1. Case Study on Robotic Systems Using Intelligent Approach
M.Yamakita
Dept. of Mechanical and Control Systems Eng.
Tokyo Inst. Of Tech.
2018/12/9

2. B A . is z
then y
and x If : 2
Rule 1 = C n
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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3. Function Approximation with Radial Basis Function
Controlled System
Operator Command
Response
Radial Basis Function
(Approximated characteristic function) u y
(Memory less) y
Inverse Map Approximation
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4. Stone-Weiestrass Theorem
Generalization of Weiestrass Theorem
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6. Function Approximation and Generalization
Given Data Set
Criterion Function
Criterion Function with Penalty term
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7. Approximation by Green Function
Optimality Condition
Weighted Sum of
Green Function G
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8. 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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9. RBF Neural Network
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10. Adaptive Control PLANT PLANT Estimation of Unknown Parameters
Based on the Model
Model Based　Adaptive　Control
CONTROLLER
(adjustable)
PLANT
PARAMETER
ESTIMATOR
Adaptive Control with ANN
Estimation of Unknown Functions
Based on an Universal Model
UNIVESAL
FUNCTION
PLANT
WEIGHT
ESTIMATOR
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11. Model and Parameter (Example)y F K D
Y(t) ,u(t)is known function
a is unknown parameter vector
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12. Structure of Simple Adaptive Control System
S.P.R.
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14. Estimate Y(t) as well as a
Y(t) of industrial systems are very complex
Estimate Y(t) as well as a
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15. Trajectory Tracking Control of Golf Robot
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16. Conventional Model Based Adaptive Controller
For
Robotic Systems
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18. Black Box Structure
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19. Structural Information + Fixed Allocation of ANN Elements
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20. Structural Information + Free Allocation of ANN Elements
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21. Experimental Results
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22. References
Gupta,N.k.Sinha：Intelligent 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)
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