Index

A

Abduction–adduction, 196, 197
Actuators, 90, 91, 170, 202
Adaptive methods, 6
Admittance, 3, 9
Admittance model, 139, 140, 150, 156, 160, 170
AMP, 200
Amplitude, 129, 137
Arbitration on message priority, see AMP
Arm, 51, 142, 195, 196
human, 2, 10, 43, 101, 102, 141, 142, 195–197, 202
lower, 10, 196
upper, 10, 196, 200
Articulations, 195
Asymptotic stability, 5, 7, 8, 13, 77, 84, 92, 99, 125, 127, 146, 147
global, 7, 96, 107
semiglobal, 13, 17, 33, 41, 44, 81, 90, 96, 106, 107, 139, 158

B

Backpropagation, 5, 104, 106
Baum–Welch algorithm, 184, 185
Boundary layer system, 59, 60

C

CAN, 49, 200, 201
Candidate, 
Lyapunov function, 16, 66, 126, 127, 130
Carrier sense multiple access, see CSMA
CD, 200
Center, 30, 70, 79, 176, 177
Centripetal, 13, 14, 55, 56, 125, 164, 175
Centroid condition, 176
Chattering, 9, 125, 129, 130, 132, 135, 137, 138
CINVESRobot-1, 48, 49, 109, 120, 121, 185, 189, 193, 195
Circle, 69, 70, 121, 122, 177, 201
Closed-loop equation, 18, 21, 38, 41, 88, 89, 97, 101, 149
final, 85, 97, 99
Closed-loop system, 8, 15–18, 23, 25, 31–33, 37, 38, 44, 45, 68, 72, 84, 85, 88, 92, 93, 96, 97, 99–101, 128, 130, 131, 141, 143, 144, 147, 165–168
Codebook, 12, 175–179, 181, 184
Codebook numbers, 177, 178, 182, 186, 188
Cohen–Coon method, 6, 26, 27, 29, 31
Collision detection, see CD
Compensations, 7, 164, 173
adaptive, 159, 165, 167
model-based, 8, 96
Compensator, 8, 126, 167
Condition number, 45, 93
Configuration, 180, 197, 202
joint, 197
Contact forces, 3, 10, 159
Continuous interval, 61, 63
Control, 43, 195
admittance, 9, 51, 102, 139, 141, 159, 161, 164, 195
classic PD, 81, 133, 159
cooperative, 9
exoskeleton robots, 3
final, 32, 33
industrial PID, 84, 99, 106, 147, 158
joint, 165, 167
linear, 37, 143, 147
linear admittance PID, 143
linear PID, 22, 28, 33, 35, 37, 44, 90, 92, 144, 146
linear stable PID, 36, 143
manual, 50, 51
neural PD, 65, 72, 81, 84, 99, 104, 106, 125, 126, 129, 135, 138, 156, 158
neural PID, 81, 85, 88, 89, 91, 92, 99, 100, 102–104, 106, 107, 145, 147
neural PID tracking, 96, 105
neural sliding mode PD, 127–129, 135, 138
normal neural PD, 84, 99, 146, 147, 156
parallel neural sliding mode PD, 129, 135
PD, 5, 7–9, 15–17, 22, 26, 58, 67, 79, 80, 114, 123, 124, 127, 154, 167, 170, 173
PD admittance, 159, 164, 167, 173
PID, 5–8, 10, 14, 17, 22, 25, 29, 33, 42, 144
PID admittance, 142, 143, 145, 158, 168
PID tracking, 96, 97, 107
robot, 6, 13, 16, 17, 28, 83, 96, 125
serial neural sliding mode PD, 129, 130, 135
task space PD, 7
Control law, 79, 135, 168, 169
PD, 16, 55, 113, 115, 119, 120
PID, 18, 37, 84, 97, 143, 147
Control programs, 
real-time, 29, 49, 120
Control results, 32, 103–105
Control signal, 134–137
Control system, 102, 198, 200
Control torque, 6, 22, 24, 32, 127, 202
final, 29, 37, 143, 146
Controller area network, see CAN
Controllers, 23, 77, 78, 90, 133, 137, 138, 154, 155, 157–159, 174
admittance, 9, 139, 150, 156, 159, 173, 174
linear PID, 18, 38, 45, 90, 104, 106, 144
neural, 81, 129, 132
neural PD, 89, 129
neural PID, 92, 104, 105
nonlinear PD, 5, 7, 8
PD, 5, 8, 22, 23, 71, 110
sliding neural, 132
Convergence, 
finite time, 130, 132
Convergence speed, 5, 135
CSMA, 200

