Abstract

We consider illumination rendering with distributed control of a lighting system with an array of light-emitting diodes (LEDs). As low-cost microprocessors become standard components in LED drivers, distributing the computation of the control signals to individual LED drivers becomes attractive. Common distributed control algorithms require each individual controller to exchange information with all the others and process it. This incurs too large a communication and processing overhead for a low-cost local controller. In this Letter, we propose a distributed control algorithm for achieving global illumination rendering, wherein a controller only needs to communicate within a selected neighborhood. We present design criteria for defining the communication neighborhood and study its impact on rendering performance.

© 2012 Optical Society of America

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References

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  1. E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
    [CrossRef]
  2. A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
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  3. I. Moreno, Opt. Lett. 37, 839 (2012).
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  4. G. Zheng, C. Kolner, and C. Yang, Opt. Lett. 36, 3987 (2011).
    [CrossRef]
  5. J. Dong, W. van Driel, and G. Q. Zhang, Opt. Express 19, 5772 (2011).
    [CrossRef]
  6. I. Moreno, Proc. SPIE 7058, 705811 (2008).
    [CrossRef]
  7. I. Moreno, M. Avendano-Alejo, and R. I. Tzonchev, Appl. Opt. 45, 2265 (2006).
    [CrossRef]
  8. H. Yang, J. W. M. Bergmans, T. Schenk, J. P. M. G. Linnartz, and R. Rietman, Opt. Express 16, 21641 (2008).
    [CrossRef]
  9. N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 53, 1616 (2008).
    [CrossRef]
  10. N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 54, 2279 (2009).
    [CrossRef]
  11. P. R. Boyce, Human Factors in Lighting, 2nd ed. (Taylor & Francis, 2003).

2012 (1)

2011 (3)

2009 (1)

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 54, 2279 (2009).
[CrossRef]

2008 (3)

H. Yang, J. W. M. Bergmans, T. Schenk, J. P. M. G. Linnartz, and R. Rietman, Opt. Express 16, 21641 (2008).
[CrossRef]

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 53, 1616 (2008).
[CrossRef]

I. Moreno, Proc. SPIE 7058, 705811 (2008).
[CrossRef]

2006 (1)

2005 (1)

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Avendano-Alejo, M.

Bergmans, J. W. M.

Boyce, P. R.

P. R. Boyce, Human Factors in Lighting, 2nd ed. (Taylor & Francis, 2003).

Caicedo, D.

A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
[CrossRef]

Dong, J.

Jadbabaie, A.

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 54, 2279 (2009).
[CrossRef]

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 53, 1616 (2008).
[CrossRef]

Kim, J. K.

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Kolner, C.

Linnartz, J. P. M. G.

Moreno, I.

Motee, N.

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 54, 2279 (2009).
[CrossRef]

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 53, 1616 (2008).
[CrossRef]

Pandharipande, A.

A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
[CrossRef]

Rietman, R.

Schenk, T.

Schubert, E. F.

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Tzonchev, R. I.

van Driel, W.

Yang, C.

Yang, H.

Zhang, G. Q.

Zheng, G.

Appl. Opt. (1)

Energy Build. (1)

A. Pandharipande and D. Caicedo, Energy Build. 43, 944 (2011).
[CrossRef]

IEEE Trans. Automat. Contr. (2)

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 53, 1616 (2008).
[CrossRef]

N. Motee and A. Jadbabaie, IEEE Trans. Automat. Contr. 54, 2279 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (1)

I. Moreno, Proc. SPIE 7058, 705811 (2008).
[CrossRef]

Science (1)

E. F. Schubert and J. K. Kim, Science 308, 1274 (2005).
[CrossRef]

Other (1)

P. R. Boyce, Human Factors in Lighting, 2nd ed. (Taylor & Francis, 2003).

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Figures (1)

Fig. 1.
Fig. 1.

(a) Checkerboard reference pattern. (b), (d), (f) Rendered patterns, respectively, by Eqs. (5) and (10) with η=0.02 and η=0.029. (c), (e) Effective neighbors (gray) of some LEDs (black) for η=0.02 (c) and η=0.029 (e). Open circles are the other nodes in the LED array.

Tables (1)

Tables Icon

Table 1. Comparison of Spatial Illumination Patterns Rendered with Different Numbers of Selected Sensor Nodes

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

y=B·u,
uo=B·r,
minuJ(u)=(Bur)T·Wy·(Bur)+uT·Wu·u.
uo=(BTWyB+Wu)1·BT·Wy·r.
uko=i=1nKki·ri.
K={B,Bnonsingular or full column rank;Q1BTWy,otherwise,andWunonsingular.
(d,h)=(μ+1)02πh2(1+d2h2)μ+32.
dki=(xkxi)2+(ykyi)2.
|Aki|ϵχ(dist(k,i)),k=1,,n,i=1,,m.
χ(x)=(1+λx)α,
ukojIkcnKkj·rjuka.
Ikcn={j||Kkj|η·max{|Kki|,i=1,,n}},
B·uoB·ua=B·(uoua).

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