–, rigid-body 261, 270
E
Earth
–, diameter 79
–, gravity 80
–, shape 79
–, surface 68, 77
east-north-up (ENU) 77
eccentricity 300
effect, Eötvös 89
effective inertia 254
EGNOS (satellite network) 151
eigenvalue 39, 158, 234, 268, 269, 290
eigenvector 39, 290
EISPACK project 9
EKF (see extendet Kalman filter and Kalman filter)
EKF SLAM (see Kalman filter, extended, SLAM)
elasticity, joint 274
ellipse 157, 299, 329
–, canonical 298, 299
–, confidence 165, 166
–, covariance 158, 164, 329
–, drawing 301
–, equation 329
–, error 158, 161
–, rotated 329
–, size 328
–, velocity 233, 242
ellipsoid 268, 299, 300
–, equation 329
–, force 242, 243
–, shape 234
–, surface 233, 243, 328
–, velocity 242
–, rotational 234
–, volume 234, 301
–, wrench 243
Elsie (robot) 93, 123
encoder 253, 254
end-effector 191
–, coordinate frame 230
–, force 242
–, inertia 273
–, torque 242
–, velocity 227, 228
ENU (see east-north-up)
General Index
correlation, covariance 152, 328, 334
correspondence, point 178
cost map 132
Coulomb friction 250, 251, 253
covariance
–, correlation 152, 328, 334
–, ellipse 158, 164, 329
–, matrix 152, 154, 156, 158, 159, 161, 163, 165, 167, 168, 174,
328
–, extending 163
curvature 139
cybernetics 1, 4, 124, 145
D
D* 132
d’Alembert force 67
damped inverse 238
data
–, association 162
–, error 151, 162
–, laser scan 177
–, type 55, 56
dead reckoning 95, 149, 153
declination
–, angle 83
–, magnetic 83
decomposition
–, Cholesky 290
–, spectral 291
Deep Phreatic Thermal Explorer (DEPTHX, AUV) 118, 119
definition
–, eigenvalue, eigenvector 39
–, frame 68
–, Mahalanobis distance 329
–, robot 5, 124, 128
degree of freedom (DOF) 37, 54, 71, 112, 118, 119, 189, 191, 193,
206, 208, 229, 232, 234, 238–240
Denavit-Hartenberg
–, notation 194, 195, 215, 216, 219, 227
–, modified 216
–, parameter 195, 198, 225
DEPTHX (see Deep Phreatic Thermal Explorer)
derivative
–, orientation 62, 66, 116
–, pose 61, 62
–, quaternion 62
–, time 61
detector, SURF (speeded up robust feature) 250
determinant 47, 233, 238, 291
differential, kinematics 227
Dijkstra method 130
dimension 15
–, curved 15
direction 307–309
displacement
–, rigid body 50, 51
–, spatial 65, 243
distance 162
–, Euclidean 16, 128, 338
–, Mahalanobis 162, 293, 329
–, Manhattan 128, 287
–, threshold 137
–, transform 128, 132, 133, 135354 Index
Eötvös, effect 89
ephemeris 150
equation
–, differential 49
–, Eulers rotation 66
–, line 295, 303
–, motion 99, 109, 269
–, Euler 114, 261
–, rigid-body 249, 261
–, nonhomogeneous 315
–, solving system 317
equivalence principle 68
error 47, 48, 167, 168
–, cumulative 168
–, edge 170
–, ellipse 157, 164, 166
–, ICP (iterated closest point) 180
–, position 249
–, vector 324
estimation 152
–, Monte-Carlo 155, 173, 181
–, pose 81
ethics 7
Euclidean
–, coordinate 27, 302
–, distance 16, 128, 338
–, geometry 16, 17, 20, 295
–, group 19, 25, 44
–, length 287
–, line 295
–, plane 17, 303
–, point 27, 295, 303, 304
–, space 17, 53, 295, 303
Euler
–, acceleration 68
–, angle 34–36, 38, 57, 73, 194, 230, 231, 245
–, singularity 37
–, force 68
–, motion equation 66, 114, 261
–, rotation theorem 30, 31, 33–35, 309
explicit complementary filter 86, 87
exponential
–, coordinate 41, 231, 322
–, rate 231
–, mapping 48, 50
–, matrix 23, 24, 41, 49
–, product of 194, 198, 199
extended Kalman filter (EKF, see also Kalman filter) 86, 88, 155,
167, 315, 334
exteroceptive sensor 5, 168
F
FastSLAM (see also SLAM and Rao-Blackwellized SLAM)
167
feature map 161, 166
feedback control 116, 258–260
feedforward control 116, 258, 260, 270, 271
fibre-optic gyroscope (FOG) 78fi
ctitious force 67, 81
field
–, magnetic, intensity 84, 85
–, robot 3, 94
file 170
–, MEX 284
filter
–, complementary explicit 86, 87
–, Kalman 88, 89, 155, 160–162, 167, 173, 180, 182, 332
