Index

Čapek, Karel, 1
accuracy, 10
Acrobot, 439, 445, 510
across variable, 353
adaptive control, 311, 327
adaptive inverse dynamics, 327
analytic approach, 36
angle convention, 443
angular momentum, 479, 490
angular velocity, 107, 108
annihilating codistribution, 484
anthropomorphic, 13
anti-windup, 308
apparent damping, 357
apparent inertia, 357
apparent stiffness, 357
application area, 9
approach vector, 85
arm singularity, 124
armature, 273
armature current, 274
armature inductance, 274
armature resistance, 274
armature voltage, 274
articulated (RRR), 9
artificial potential field, see also potential field
assembly robots, 9
asymptotic stability, 542
Atan2, 523
axis-angle representation, 53, 58

back emf, 273
back emf constant, 275
backlash, 272
balance control, 473
bang-bang trajectory, 260
Barbalat's lemma, 333, 514, 549
base frame, 20
base variables, 500
baseline distance, 402
basic homogeneous transformation, 63
basic rotation matrix, 42
basis, 526
- change of, 530
- reciprocal, 348
bilinear form, 349
blend time, 257
body-attached frame, 177
Brockett's theorem, 480, 509
Brunovsky canonical form, 420

camera calibration, 371, 555
- extrinsic camera parameters, 556
- intrinsic camera parameters, 557
camera coordinate frame, 369
capacitive environment, 354
capacitive impedance, 354
cart-pole system, 443, 460
Cartesian (PPP), 9
center of projection, 369
central limit theorem, 235
centrifugal force, 183
chained form, 499
characteristic polynomial, 418, 530
Chow's theorem, 480, 497
Christoffel symbols, 183
closed-loop, 8
codistribution, 412, 484
commutator, 274
compensator, 272
completely integrable, 416
compliance, 272
compliance frame, 349
computed torque, 25
computer interface, 10
computer vision, 1
configuration, 5, 217
configuration space, 5, 217
configuration space obstacle, 218
configuration space roadmap, 246
connectivity graph, 227
constraint, 347
- artificial, 349, 351
- holonomic, 165, 171, 461, 480
- natural, 349, 350
- nonholonomic, 171, 439, 479
- Pfaffian, 481
- unilateral, 439
- virtual, 461, 466
constraint frame, 349
continuous function, 539
continuous path control, 9
continuous path tracking, 271
control, 1
- adaptive, 311, 327, 332
- chattering, 326
- discontinuous, 325
- independent joint, 272
- inner loop, 320, 409
- inner-loop/outer-loop, 418
- inverse dynamics, 318
- linear quadratic optimal, 301
- multivariable, 311
- optimal, 334
- outer loop, 320, 356, 409, 418
- passivity-based, 329
- pointwise optimal, 335
- robust, 311, 331
- state feedback, 299
control architecture, 320
controllability, 299, 496
controllability matrix, 299
controllability rank condition, 498
controllable system, 299
controlled-invariant manifold, 466
controller resolution, 11
convex spatial decomposition, 227
Coriolis force, 183
cotangent space, 411
covector field, 411
critical eigenvalues, 544
cross product, 532
cross product of inertia, 179
current frame, 49, 52
cylindrical (RPP), 9

D'Alembert's principle, 174
DC motor, 167, 272
decoupling matrix, 462
degree of nonholonomy, 486
degree of underactuation, 440
degrees of freedom, 6
Denavit-Hartenberg convention, 21, 79
dexterous workspace, 7
DH convention, 79
diffeomorphism, 410, 420, 432
differential flatness, 506
differential drive robot, 491
direct method of Lyapunov, 26
direct-drive robot, 30, 272
directional derivative, 410, 413
distribution, 412
- annihilating, 484
- involutive, 416, 484
- involutive closure of, 486
disturbance, 272
disturbance rejection, 272
dot product, 527
double integrator, 318, 456
driftless system, 479, 484
- controllability of, 495
dual space, 411
dynamic extension, 493, 512
dynamic feedback linearization, 517
dynamics, 1, 24, 165
- Newton-Euler formulation, 165

effort, 353
eigenvalues, 530
elbow, 14
elbow manipulator, 13
end effector, 12
end-of-arm tooling, 10
energy, 353
- kinetic, 165
- potential, 165, 167
environment, 345
- capacitive, 354
- classification of, 358
- inertial, 354
- resistive, 354
environment stiffness, 352
equilibrium, 449
equilibrium point, 542
estimation error, 302
Euler angles, 53, 90, 172
Euler-Lagrange equations, 165
Euler-Lagrange equations, 166
exponential coordinates, 59
exponential stability, 543, 546
external power source, 10
eye-in-hand configuration, 366

