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Fourier Series Neural Network: Application to Robot Control CS679 Term Project by Choon-Young Lee

Fourier Series Neural Network: Application to Robot Control CS679 Term Project by Choon-Young Lee Department of Electrical Engineering KAIST. Contents. Brief Motivation on This Topic Introduction Fourier Series Neural Network (FSNN) Architecture Learning Rule and its Minima

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Fourier Series Neural Network: Application to Robot Control CS679 Term Project by Choon-Young Lee

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  1. Fourier Series Neural Network: Application to Robot Control CS679 Term Project by Choon-Young Lee Department of Electrical Engineering KAIST

  2. Contents • Brief Motivation on This Topic • Introduction • Fourier Series Neural Network (FSNN) Architecture • Learning Rule and its Minima • Application to Inverse Kinematics of Robot Manipulator • Conclusion

  3. Why FSNN? • Most Artificial Neural Networks have difficulty in relating neural network with the “control engineering languages” • differential equations • transfer functions • frequency responses • Interpretation of Neural Network • What do the weights mean?

  4. Neural Networks in Control Engineering • Inverse Dynamics/Kinematics Mapping • Inverse dynamics/kinematics is used for certain system to track the given reference trajectory • Generally we cannot obtain inverse dynamics/kinematics of highly complicated system • Neural Networks such as FFNN, RBFNN, RNN • Unknown System Identification • First step to control unknown system • Get I/O pair and train NN • Design controller based on NN • Learning Control Sequence • Trial and Error • Unsupervised Learning: we don’t know how to control • Iterative Learning Control

  5. FSNN Architecture • Multi-Input Single-Output FSNN • Wn1..nm : output weights • h(.) : harmonic function which is a complex exponential function with state weight • function y is represented as weighted sum of harmonic functions • orthogonality between harmonic functions gives the following simple structure.

  6. x1 x2 …. …. FSNN Architecture ( 2 input 1 output) Harmonic neuron bias W sum …….. output Product node

  7. Learning Stability • Delta Rule • V is quadratic output error defined by • Taking partial derivative

  8. Local Minima Free • Think about under what condition the above eq. is zero. • Harmonic function is not zero for some particular value of x • E should be zero and it is the only extreme point for the minimum of Lyapunov function V • Note that no further weight modification means global minimum.

  9. Nonlinear Inverse Robot Kinematics • A Two Link Planar Robot Model y 1.4 2 L2 L1 1 1.4 x

  10. Application of FSNN • Cosine expansion of Fourier Series • Learning Rule

  11. Error Convergence Process 0.0182 0.0094

  12. Error Surface (theta 1) Mean is 0.0182

  13. Summary • Samples for training: 8100 • harmonic node: 18 • Samples for testing: 11881 • Training Error: 0.0182 and 0.0094 • Generalization Error: 0.0153 and 0.0112

  14. Conclusion • Study FSNN and applied to control system • free of local minima and approximation ability • In Report • Cartesian space robot control using the obtained FSNN • Comparison to RBF

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