–, extended (EKF) 86, 88, 155, 167, 315, 334
–, unscented (UKF) 182
–, Kalman-Bucy 333
–, particle 167, 173–176
flow, current 83fl
ux line, magnetic 83
FOG (see fibre-optic gyroscope)
font, Hershey 218
force 50, 66, 242, 249
–, apparent 67
–, control 273
–, Coriolis 261, 262, 265, 273
–, d’Alembert 67
–, ellipsoid 242, 243
–, fictitious 67, 81
–, gyroscopic 273
–, inertial 67
–, pseudo 67
–, translational 67
form, homogeneous 27
formula, Rodrigues rotation 35, 40, 41, 50, 51, 59, 64, 309
forward
–, dynamics 114, 269
–, kinematics 191, 192, 199, 202, 228
–, instantaneous 229
frame
–, body-fixed 53, 68, 77
–, coordinate 15, 16, 20
–, reference 67
–, inertial 66, 67, 77, 81
–, noninertial 68
–, right-handed coordinate 29
–, world coordinate 16, 77
friction 249–251, 260, 261, 266
–, aerodynamic 113
–, Coulomb 250, 251, 253, 266, 270
–, stiction 250
–, viscous 244, 250, 251, 253, 266, 269, 270
front end 168
function
–, Gaussian 327
–, Huber loss 321
–, observation 162
–, probability density (PDF) 151, 158, 159, 173, 327, 328
–, Gaussian 173
–, scalar 313
–, Tukey biweight 321
fusion, sensor 85, 86, 161
G
gait pattern 223
Galileo (satellite navigation system) 151
gantry robot 189
Gaussian
–, distribution 331, 332
–, function 327, 329
–, multivariate 328
–, noise 155, 158, 162, 332, 333
–, probability 158, 162, 329
–, random variable 327, 332, 334
gearbox 252–254355
generalized
–, coordinate 53, 98, 107, 111, 117, 118, 192, 261
–, joint 196, 216, 261
–, forces 261
–, joint 242, 244, 261, 262, 264, 266, 267
–, matrix inverse 292
–, Voronoi diagram 134
generator matrix 308, 310
Genghis (robot) 145
geomagnet 83
geometric Jacobian 229
geometry
–, algebraic 48
–, analytic 17
–, Cartesian 17
–, Euclidean 16, 17, 20, 295
gimbal 203
–, lock 36, 206, 213, 232
–, low-friction 78
Global Hawk unmanned aerial vehicle (UAV) 4, 112
Global Positioning System (GPS) 5, 115, 149, 151, 163
–, differential 151
–, multi-pathing 151
–, RTK 151
–, selective availability 151
GLONASS (satellite navigation system) 151
goal seeking 126
gradient, descent 319, 320
graph 134, 137, 337
–, A* search 132, 137, 140, 339
–, embedded 337
gravity 68, 82, 113, 249, 251
–, compensation 116
–, disturbance 258
–, load 249, 258, 261–263, 269
–, term 262
–, torque 252, 262
–, vector 82, 261
great circle 74
ground effect 113
group
–, algebraic 308
–, Euclidean 19
–, Lie 307
–, orthogonal 22, 32, 290
gyroscope 36, 77, 85, 99, 153
–, fibre-optic (FOG) 78
–, ring-laser (RLG) 78
–, strapdown 78
–, triaxial 78
H
Hall effect 83
–, sensor 83
hard-iron distortion 85
heading 83
–, angle 85
–, rate (see yaw rate)
helicopter 119
Hershey font 218
Hessian 313, 314, 320
–, approximate 314, 320
–, matrix 314
histogram, cumulative 174
holonomic constraint 54
homogeneous
–, equation 318
–, form 25
–, transformation 25, 44, 51, 52, 75, 197, 201, 303
–, normalization 48
homography 162
hovercraft 117–119
Huber loss function 321
humanoid robot 3, 6
hybrid, trajectory 70
hypersurface, quadric 304
I
ICP (see iterated closest point)
ICR (see instantaneous center of rotation)
ideal
–, line 303
–, point 303, 304
identity quaternion 43
image
–, plane 303
–, processing 128, 134
IMU (see inertial measurement unit)
inclination
–, angle 83
–, magnetic 83, 84
incremental replanning 132
inertia 251–253
–, effective 254
–, end-effector 273
–, load 253
–, matrix 114, 264
–, motor 253
inertial
–, force 67
–, measurement unit (IMU) 37, 85
–, navigation system (INS) 77, 85, 115
–, reference frame 66, 67, 77, 81
–, sensor 85
inflation, obstacle 130
innovation 87, 160, 168, 333
INS (see inertial navigation system)
instantaneous center of rotation (ICR) 98, 107
integral
–, dynamics 269
–, windup 258
intelligence, artificial 12
intensity
–, light 123
–, magnetic field 83, 85
interpolation
–, linear 73
–, orientation 73
