INDEX

J-space monotonicity, 312

P P P (Cartesian) robot arm, 276

X X P robot arms, 274

X X X robot arms, 274

l_i-front monotonicity, 285

l_i-rear monotonicity, 285

l_i-Link-Arm Algorithm, 210

A

actuators, 18

algorithm convergence, 57

ANOVA, 362

arm base, 18

arm configuration, 18

arm joints range, 200

arm solution, 187

arm's minimal configuration, 180

B

Bug1 algorithm, 84

Bug2 algorithm, 90

Bug2 path, 109

BugM1 algorithm, 101

C

canonical solution, 144, 159

Cartesian (PP) robot arm, 182

Cartesian coordinates, 19

Class 1 algorithms, 77

Class 2 algorithms, 77

collision avoidance, 48

complementary M-lines, 203

compliant motion, 40

computational complexity, 53

configuration space (C-space), 18

configuration space anisotropy, 285

connectedness, uniform, 252

connectivity graph, 305, 323

contiguous sets, 107

conventional projection, 295

D

deformation retract, 305

deformation retract theorems, 317

degrees of freedom (DOF), 18

direct kinematics solution, 30

dynamics, 33

E

effect of vision, 104

end effector, 18

end effector, gross motion, 180

end effector, orientation, 180

Euler, Leonhard, 59

exhaustive search, 64

F

feedback control, 37

Fraenkel's algorithm, 65

Frenet frame, 146, 161

front contact, 229

front shadow, 229

G

generalized cylinder, 277, 308

generic path, 321

geodesic curves in C-space, 194

graph searching, 61

guarded motion, 40

H

heuristic algorithms, 50

hinged robot body, 15

hit point, 79, 106, 146, 186, 283

human motion planning, 329

humans, test factors, 349

I

in-position condition, 93

input information, 15

intermediate target, 106

inverse kinematics solution, 30

J

Jogger's Problem, 140

joint coordinates, 19

joint value, 187

joint, arm joints, 18

Jordan Curve Theorem, 77, 195

K

Königsberg Bridge Problem, 59

kinematics, 29

Klein bottle, 77

L

leave point, 79, 107, 146, 186, 283

LED (light-emitting diode), 393

limit areas of PR arm, 234

link, arm links, 18

local cycle, 207

local direction, 79, 107, 186, 282

lower bound, Class 1 algorithms, 103

lower bound, Class 2 algorithms, 103

M

M-line (Main line), 61, 90, 106

M-plane, 281

MA, moving automaton, 78

Main line (M-line), 188, 280

main semiplane, 107

major linkage, 19, 180, 273

Mann–Whitney U-test, 358

MANOVA, 372

Maximum Turn Strategy, 144

maze searching, 60

maze-to-graph transition, 66

minimal projection, 295

Minimum Time Strategy, 144

minor linkage, 19, 180, 273

Moebius strip, 77

monotonicity property, 320

motion planning with complete information, 49

motion planning with incomplete information, 49

N

near-canonical solution, 159

nonparametric statistics, 358

null hypothesis, 363

O

obstacle, 15

obstacle monotonicity, 285

obstacle of Type I, 198, 286

obstacle of Type II, 198, 286

obstacle of Type III, 286

obstacle's shadow, 190, 280

obstacles

stalactites in C-space, 290

stalagmites in C-space, 290

one-way analysis of variance, 363

order statistics, 358

osculating plane, 146, 161

out-position condition, 93

P

passing around an obstacle, 192

path coordinate frame, 146

Piano Movers paradigm, 49

planar arms, 180

point mass, 160

PP-arm Algorithm, 228

PR-arm Algorithm, 245

primary path frame, 160

Principal Components Analysis (PCA), 354, 355

prismatic joint, 18

prismatic-prismatic (PP) arm, 182

prismatic-revolute (PR) arm, 182

Procedure Compute T_i-21, 110

Procedure Compute T_i-22, 121

provable algorithms, 50

Q

quasi-Bug2 path, 121

R

radius of vision, 106

rank, statistics indexing, 358

rear contact, 229

rear shadow, 229

regular grating, 262

revolute joint, 18, 180

revolute–prismatic (RP) arm, 182

revolute–revolute (RR) arm, 181

robot, 13

robot arm manipulator, 18

robot's path, 20

RP-arm Algorithm, 233

RR-Arm Algorithm, 210

S

scanning, 106

SCARA arm manipulator, 179

secondary path frame, 161

secondary semiplane, 107

sensitive skin, 17, 392

sensitive skin diagram, 390

separable arm, 180, 273

separation theorems, 261

sequential linkage, 18

SIM (Sensing-Intelligence-Motion) paradigm, 49, 55, 74, 177

skin properties, 392

skin, full coverage, 391

skin, locality identification, 391

sliding (prismatic) joint, 18, 180

space anisotropy, 273

space monotonicity, 273

statics, 33

step planning, 212

stopping path, 140

straight-line interpolation, 46

T

Tarry's Rule, 64

terrain acquisition, 125

test for target reachability, 89

Bug1, 88

Bug2, 99

topology of obstacles, 285

trajectory, 20

Tremaux, 64

two-way analysis of variance, 365

Type I monotonicity, 287

Type II monotonicity, 287

Type III monotonicity, 290

U

uncertainty, 16

univariate analysis of variance, 355

universal lower bound, 80

V

V-plane, 281

virtual boundary, 185, 194

virtual line, 192

virtual obstacle, 191

VisBug-21 Algorithm, 110

VisBug-22 Algorithm, 120

vision, adding to algorithms, 104, 213

W

Wiener's Algorithm, 64

workspace (W-space), 18

world coordinate frame, 146