feedback linearizable, 419
feedback linearization, 27, 317, 409, 426, 461, 515
feedforward control, 25, 288
fiber variables, 500
Filippov solution, 326
filtration, 486
final value theorem, 285
five-bar linkage, 191
fixed frame, 50, 52
fixed point, 449, 542
fixed-camera configuration, 366
flat output, 507
flexibility, 292
flow, 353
focal center, 369
focal length, 370
force control, 26, 345
forward kinematics, 19, 21, 75
forward kinematics problem, 20
frame, 76
- base, 76
- current, 52
- end-effector, 85
- fixed, 52
- inertial, 76
- tool, 85
- world, 76
friction, 272
Frobenius theorem, 27, 414, 422, 484

gain
- derivative, 282
- integral, 281
- proportional, 281
gear
- harmonic, 292
- strain wave, 292
gear ratio, 276
gear train, 167
generalized coordinates, 167, 171
generalized force, 168, 175
generalized Voronoi diagram, 224
geometric nonlinear control, 409
global stability, 542, 543, 546
gradient, 449, 541
gravitational force, 167
group, 67
gyroscopic force, 200

Hamilton's principle, 166
Hamiltonian, 500
hand, 12
hardware/software trade-off, 271
harmonic gear, 292, 293
Hessian, 541
HOG feature detector, 377
home position, 95
homoclinic orbit, 468
homogeneous coordinates, 21
homogeneous representation, 63
homogeneous transformation, 21, 63
hopping robot, 490
Hurwitz matrix, 325, 544
Hurwitz polynomial, 289
hybrid control, 26
hybrid impedance control, 358

image feature, 373
image feature velocity, 378
image features, 369
image Jacobian, 379
image-plane coordinates, 370
impedance, 353, 354
- dual, 358
impedance control, 26, 356
impedance control, hybrid, 358
impedance operator, 353
implicit function theorem, 416
independent joint control, 272
industrial manipulator, 1
inertia
- apparent, 357
inertia matrix, 180
inertia tensor, 178
inertial environment, 354
inertial impedance, 354
integral manifold, 415
integrating factor, 482
integrator windup, 308
interaction matrix, 379, 380, 385
internal dynamics, 458, 460
inverse dynamics, 26, 317, 356, 409
inverse dynamics control, 318
inverse kinematics, 22, 141
inverse orientation kinematics, 144
inverse position kinematics, 144
inverted pendulum, 443
involutivity, 416

Jacobi identity, 533
Jacobian, 21, 101, 111, 130, 541
Jacobian matrix, 413
jerk, 256
joint
- prismatic, 5
- revolute, 5
joint angle, 79
joint elasticity, 292
joint flexibility, 292, 409, 423
joint variable, 5

Killing form, 349
kinematic car, 488
kinematic chain, 5, 75
kinematically redundant, 6
kinematics, 1
kinetic energy, 165, 166
Kinova robot, 6
Klein form, 349
KUKA 500 FORTEC robot, 2

Lagrange multiplier, 336, 493, 500
Lagrangian, 165, 167, 177
Lagrangian dynamics, 24
Laplace domain, 354
Laplace transform, 354
LaSalle's theorem, 469, 548
law of cosines, 23
Lie bracket, 412, 417
Lie derivative, 413
linear approximation, 544
linear controllability, 450
linearity-in-the-parameters, 197
linearly independent, 526
link length, 79
link offset, 79
link twist, 79
lower-actuated, 441
LSPB, 257
Lyapunov
- direct method, 544
Lyapunov design, 513
Lyapunov function, 545, 546
Lyapunov function candidate., 545
Lyapunov redesign, 323
Lyapunov's direct method, 544
Lyapunov's indirect method, 544

magnetic flux, 273
manifold, 410, 466
- integral, 415
manipulability ellipsoid, 133
manipulator
- cylindrical, 89, 91
- elbow, 87
- industrial, 1
- SCARA, 95
- spherical, 14
- Stanford, 93
matrix
- range, 531
matrix inverse, 530
matrix Lyapunov equation, 548
mechanical impedance, 353
mechatronics, 4
minimum phase, 290
mobile robot, 4, 479
mobility tensor, 356
motion perceptibility, 397
motion planning, 1
multivariable control, 311
multivariable system, 311

narrow passage problem, 248
network model, 353
Newton-Euler formulation, 198
nonassembly robots, 9
nonholonomic constraint, 439
nonlinear control, 25
nonservo controlled robots, 8
normal form, 458, 460
normal vector, 85
Norton equivalent, 355
Norton network, 355
null solution, 542
numerically controlled
milling machines, 2
nutation, 122

observability, 302
observability matrix, 302
observable, 302
observer, 301
one-port network, 353
open-loop, 8
orthogonal complement, 528
orthogonal matrix, 40
orthonormal basis, 350
outer product, 533
output linearization, 461
overhead crane, 443