–, quaternion 58, 74
–, rotational 74
–, scalar 210
–, unit-quaternion 74, 75
inverse
–, dynamic control 272
–, dynamics 261, 271, 272
–, left-generalized 317
–, pseudo 238, 240, 292, 317
iterated closest point (ICP) 177, 180, 181
General Index356 Index
J
Jacobian, Jacobian matrix 213, 216, 227, 228, 245, 313, 315
–, analytical 230, 231
–, condition 232
–, damped inverse 238
–, end-effector coordinate frame 230
–, geometric 229
–, insertion 163, 165
–, manipulability 232, 233
–, manipulator 227, 229, 245, 261
–, matrix 156, 170, 190, 213, 227, 228
–, numerical approximation 315
–, over-actuated robot 240
–, singularity 232, 238
–, transpose 227, 243, 244
–, under-actuated robot 239
jerk 68
Johns Hopkins Beast (robot) 145
joint
–, actuator 250
–, angle 5, 12, 196
–, control, independent 249
–, elasticity 274
–, position 273
–, prismatic 191, 193
–, revolute 191
–, sliding 191
–, space 196, 210, 242
–, velocity 227, 228
Joseph form 333
K
Kalman filter 88, 89, 155, 160–162, 167, 173, 180, 182, 332
–, extended (EKF) 86, 88, 155, 167, 315, 334
–, SLAM (EKF SLAM) 167
–, gain 333
–, unscented (UKF) 182
kernel, density approach 181
kinematic
–, configuration 196, 206, 207, 213, 214, 236
–, model 99, 105, 109, 112, 141, 143, 200
kinematics 191
–, differential 227
–, forward 191, 192, 199, 202, 228
–, instantaneous 229
–, symbolic 204, 228
–, inverse
–, closed form 203
–, numerical 204, 207, 243
–, velocity 227
Klein quadric 304
L
landmark 150, 162, 167, 180
–, identity 162
–, navigation 149
–, observation 159
laser
–, odometry 177
–, rangefinder 176, 177, 179
–, noise 178
–, scanner 168
lateral motion 98
lattice planner 138
law
–, Newton
–, first 67
–, second 66, 68, 80, 113, 261, 277
–, of robotics 1
least squares problem 238, 239, 244, 317
–, nonlinear 169, 314, 320, 321
–, rotation matrix 318
Levenberg-Marquardt
–, algorithm 244, 320, 321
–, optimization 244, 323
lever arm effect 251
Lie
–, algebra 51, 52, 307–310
–, group 23, 48, 307, 307–310
light intensity 123
line 304
–, 2D 295
–, 3D 296
–, equation 295, 303
–, Euclidean 295
–, ideal 303
–, of no motion 98
–, Plücker 296–298
–, projection 304
linear segment with parabolic blend (LSPB) trajectory 70, 259, 260
linearization 313
–, general 313
link 250
–, effect 251
–, elasticity 274
–, mass 251, 262
LINPACK project 9
load 275
–, gravity 249, 258, 261–263, 269
–, inertia 253
localization 9, 149, 165, 179
–, CML (concurrent mapping and localization) 165
–, error 151
–, laser-based 180
–, Monte-Carlo 173
–, problem 151, 152
–, SLAM (simultaneous localization and mapping) 165,
167–169, 173
longitude problem 150
longitudinal motion 98
LORAN (radio-based localization system) 151
LORD MicroStrain 77
LSPB (see linear segment with parabolic blend)
M
magnetic
–, declination 83
–, field 84, 85
–, flux 83
–, inclination 83, 84
–, north 83, 85
–, pole 83, 84
magnetometer 83, 85
Mahalanobis distance 162, 293, 329
Manhattan distance 128, 287
manifold 307–309357
manipulability 213, 232–235
–, dynamic 267, 269
manipulator (see also robot) 189
–, Jacobian 229, 242, 261
–, kinematics 227
–, over-actuated 54, 238, 240
–, serial-link, dynamics 249
–, under-actuated 54, 208, 238, 239
manoeuvre 118, 119
manufacturing robot 3
map 158, 162, 167
–, building, laser-based 179
–, feature 161, 166
–, obstacle 129
mapping 165
–, CML (concurrent mapping and localization) 165
–, exponential 48, 50
–, point 54
–, PTAM (parallel tracking and mapping) 173
–, SLAM (simultaneous localization and mapping) 165,
167–169, 173
Mars rover 4, 6
mass 66, 275
–, center of 62, 66, 113, 251, 262
–, distribution 66
–, link 251, 262
–, payload 266
–, proof 80
mathematical morphology 134
MATLAB®
–, code 9
–, command prompt 9
–, matrix xxv
–, MEX-file 284
–, object 8
–, software 8
–, Toolbox conventions xxv
matrix 288
–, adjoint 63, 67, 199, 245, 297, 311
