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J -space monotonicity, 312 P P P (Cartesian) robot arm, 276 XXP robot arms, 274 XXX robot arms, 274 li -front monotonicity, 285 li -rear monotonicity, 285 2-Link-Arm Algorithm, 210 A actuators, 18 algorithm convergence, 57 ANOVA, 362 arm base, 18 arm con guration, 18 arm joints range, 200 arm solution, 187 arm s minimal con guration, 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 con guration space (C-space), 18 con guration space anisotropy, 285 connectedness, uniform, 252 connectivity graph, 305, 323
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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
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Sensing, Intelligence, Motion, by Vladimir J. Lumelsky Copyright 2006 John Wiley & Sons, Inc.
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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 K nigsberg Bridge Problem, 59 o 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
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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 Ti -21, 110 Procedure Compute Ti -22, 121 provable algorithms, 50 Q quasi-Bug2 path, 121 R radius of vision, 106 rank, statistics indexing, 358
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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 identi cation, 391 sliding (prismatic) joint, 18, 180 space anisotropy, 273 space monotonicity, 273 statics, 33 step planning, 212 stopping path, 140 straight-line interpolation, 46
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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
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