Kinematic Control of Redundant Robot Arms Using Neural Networks

Index

a

• adaptive dynamic programming strategy
  • Euler–Lagrange system
    • action mapping and critic mapping  21–23
    • optimality condition  21
  • problem formulation  19–20
  • sensor–actuator system
    • Coriolis force and friction  18
    • Euler–Lagrange system  18
    • inertial force  18
    • stability consideration  19
  • simulation experiment
    • cart–pole model  23–24
    • experiment setup and results  24–25

b

• backpropagation neural network  114
• backstepping-based design  18
• bang-bang controllers  28
• Barbalat’s lemma  89

c

• cart–pole model  23–24
• circular trajectory  122–127
• communication graph  151
• constrained quadratic program
  • objective function  92–93
  • reformulation and convexification  94
  • set constraint  93–94
  • speed level resolution  91
• control redundant manipulators  67
• convexity restriction  33

d

• degrees of freedom (DOFs)  67, 87
• dual neural networks  68, 132
  • convergence analysis  71–72
  • Karush–Kuhn–Tucker condition  70
  • Lagrange function  70
  • quadratic cost function  69

e

• end-effector trajectory 1424
• error accumulation  33
• Euler–Lagrange system  18
  • action mapping and critic mapping  21–23
  • feedback linearization  17
  • optimality condition  21
  • extreme learning machine (ELM)  115

f

• feed-forward neural networks  28, 67, 114

g

• Gaussian elimination  27
• geometric relation  109–110
• gradient-based neural network (GNN)  149
• Gram–Schmidt orthogonalization procedure  132

i

• infinity-sign trajectory  127
• inherent nonlinearity  17

j

• Jacobian matrix  60–61, 67
• Jacobian matrix pseudoinversion  3