D

Damping, 140, 142
Dead zone, 74, 75
Degrees-of-freedom, see DoF
Demonstrations, 175–179, 181, 184, 187–192
Design, 91, 195, 198
modular, 195, 198
Design parameters, 132, 136
Design positive constant, 19, 38, 45, 86, 93, 148
Diagonal matrices, 156, 170
positive definite, 37, 44, 55, 84, 92, 96, 125, 143, 147
Dimension, 35, 49, 105, 121, 140, 177, 198
DoF, 43, 156, 160, 163, 164, 197, 198
Domain, 
frequency, 6, 26, 142
Domain of attraction, 22, 42, 45, 88, 93, 149
arbitrary large, 17, 37, 83, 96, 143, 145
Drive, 
harmonic, 198, 199
DTW, 11, 175, 177, 178, 186, 188, 191
Dynamic models, 36, 43, 133, 156, 159
Dynamic time warping, see DTW
Dynamics, 2, 7, 13, 16, 35, 55, 78, 111, 125, 142, 159, 175, 195
inverse, 3, 6, 10
joint-space, 149
robot, 17, 22, 25, 55, 82, 150, 154, 155, 164, 167
unmodeled, 4, 7, 8, 55

E

Eigenvalues, 
maximum, 18, 36, 76, 82, 88, 164
minimum, 18, 36, 82, 164, 166
Elbow, 170, 195–197, 201
End-effector, 3, 35, 36, 43, 51, 52, 140, 141, 143, 145, 150, 152, 159
Energy exchange, 50
Equilibrium, 18, 28, 38, 44, 45, 85, 92, 93, 97, 100, 144
stable, 21, 41, 88, 97, 101, 149
Equilibrium point, 18, 38, 56, 59, 60, 85, 131
Error, 
estimation, 17
filtered, 84, 96, 97, 99
filtered regulation, 109, 115, 119
neural approximation, 82, 83, 98, 127–129, 145, 146
nominal, 164, 166, 168, 169
observer, 55, 57, 61, 64, 72, 73, 77, 112, 113, 115, 116
position, 37, 105, 141
regulation, 5, 9, 15–17, 36, 83, 89, 104, 125, 143, 145
steady-state, 5, 7, 16, 22, 28, 104, 134, 135, 137, 138, 156
tracking, 8, 9, 15, 58, 61, 66, 68, 71, 81, 96, 101, 115, 116, 119, 125, 126, 129, 130, 132, 136–138
Error equation, 64, 65
Estimation, 44, 66, 70, 80, 91, 124
Exoskeleton, 1, 9, 10, 30, 31, 36, 43, 49, 101, 143, 152, 195, 198, 200–202
4-DoF, 49, 51, 159, 170
Exoskeleton robots, 1, 3, 29, 51, 102, 103, 107, 140, 158
heavy duty, 48, 49

F

F/T sensor, 139, 140, 150, 151, 156, 163, 164, 170, 174
Filter, impedance, 141
Flexion–extension, 196, 197, 201
Force/torque sensor, see F/T sensor
Forces, 3, 9, 10, 51–53, 140–142, 150, 151, 160, 162–164
gravitational, 109, 156
gravity, 7, 8, 42, 55, 144
Frequency domain methods, 6
Friction, 7, 8, 16, 55, 66, 70–72, 75, 78–81, 98, 104, 106, 109, 111, 120, 121, 124, 135, 156
Frictional terms, 13, 55, 125, 175
Functions, 
Gaussian, 71, 78, 82, 83, 98, 103, 105, 116, 120, 145
Lyapunov, 19, 38, 39, 42, 45, 61, 64, 73, 86, 89, 93, 97, 100, 115, 128, 131, 148, 155, 166, 167
membership, 5, 109, 110, 115, 116, 119–122
state dependent, 155, 166, 167
Fuzzy comparison, 123
Fuzzy compensation, 114, 115, 119, 121, 124
Fuzzy compensator, 8, 96, 109–112, 117, 121, 124
Fuzzy rules, 4, 8, 110, 120, 121
Fuzzy systems, 5, 8, 109, 121

G

Gains, 
big PD, 134, 135
control, 18, 28, 38, 45, 85, 97, 100, 144, 147
derivative, 8, 17, 22, 33, 37, 83, 102, 104, 142, 143
feedback, 156
integral, 17, 22, 37, 42, 83, 104, 142, 143, 156
linear PID, 35, 104, 106
matrix, 154, 165, 166
observer, 55, 113
PID, 5, 6, 25, 27, 28, 42, 48, 95, 103, 145
proportional, 17, 22, 33, 37, 83, 102, 142, 143
sliding mode, 129, 130, 132
Gradient descent, 4, 5
Gravity, 16, 17, 25, 55, 66, 70, 71, 75, 78–80, 98, 104, 106, 109, 111, 120, 121, 124, 135, 156
Gravity compensation, 17, 24, 29, 31
approximate, 42, 144, 145