–, adjugate 289
–, angular velocity 64
–, anti-symmetric 289
–, condition number 233, 293
–, covariance 152, 154, 156, 158, 159, 161, 163, 165, 167, 168,
174, 328
–, diagonal 159
–, extending 163
–, odometry 158
–, sensor 159
–, definite
–, negative 314
–, positive 314, 322
–, diagonalization 291
–, estimation 9
–, exponential 23, 24, 41, 49
–, exponentiation 48
–, generator 308, 310
–, Hessian 314
–, homography 9
–, identity 64
–, indefinite 314
–, inertia 114, 264
–, inverse
–, damped 238
–, pseudo 238–240
–, Jacobian 170, 227, 228
–, logarithm 23
–, MATLAB® xxv
–, normalization 47
–, orthogonal 22
–, orthonormal 32, 47
–, rank 232, 292
–, rotation 22, 33, 40, 48, 64
–, determinant 47
–, normalization 65
–, product 23
–, singular value decomposition 292, 318
–, skew-symmetric 23, 40, 41, 35, 41, 48, 49, 61, 64, 289,
309
–, augmented 310
–, sparse 324
–, transformation, homogeneous 50, 62
MAV (see micro air vehicle)
maximum
–, torque 257
–, velocity 70
measurement
–, odometry 154
–, random 154
–, strapdown inertial 85
–, unit, inertial (IMU) 38, 85
mecanum wheel 110
MEMS (see micro-electro-mechanical system)
method
–, Newton’s 320
–, Newton-Raphson 319
–, roadmap 134
MEX-file 284
micro-electro-mechanical system (MEMS) 78
micro air vehicle (MAV) 112
Mikrokopter (software project) 120
minimization, nonlinear 319
minimum-norm solution 208, 213, 240
mobile robot 3, 93, 97
mobility 119
model
–, bicycle 98, 105, 142, 143
–, kinematic 99, 105, 109, 112, 141, 143, 200
–, motion 97, 107, 110, 112, 113, 138, 142, 153, 269,
331, 332
–, nonlinear 86
–, process 331
–, quadrotor 113
–, screw 46
–, unicycle 105, 109
–, vehicle 105
model-based control 270
moment 50
–, image
–, line 296
–, matrix 318
–, of inertia 66, 262
–, torque 66, 113, 114, 242, 267
–, vector 28, 45, 50, 296
momentum, angular 66, 77
Monte-Carlo
–, estimation 155, 173, 181
–, localization 173
Moore-Penrose pseudo inverse 292
morphology (see mathematical morphology)
General Index358 Index
motion 61, 82
–, axis of 71
–, Cartesian 75, 209, 212, 236
–, complex 12
–, control, resolved-rate 232, 236, 237
–, discontinuity 76
–, end-effector 236
–, equation 66, 99, 109, 114, 249, 261, 269
–, inertial frame 82
–, joint-space 209, 214
–, lateral 110
–, longitudinal 98
–, model 97, 107, 110, 112, 113, 138, 142, 153, 269, 331, 332
–, multi-dimensional 71
–, null-space 12
–, omnidirectional 97, 110, 126, 138
–, planner 103
–, resolved-rate 12
–, rigid-body 25, 44, 45, 52, 307, 308
–, incremental 65
–, rotational 49, 50, 66
–, screw 45, 46
–, segment 72
–, sickness 81
–, singularity 213
–, straight-line 212
–, translational 28, 29, 49, 51, 66
motor 253, 254, 275
–, DC 249
–, high-torque 252
–, inertia 253
–, limit 257
–, servo 249
–, stepper 249
–, torque 250
multi-pathing 151
multi-segment trajectory 72
N
nautical
–, angle 36
–, chronometer 150
–, mile 149
navigation 95, 120, 123, 149
–, aerospace 42
–, algorithm 129
–, Beidou (satellite navigation system) 151
–, chart 151
–, dead reckoning 149
–, Galileo (satellite navigation system) 151
–, GLONASS (satellite navigation system) 151
–, GPS (Global Positioning System) 5, 115, 149, 151, 163
–, inertial 61, 64, 77, 85, 115
–, landmark 149
–, map-based 123
–, marine 165
–, radio 77
–, reactive 123, 124
–, satellite 5, 115, 149, 151, 163
–, spacecraft 36, 78
–, system 77, 85, 115
Navlab project 120
NED (see north-east-down)
nested control loop 249
Newton’s
–, first law 67
–, method 320
–, second law 66, 68, 80, 113, 261, 277
Newton-Euler method 261, 276, 277
Newton-Raphson method 319
node, graph 18, 137, 139, 142, 168, 337
noise 86, 154, 178
–, Gaussian 155, 158, 162, 332, 333
–, odometry 154, 156, 331
–, random 86, 154, 175
–, scanning laser rangefinder 178
–, sensor 160, 173
nonholonomy, nonholonomic 97
–, constraint 99, 109