parallel manipulator, 9
parameter drift, 344
partial feedback linearization, 456
- collocated, 456, 457
- noncollocated, 456, 459
partitioned methods, 394
passivity, 329, 466
passivity property, 195
passivity-based adaptive control, 332
passivity-based control, 26, 329, 466
path planning, 24
PD control, 313
peg in hole, 9
Pendubot, 439, 446, 449, 454
perspective projection, 371
phase portrait, 468
pinhole lens model, 369
pitch, 56
pixel, 368
pixel coordinates, 371
point-to-point, 252
point-to-point control, 8
point-to-point motion, 271
port variable, 353
position control, 25
positive definite, 545
positive definite matrix, 181
positively invariant set, 548
potential energy, 165, 167, 449
potential field, 229
- attractive potential, 230
- conic well potential, 230
- parabolic well potential, 230
- repulsive potential, 231
- workspace potential, 229
power, 353
precession, 122
primal-dual method, 336
principal moment of inertia, 179
principal point, 370
principle of virtual work, 166, 173
prismatic joint, 5
PRM, 246
probabilistic roadmap, 246
product of exponentials, 100
programmable robot, 30
projection ray, 385
proper rational function, 290
pseudoinverse, 459

quadratic form, 545
quadratic programming, 334
quaternion, 70

radially unbounded, 546
randomized methods, 234
range space, 531
rank, 528
rapidly-exploring random tree, 246, 250
reachable workspace, 7
Reaction-Wheel Pendulum, 447, 452, 460
reciprocity, 348
reference trajectory, 25
regressor, 197
relative degree, 461, 462
repeatability, 10
representational singularities, 122
resistive environment, 354
resistive impedance, 354
resolvability, 407
revolute, 13
revolute joint, 5
Riccati equation, 301
rigid motion, 19
robot, 1
- definition of, 2
- direct-drive, 272
- flexible joint, 439
- industrial, 1
- mobile, 4
- parallel, 18
- underactuated, 440
robot geometry, 9
Robot Institute of America, 2
robota, 1
robotic system, 10
robust control, 311, 331
Rodrigues’ formula, 61
roll, 56
roll-pitch-yaw angles, 53
root locus, 295
rotation matrix, 20, 39
rotor, 273
Routh-Hurwitz criterion, 288
RRT, 246, 250

sampling-based planner, 245
saturation, 286, 334, 470
scalar product, 527
SCARA (RRP), 9
SCARA robot, 14
Schur complement, 458
second moment matrix, 376
second-order normal form, 458, 460
sensor
- force, 346
- tactile, 346
- torque, 346
separation principle, 303
serial manipulator, 9
servo controlled robots, 8
set-point tracking, 284
shoulder elevation, 14
single-input/single-output system, 25
singular configuration, 22, 102, 123
singular value decomposition, 537
singular values, 537
singularity, 123
sinusoids, 500
SISO system, 25, 272
skew symmetry property, 194
skew-symmetric matrix, 59, 103
sliding vector, 85
sliding-mode control, 511
spherical (RRP), 9
spherical manipulator, 14
spherical wrist, 12, 90
spin, 122
square integrable function, 549
stability
- asymptotic, 542
- exponential, 543
- global, 546
stable equilibrium, 542
Stanford arm, 30
state space, 6, 542
stator, 273
steering, 500
stereo cameras, 402
strain gauge, 346
strain wave gear, 292
strong inertial coupling, 459
structure tensor, 376
superposition, 283
swingup control, 473
switching control, 511
switching time, 260
symmetric matrix, 181
synthetic approach, 36
system
- multivariable, 311
system type number, 285

tangent plane, 415
tangent space, 410
task space, 355
teach and playback mode, 252
teach pendant, 9, 11
teleoperator, 2
through variable, 353
Thevenin equivalent, 355
Thevenin network, 355
tool, 12
torque constant, 275
torque optimization, 333
tracking, 272
tracking and disturbance rejection, 25
tracking error, 281
trajectory, 252
trajectory generation, 24
trajectory planning, 24
trajectory tracking, 513
transformation
- basic homogeneous, 63
- homogeneous, 63
- matrix, 77
transformation matrix, 77
trapezoidal decomposition, 227
trapezoidal velocity profile, 257
two-argument arctangent function, 54, 523
type-1 system, 285

ultimate boundedness, 323
uncertainty, 322
underactuated mechanical system, 439
underactuated robot, 439
underactuation, 439
unicycle, 479, 487, 510
uniform continuity, 539
uniform ultimate boundedness, 332, 550
unilateral constraint, 439
Unimate, 30
unstable equilibrium, 542
upper-actuated, 440

vanishing point, 373, 557
vector field, 411, 541
- complete, 495
vector product, 532
velocity
- angular, 107
velocity kinematics, 21
via points, 252, 261
virtual displacement, 130, 172
virtual holonomic constraint, 466
virtual work, 130, 165, 166
visibility graph, 222
vision-based control, 26, 365
visual servo control
- image-based, 366, 368, 386
- partitioned methods, 368
- position-based, 367

waist rotation, 14
workspace, 7
- dexterous, 7
- reachable, 7
world frame, 20
wrist, 12
wrist center, 90, 144
wrist center point, 12
wrist singularity, 124

yaw, 56

zero dynamics, 461, 462, 517
zero dynamics manifold, 462