H

Heuristic methods, 6, 26
Hidden Markov model, see HMM
HMI, 2, 200
HMM, 11, 12, 175, 177, 179–183, 185–188, 190
modified, 185, 188–190
Human machine interface, see HMI
Human–machine integration, 2, 4, 9, 10
Human–robot system, 142

I

Impedance control, 6, 141
Inertia, 10, 140–142, 166
Integrator, 22, 23, 81, 84, 99, 104, 147
Intelligent methods, 6

J

Jacobian, 150–152, 161, 165
angular velocity, 151, 152
Jacobian approximation, 152–154, 157
JHMM, 186, 188, 190, 191, 193
Joint angles, 109, 161–163, 175, 177, 189
desired, 3, 159, 187
Joint positions, 7, 13, 35, 57, 101, 162
desired, 14, 15, 17, 125
Joint space, 3, 6, 35, 36, 43, 102, 144, 159, 160, 175, 180
Joint velocities, 7, 13, 31, 82, 91, 101, 103, 106
desired, 14, 109, 125
Joint-1, 49, 103, 177, 187
Joint-2, 49, 104, 187
Joint-3, 49

K

Key-point numbers, 177, 178, 182, 187, 188, 190
Key-points, 12, 177–179, 181, 184, 185
Kinematics, 2, 142, 159, 195
forward, 35, 43, 52, 151, 159, 186, 189
inverse, 10, 11, 36, 139, 144, 159, 160, 174, 175, 186, 188, 192
robots, 150

L

LaSalle's invariance principle, 126–128, 131
LaSalle's theorem, 21, 41, 88, 97, 101, 149
Learning from demonstration, see LfD
Learning law, 72, 111, 116, 120
Learning rules, 55, 71, 109
LfD, 3, 9
Linear combinations, 7, 160, 162, 163
Linear-in-the-parameter net, 82, 98, 145
Link positions, 15, 55, 81, 125, 134, 136, 137, 140, 159
Links velocities, 55, 78, 125, 175
Lipschitz condition, 42, 67, 71, 83, 91, 145, 146
Lloyd's algorithm, 175–179, 182, 185, 187, 188, 192
Lyapunov approach, 6, 125

M

Manipulators, 7, 75, 83, 140, 141
industrial, 5
planar elbow, 185, 186
robot, 23, 24, 33, 35, 37, 55, 57, 63, 81, 106, 125, 129
robotic, 2, 9
two-link robot, 133, 134, 136, 137
Matrix, 
Coriolis, 10, 13, 14, 36, 55, 56, 82, 109, 125, 159, 164, 175
inertia, 13, 14, 35, 36, 50, 55, 81, 82, 102, 125, 140, 159, 164, 175
Jacobian, 35, 37, 43, 141, 159
positive defined, 73, 74
positive definite, 15, 60, 63, 67, 71, 115, 116
Mechanical impedance, 140, 141
Model-based analytical tuning, 6
Modeling error, 10, 15, 89, 111, 126, 130, 132
neural, 9, 129, 130, 132, 146
Movements, 52, 153, 201, 202
basic, 201, 202

N

Neural compensation, 71, 127
PD controller, 79
Neural compensator, 8, 55, 67, 71, 85, 96, 99, 104, 106, 147, 156, 158
Neural control, 8, 129, 132, 135, 138
sliding, 132
Neural identification, 4
Neural networks, 5, 8, 55, 65, 67, 82, 84, 92, 99, 105, 125, 126, 129, 130, 145, 146
RBF, 5, 55, 70, 71, 80
simplest, 82, 98, 145
weights of, 67, 68, 72, 73, 93, 127
Neural networks compensation, 70, 79
Neural PD, 104, 125, 133
Neural PID, 81, 90, 91, 103, 106, 107
Noises, 5, 49, 77, 121
Nominal reference, 154, 164
Number, 
hidden state, 180, 182
region, 176, 177

O

Observation symbols, 177–179, 182, 184
Observations, 177, 182, 183
sequence of, 180, 182, 184
Observer, 55, 65, 72, 77, 78, 112, 113
high-gain, 7, 55, 57, 58, 61, 63–65, 67, 72, 76, 77, 80, 109, 111–113, 124
model-based, 7
model-free, 7
velocity, 7, 35, 77, 81, 82, 92, 111, 112
Optimization methods, 6
Orientations, 6, 35, 36, 43, 52, 143, 145, 149–153, 160–163
Origin, 18, 21, 38, 41, 61, 85, 87, 88, 97, 101, 149
Output vector, 110, 114, 140