–, system 119
normalization
–, homogeneous transformation 48
–, rotation matrix 47
normal matrix 290
north
–, magnetic 83, 85
–, true 83
north-east-down (NED) 77
null space of matrix 240, 292, 318
number
–, denominate 15
–, dual 53
–, random 137, 172, 331
O
observation 159
obstacle
–, inflation 128
–, map 129
occupancy grid 126, 128, 129, 179
odometer 153
odometry 153, 154, 168
–, differential 153
–, laser 177
–, noise 154, 156, 331
–, wheel 153
omnidirectional
–, motion 97, 110, 126, 138
–, vehicle 110
–, wheel 110
OmniSTAR satellite network 151
operational space 53
–, control 273, 274
operator 69
–, associative binary 19
–, asterisc 79
–, backslash 69, 317, 319
–, group 308
–, inverse 65
–, multiplication 52
–, spatial displacement 65
optical axis 38
optimization 171, 173, 180
–, algorithm 244
–, graph 173
–, Levenberg-Marquardt 244, 323
–, pose graph 170–172, 181
–, problem 169, 204359
orientation 15
–, 2-dimensional 21
–, 3-dimensional 30
–, derivative 62, 66, 116
–, end-effector 194
–, error 86
–, estimation 78, 82, 87
–, interpolation 73
–, vector 38
–, vehicle 99, 106
origin 15
orthogonal or orthonormal matrix 32, 289, 292
over-actuated robot 54, 238, 240
over-actuation 119, 238
P
parabolic blend 70
parallel tracking and mapping (PTAM) system 173
parallel-link robot 189
parameter
–, Denavit-Hartenberg 195, 198, 225
–, ellipse 288
particle filter 167, 173
path 68, 129, 132
payload 12, 249, 260
–, effect 266
–, lift capability 113
–, mass 266
PDF (see probability density function)
peak 151
–, velocity 70
pendulum, bifilar 277
phototaxis 124
pitch
–, angle 35
–, screw 45, 50
planar
–, robot 203
–, surface 95, 117
–, transformation 29
plane 298, 304
–, Cartesian 17
–, Euclidean 17, 303
–, image 303
planning
–, algorithm 133
–, map-based 128
–, robot path 128, 132
–, trajectory 145
Plücker
–, coordinate 50, 52, 296
–, line 296–298
point 15
–, 3D 29
–, Cartesian 177
–, cloud 179, 182
–, coordinate 24
–, homogeneous 49
–, vector 20, 45
–, corresponding, correspondence 178
–, equation
–, ellipsoid surface 233, 243
–, line 303
–, Euclidean 27, 295, 304
–, homogeneous form 27
–, ideal 303, 304
–, instantaneous center of rotation (ICR) 98, 107
–, line equation 303
–, mapping 54
–, moving to 100
–, task space 54
–, tool center (TCP) 201
–, transformation 22
–, vector xxv, 15, 20
–, velocity, angular 62
polar-coordinate robot arm 194
pole
–, magnetic 83, 84
–, rotational 28
polynomial
–, ellipse 300
–, function of time 69
–, matrix approximation 50
–, trajectory 69
pose 15, 53, 58, 168
–, 2D 55
–, 3D 56
–, camera 173
–, change 61
–, derivative 61, 62
–, end-effector 191, 227
–, error 168, 243
–, estimation 81
–, graph 168, 169
–, optimization 170–172, 181
–, SLAM (simultaneous localization and mapping) 165,
167–169, 173
–, robot (see also manipulator) 177, 179
–, singular 232
–, trajectory 75
position 15
positive definite 290
posterior probability 155
power series 50
probabilistic roadmap (PRM) 135
probability 10, 35, 152, 155, 172
–, conditional 155
–, density function (PDF) 151, 158, 159, 173, 327, 328
–, Gaussian 158, 162, 329
–, posterior 155
–, prior 155
process noise 154, 332
product
–, of exponential 198, 199
–, of inertia 66
projection, line 304
Prometheus Project 120
proof mass 80
proprioceptive sensor 5
pseudo
–, force 67
–, inverse 238, 240, 292, 317
–, Moore-Penrose 292
–, random numbers 172
PTAM (see parallel tracking and mapping)
Puma 560 robot 194, 200, 254, 274
pure
–, pursuit 103
–, quaternion 43, 53, 62
General Index360 Index
Q
quadric 304
–, hypersurface 304
–, Klein 304
quadrotor 54, 95, 97, 112, 118
–, control system 115
–, dynamics 113, 114
–, model 113
quaternion 42
–, computational efficiency 43
–, conjugate 43
–, convert to rotation matrix 43
–, derivative 62
–, double cover 42
–, dual 53
