M.Yamakita

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Case Study on Robotic Systems Using Intelligent
Approach

• M.Yamakita
• Dept. of Mechanical and Control Systems Eng.
• Tokyo Inst. Of Tech.

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If part specifies a degree of matching of the
observation to each rule. If Ci is defuzzy value,
control input is a weighted sum of the value
according to the degree.
Smooth interpolation of control input
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Function Approximation with Radial Basis Function
u
Radial Basis Function
(Approximated characteristic function)
u
y
(Memory less)
y
Inverse Map Approximation
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Stone-Weiestrass Theorem
Weiestrass Theorem
Generalization of Weiestrass Theorem
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Function Approximation and Generalization
Given Data Set
Criterion Function
Criterion Function with Penalty term
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Approximation by Green Function
Optimality Condition
Weighted Sum of Green Function G
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Definition of Radial Basis Function
Pseudo Partial Derivative
Corresponding Basis Function
(Function value is just depend on distance)
Radial Basis Function
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RBF Neural Network
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Adaptive Control
Estimation of Unknown Parameters Based on the
Model
Model Based Adaptive Control
PLANT
CONTROLLER (adjustable)
PARAMETER ESTIMATOR
Adaptive Control with ANN
Estimation of Unknown Functions Based on an
Universal Model
PLANT
UNIVESAL FUNCTION
WEIGHT ESTIMATOR
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Model and Parameter (Example)
Y(t) ,u(t)is known function a is unknown
parameter vector
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Structure of Simple Adaptive Control System
S.P.R.
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Trajectory Tracking Control of Golf Robot
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Conventional Model Based Adaptive
Controller For Robotic Systems
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Black Box Structure
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Structural Information Fixed Allocation of ANN
Elements
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Structural Information Free Allocation of ANN
Elements
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Experimental Results
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References

• Gupta,N.k.SinhaIntelligent Control Systems, IEEE
  Press. (1996)
• K.Furuta et.Intelligent Control, Corona Pub.
  (1988) (in Japanese)
• B.Widrow, E.Walach Adaptive Inverse
  Control,Prentice Hall (1996)
• M. Yamakia, T.Satoh Adaptive ANN Control of
  Robot Arm using Structure of Lagrange Equation,
  Proc. ACC'99, pp. 2834/2836, (1999)