P

Parameters, 5, 8, 26, 30, 35, 42, 120, 156, 158, 166, 170, 173
physics, 198
Path planning, 3, 15, 125
PbD, 3
PD, 5, 133, 150, 159
PD control signals, 134
neural sliding mode, 136, 137
PID, 5, 31, 37
linear, 13, 17, 35, 103, 139, 156
PID controllers, 22
PID tuning, 5, 6, 13, 24, 26–29, 33
PID tuning via neural net, 104
Positions, 3, 6, 7, 9, 15, 35, 43, 77, 133, 135, 140, 150
desired, 14, 36, 51, 58, 67, 71, 77, 109, 121, 125, 141, 143, 145
Power exchange, 
average, 50, 51
PowerCube unit, 198, 199
Probability, 182–184
joint, 182
Probability distribution, 180, 181
Programming by demonstration, see PbD
Proportional-derivative, see PD
Proportional-integral-derivative, see PID

R

Radius, 
ball of, 21, 41, 87, 88, 97, 101, 113, 149
Regressor, 154, 164, 165, 168
Rigidity, 142
Robot exoskeleton, 3, 195
Robot models, 10, 25, 159
Robot parameters, 75, 133
Robot trajectory generation, 3, 180
Robots, 14, 22, 102, 109, 177, 187, 190
1-DoF, 160
2-DoF, 151, 160
2-DoF pan and tilt, 139, 159, 161, 170, 174
3-DoF exoskeleton, 81
4-DoF, 152, 156–158, 161, 162
4-DoF exoskeleton, 53, 170, 175, 185
5-DoF, 153, 163
6-DoF, 153, 163
7-DoF exoskeleton, 30
humanoid, 3
n-link, 159, 175
nonredundant, 35
pan and tilt, 151, 153, 156, 160, 161
portable exoskeleton, 101, 102, 201, 203
surgical, 3
two-link planar, 10, 11, 175
UCSC 7-DoF exoskeleton, 30
upper limb exoskeleton, 29
wearable, 1, 9
Rotation, 198, 200, 201
high speed, 199
high torque, 199
internal–external, 196, 197
low speed, 199
Rotation axes, 197, 202

S

Servomotors, 101, 202
Shoulder, 106, 170, 195, 196, 201, 202
Simulation, 75, 121, 133, 192
Sliding mode compensation, 126, 127, 132, 135, 158, 159, 167, 174
Sliding mode control, see SMC
Sliding modes, 9, 127, 130, 132, 133, 135–138
second-order, 130, 131, 155, 167
SMC, 9, 129, 130, 132, 135, 138, 154, 167
Space, 186, 189, 190
Cartesian, 6, 35, 149
Spline, 
circular, 198–200
flex, 198–200
Stability, 23, 37, 55, 80, 104, 106, 120, 126, 130, 174
Stability analysis, 6, 14, 22, 71, 85, 88, 97, 99, 114, 138, 147, 170
Stability conditions, 33, 53, 84, 89, 99
Stability properties, 16, 23, 59, 61, 91
Step responses, 26, 27, 31–33
Stiffness, 140, 141, 196
Subsystems, 61, 118, 198
fast, 56, 60
slow, 56, 60, 61

T

Task space, 3, 6, 35–37, 43, 53, 143–145, 158, 160, 161, 180, 187–191, 193
augmented, 43
neural PID control in, 145, 146
Taylor series, 25, 26, 67, 117
THMM, 186, 190, 191
Time, 
finite, 69, 112, 113, 130, 132
total, 69, 70, 113, 185
Time constant, derivative, 28, 31, 143
Torques, 10, 17, 51, 52, 105, 141, 150, 151, 159, 160, 162, 164, 171, 172
gravitational, 5, 10, 13, 156, 157
gravity, 35, 81, 90, 140
high, 199
joint, 33
Tracking, 73, 77, 134–137, 157, 158, 171–173
joint angle, 3
Training demonstrations, 190–193
Trajectories, 10, 52, 139, 175, 177, 181, 182, 185, 190, 192
generated, 187–190
smooth, 11, 185
Trajectory generation, 12, 139, 185
Trajectory planning, 3, 10, 15, 125, 139
Tuning procedures, 13, 22, 42, 88, 144

U

Upper limb exoskeleton, 13, 33, 48, 52, 101, 109, 120, 141, 189, 195, 197
4-DoF, 35, 139, 195
USB, 120, 200, 201

V

Vectors, 6, 35, 57, 81, 110, 140, 149, 154, 159, 164, 165
gravitational torques, 7, 10, 13, 14, 17, 36, 165
velocity, 111
Velocities, 3, 9, 25, 44, 58, 67, 71, 72, 77, 80, 105, 111, 112, 141, 177
Viscosities, 140, 141

W

Wave generator, 198–200
Weights, 5, 8, 31, 55, 70, 82, 85, 93, 98, 100, 126, 127, 130, 145, 147
Weights updating law, 128, 130, 135

Z

Ziegler–Nichols tuning, 27
Ziegler–Nichols methods, 6, 26, 27, 31
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3.142.35.75