–, identity 43
–, interpolation 58, 74
–, pure 43, 53, 62
–, unit 42, 43, 45, 48, 53, 56, 62, 74
quintic polynomial 69
R
radio navigation 77, 151
radius, turning 139
random
–, coordinate 337
–, measurement 154
–, noise 86, 154, 175
–, number 137, 172, 331
–, sampling 137, 143
–, variable 327
–, Gaussian 327, 332, 334
rangefinder
–, remission 177
–, scanning laser 176–179
rank, matrix 232, 292
Rao-Blackwellized SLAM (see also FastSLAM) 167
rapidly-exploring random tree (RRT) 142, 143
rate
–, angular 86
–, exponential coordinate 231
–, roll-pitch-yaw angle 74, 116, 231
–, rotation matrix 62
ratio 266
–, gear 252, 262
recursive Newton-Euler 261
redundant robot 54, 208, 224, 238
Reeds-Shepp path 99
reference
–, frame 67
–, inertial 66, 67, 77, 81
–, noninertial 68
–, system, attitude and heading (AHRS) 85
reflectance, reflectivity 177, 178
–, specular 178
remission 177
renormalization 53
replanning, incremental 132
representational singularity 231
resampling 174
resectioning 150
resolved-rate motion control 232, 235
response
–, position loop 260
–, velocity loop 256–258
right-hand rule 29
rigid-body
–, displacement 44, 50, 51
–, dynamics 261, 270
–, motion 25, 44, 45, 52, 65, 307, 308
ring-laser gyroscope (RLG) 78
roadmap 134
robot (see also manipulator) 189
–, arm 119
–, model 198
–, planar 192, 243
–, polar-coordinate 194
–, PUMA 193
–, serial-link 194
–, SCARA (Selective Compliance Assembly Robot Arm)
189, 193, 208
–, Stanford 193
–, Asimo humanoid 6
–, base transform 201, 216
–, Baxter 209, 275
–, behavior-based 125
–, definition of 5, 124, 128
–, DEPTHX (Deep Phreatic Thermal Explorer, AUV) 118, 119
–, Elsie 94
–, end-effector 190
–, field 3, 94
–, gantry 189
–, high-speed 274
–, humanoid 3, 6
–, joint
–, modelling 253
–, structure 193
–, kidnapped 176
–, law 1
–, manipulability 213, 234
–, manufacturing 3
–, maximum payload 266
–, mobile 3, 93, 97
–, over-actuated 54, 240
–, path planning 129, 132
–, parallel-link 189
–, planar 203
–, pose 177, 179
–, Puma 560 194, 200, 254, 274
–, redundant 54, 208, 224, 238
–, Shakey 93
–, service 3
–, singularity 206, 213
–, tele- 5
–, tool transform 201, 202, 216, 220
–, tortoise 93
–, trajectory 167
–, under-actuated 54, 208, 238, 239
–, walking 219
–, wrist 194, 213
Rodrigues
–, rotation formula 35, 40, 50, 51, 59, 64, 309
–, vector 40
roll angle 35
roll-pitch-yaw angle 35, 36, 38, 230, 231
–, rate 74, 116, 231361
–, singularity 36
–, XYZ 35, 36, 212, 230
–, ZYX 35
rolling, constraint 119
root, finding 318
Rossum’s Universal Robots (RUR) 3
rotation, rotational 45, 48, 52
–, angle 23, 24, 29, 33, 35, 37, 41
–, axis 30, 37, 39, 41, 46, 48, 61, 66
–, direction 74
–, formula 35, 40, 50, 51, 59, 64, 309
–, incremental 64
–, inertia 66
–, interpolation 74
–, matrix 22, 33, 34, 38, 40, 43, 48, 64, 230
–, determinant 47
–, estimating 318
–, least squares problem 318
–, normalization 65
–, product 23
–, reading 33
–, motion 49, 50, 66
–, pole 28
–, rate 62
–, theorem, Euler’s 30, 31, 33–35, 309
–, torque 67
–, twist 28
–, vector 28
–, velocity 61, 63, 67
row space 291
RRT (see rapidly-exploring random tree)
RTK GPS (see Global Positioning System (GPS), RTK)
rule, right-hand 29
RUR (see Rossum’s Universal Robots)
S
saccule 81
sampling
–, importance 174
–, probabilistic 145
–, random 137, 143
satellite navigation
–, system 5, 115, 149, 151, 163
–, network 151
saturation, actuator 116
scalar 15, 52
–, field 314
–, function 313, 314
–, interpolation 210
–, multiplication 287
scale factor 86
scanning laser rangefinder 176, 177, 179
–, noise 178
SCARA (see Selective Compliance Assembly Robot Arm)
Schur complement 324
screw 45, 50
–, axis 45, 50
–, model 46
–, motion 45, 46
–, pitch 45, 50
–, theory 50
SE(2) 25, 32
se(3) 51, 52, 310
SE(3) 44, 46, 51, 52, 71, 75, 310, 311, 322
SEA (see series-elastic actuator)
