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Sparse Command Generator for
        Remote Control


     Masaaki Nagahara (Kyoto Univ.)
Daniel E. Quevedo (The Univ. of Newcastle)
      Jan Østergaard (Aalborg Univ.)
     Takahiro Matsuda (Osaka Univ.)
      Kazunori Hayashi (Kyoto Univ.)
Remote Control System

        Comamnd
        Generator
                              Robot


In remote control (RC), one
has to transmit control
commands through rate-
limited networks such as
wireless networks.
Remote Control in Sparse Land

        Comamnd
        Generator
                               Robot


For rate-limited networks,
control commands should be
compressed.
Sparse Representation can
effectively compress control
commands without much
distortion.
Table of Contents
Table of Contents
Remote Control Systems
                                Target points




                Radio Control Helicopter
Remote Control Systems




                              Regularization parameter for tradeoff between
                              tracking error and control energy




Tracking error on the sampling instants          Energy limitation
Solution to Energy-limiting control
 The optimal control is given by




                                   [S. Sun et al., IEEE TAC, 2000]
Reference vector   Transmitted vector    Control input   Output




                             D/A conversion     Plant
                             Actuator
Table of Contents
Sparsity-Promoting Optimization
Sparsity-Promoting Optimization
Feasible set
Feasible set




Sparse!
Feasible set




Not sparse
• The solution of


  can be effectively obtained via a fast algorithm.




                       [Beck-Teboulle, SIAM J. Imag. Sci., 2009]
                       [Zibulevsky-Elad, IEEE SP Mag., 2010]
• The solution of


  can be effectively obtained via a fast algorithm.




                       [Beck-Teboulle, SIAM J. Imag. Sci., 2009]
                       [Zibulevsky-Elad, IEEE SP Mag., 2010]
Proposed Remote Control




 Fast Algorithm
A simple way to send a sparse vector
Table of Contents
Examples
Vectors to be sent
Sparse Command Generator for Remote Control
Sparse Command Generator for Remote Control
Tracking error
Quantizing control vectors
We quantize the vectors by a uniform quantizer to encode them.
Tracking error with quantization
Conclusion




Thank you for your attention!

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Sparse Command Generator for Remote Control