selective availability 151
Selective Compliance Assembly Robot Arm (SCARA) 189, 193,
208
sensor 168
–, acceleration 81, 85
–, bias 86
–, calibration 86
–, drift 86
–, error 168
–, fusion 86, 161
–, Hall effect 83
–, inertial 85
–, noise 160, 173
–, range and bearing 159
serial-link manipulator 191
series-elastic actuator (SEA) 274, 275
Shakey (robot) 93
shape
–, change 233, 243
–, Earth 79
–, ellipsoid 234
shared control 7
similarity transform, transformation 291
similar matrix 291
Simulink 10, 270
–, block 99
–, library 109
–, kinematics 212
simultaneous localization and mapping (SLAM) 165
–, back end 168, 172, 173
–, EKF (extended Kalman filter) 167
–, Fast 167
–, front end 168, 172
–, pose graph 165, 167–169, 173
–, Rao-Blackwellized 167
–, system, vision-based 173
singular
–, pose 232
–, value 292
–, decomposition 292
–, vector 292
singularity 35, 36, 206, 213
–, angle
–, Euler 37
–, roll-pitch-yaw 36
–, Jacobian 232, 238
–, motion 213
–, representational 231
–, three angle representation 36
–, wrist 206, 213
singular value decomposition (SVD) 292, 317, 318
skeleton 135, 201
–, topological 134
skeletonization 134, 135
skew-symmetric matrix 23–25, 40, 41, 48, 49, 61, 64, 88, 289, 304,
309
–, augmented 310
skid steering 109
SLAM (see simultaneous localization and mapping)
SO(2) 22, 307, 308
so(3) 52, 231, 309
SO(3) 32, 66, 71, 73, 79, 308, 309
General Index362 Index
soft-iron distortion 85
solution
–, closed-form 203
–, minimum-norm 240
–, numerical 204
solving system 317
space
–, configuration 53, 54, 112, 117, 119, 143, 196, 199, 208, 209
–, control 273, 274
–, Euclidean 17, 53, 295, 303
–, inertial reference equipment (SPIRE) 77
–, joint 196, 210, 242
–, operational 53
–, control 273, 274
–, task 53, 54, 208, 209
–, vector 287
sparse matrix 324
spatial
–, displacement 65, 243
–, operator 65
–, velocity 62, 63, 67, 229, 230, 237
–, vector 62
special
–, Euclidean group 19, 25, 44
–, orthogonal group 22, 32, 290
spectral decomposition 291
specular reflection 178
speeded up robust feature (SURF) detector 250
spherical
–, linear interpolation 74
–, wrist 197, 203, 205
SPIRE (see space inertial reference equipment)
spring 80, 275
–, torsional 275
Stanford, robot arm 193
steering
–, Ackermann 99, 121
–, angle 99, 100, 139, 143
–, mechanism 97
–, skid 109
stereo glasses 33
stiction 250
straight-line motion 212
strapdown
–, configuration 78
–, gyroscope 78
–, inertial measurement 85
subsumption architecture 125
surface
–, 3D 130
–, Earth 68, 77
–, ellipsoid 233, 243, 328
–, hypersphere 233
–, planar 95, 117
–, polished 178
–, writing on 218
SVD (see singular value decomposition)
Swedish wheel 110
symmetric matrix 264, 289
system
–, attitude and heading reference (AHRS) 85
–, configuration 53
–, coordinate 17
–, homogeneous 318
–, inertial navigation (INS) 77, 85, 115
–, nonholonomic 119
–, nonhomogeneous 317
–, nonintegrable 119
–, nonlinear 334
–, under-actuated 118
–, vestibular 78, 81
T
tag, April 162
Tait-Bryan angle 36
tangent space 308
task space 53, 54, 208, 209
taxis 124
Taylor series 313
TCP (see tool center point)
telerobot 5
temperature drift 86
tensor 287
theorem
–, Chasles 50
–, Euler’s rotation 30
theory
–, Lie group 23
–, screw 50
thinning (also skeletonization) 134, 135
threshold distance 137
thrust 113
time 61
–, derivative 61
–, series xxv
–, varying pose 61, 68
tool
–, center point (TCP) 201
–, transform 197, 201, 202, 216, 220
toolbox
–, functions 55–57
–, obtaining 283
topological skeleton 134
topology, algebraic 48
torque 249, 251, 252, 273
–, control 270
–, computed 270, 272
–, feedforward 258, 270, 271
–, disturbance 249
–, end-effector 242
–, gravity 252, 262
–, maximum 257
–, moment 66, 113, 114, 242, 267
–, motor 250
–, rotational 67
trace of matrix 291
traded control 6
trajectory 68, 72, 74–76, 88, 137, 167, 207, 209, 221, 223, 249, 261
–, Cartesian 89, 212, 222
–, continuous 72, 218
–, end-effector 249
–, following 103, 138
–, hybrid 70
–, joint-space 210–212, 214
–, lane-changing 100
–, leg 219
–, multi-axis 71363
–, multi-segment 72
–, planning 145
–, polynomial 69
–, pose 75
–, robot 167
transconductance 250
transform
–, base 197
–, distance 128, 132, 133, 135
–, planar 29
–, SE(2) 29
–, tool 197, 201, 202, 216, 220
–, homogeneous 25, 44, 51, 52, 75, 197, 201
–, matrix 50, 62
–, point 22
–, SE(2) 25
–, SE(3) 44
–, wrench 242
translation 44, 51, 52
transmission 249, 274
–, flexible 12
–, mechanical 107
transpose, Jacobian 244
trapezoidal trajectory 70
traversability 128, 132
triangulation 150
triaxial
–, accelerometer 81, 85
–, gyroscope 78
–, magnetometer 83
triple point 134
true north 83
Tukey biweight function 321
turning radius 98, 139
twist 28, 46, 50, 51, 198, 245, 310
–, axis 45
–, Jacobian computing 245
–, nonunit 29, 46
–, rotational 28
–, transforming 310
–, unit 28, 46, 50, 52
–, vector 28, 29, 45
–, velocity 63, 245
U
UAV (see unmanned aerial vehicle)
UKF (see unscented Kalman Filter)
uncertainty 158, 159, 161
under-actuated 54, 97, 118, 119, 193, 227
–, robot, manipulator 54, 208, 238, 239
–, system 118
unicycle, model 109
Unimation Inc. 2
unit
–, inertial measurement (IMU) 38, 85
–, quaternion 42, 43, 45, 53, 56
–, derivative 62
–, interpolation 74
–, normalization 48
–, twist 28, 46, 50, 52
unmanned aerial vehicle (UAV) 112
unscented Kalman Filter (UKF) 182
utricle 81
V
VaMoRs system (autonomous van) 120
variable, Gaussian random 332
Vaucanson’s duck 1
vector 15, 287
–, addition 287
–, approach 38
–, bound 15
–, coordinate 15–17, 287, 295, 302
–, error 324
–, field 315
–, gravity 82, 261
–, moment 28, 45, 50, 296
–, normal 38
–, orientation 38
–, point xxv, 15, 20
–, Rodrigues 40
–, rotation 28
–, scalar function of 314
–, singular 292
–, space 287
–, twist 28, 29, 45
–, vector function of 314
–, velocity 62, 228
vehicle
–, aerial 119
–, autonomous 6, 94
–, surface (ASV) 94
–, underwater (AUV) 94
–, Braitenberg 124
–, car-like 97, 98
–, configuration 98
–, coordinate system 98
–, differentially-steered 97, 107
–, frame 98
–, micro air (MAV) 112
–, mobile robot 3, 93, 97
–, model 105
–, omnidirectional 110
–, orientation 99, 106
–, path 101, 103, 107
–, underwater 119
–, unmanned aerial (UAV) 94, 112
–, velocity 99
–, wheeled 95, 97
velocity 249, 273
–, angular 48, 50, 62, 66, 68, 77, 78, 153, 231,
332
–, time-varying 66
–, vector 64
–, control 100, 255, 259
–, feedforward 260
–, loop 255, 259
–, coupling torque 262
–, discontinuity 76
–, ellipse, ellipsoid 233, 234, 242
–, end-effector 227, 228
–, joint 227, 228
–, kinematics 227
–, linear 50, 66
–, maximum 70
–, peak 70
–, rotational 61, 63, 67
General Index364 Index
–, spatial 62, 63, 67, 229, 230, 237
–, translational 61, 63, 67
–, twist 63, 245
–, vector 62, 228
–, vehicle 99
vestibular system 78, 81
via point 72
viscous friction coefficient 250
visual simultaneous localization and mapping (VSLAM)
182
von Mises distribution 154
Voronoi
–, cell 135
–, diagram 134, 135
–, roadmap 135
–, tessellation 135
VSLAM (see visual simultaneous localization and mapping)
W
WAAS (see wide area augmentation system)
walking robot 219
waypoint 155
Wide Area Augmentation System (WAAS) 151
world coordinate frame 16, 77
wrench 63, 67, 242, 243, 261, 267
–, ellipsoid 243
–, end-effector 242, 243
–, transformation 242
wrist 206
–, coordinate frame 201
–, robot 194, 213
–, singularity 206, 213
–, spherical 197, 203, 205
X
XYZ, roll-pitch-yaw angle 36, 212, 230
Y
yaw angle 35
yaw rate 99, 161
Yoshikawa’s manipulability measure 234
Z
zero-angle configuration 195
ZYX roll-pitch-yaw angle 35
ZYZ Euler angles 34


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