Skip to main content
Springer Nature Link
Log in

ALBATROS: adaptive line-based sampling trajectories for sequential measurements

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Measurements in 2D or 3D spaces are ubiquitous among many fields of science and engineering. Often, data samples are gathered via autonomous robots or drones. The path through the measurement space and the location of the samples is traditionally determined upfront using a one-shot design of experiments. However, in certain cases, a sequential approach is preferred. For example, when dealing with a limited sampling budget or when a quick low-resolution overview is desired followed by a steady uniform increase in sampling density, instead of a slow high-resolution one-shot sampling. State-of-the-art sequential design of experiment methods are point-based and are often used to set up experiments both in virtual (simulation) as well as real-world (measurement) environments. In contrast to virtual experimentation, physical measurements require movement of a sensor probe through the measurement space. In these cases, the algorithm not only needs to optimize the sample locations and order but also the path to be traversed by sampling points along measurement lines. In this work, a sequential line-based sampling method is proposed which aims to gradually increase the sampling density across the entire measurement space while minimizing the overall path length. The algorithm is illustrated on a 2D and 3D unit space as well as a complex 3D space and the effectiveness is validated on an engineering measurement use-case. A computer code implementation of the algorithm is provided as an open-source toolbox.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. MATLAB, The MathWorks, Inc., Natick, Massachusetts, United States.

References

  1. Aurenhammer F (1991) Voronoi diagrams—a survey of a fundamental geometric data structure. ACM Comput. Surv. CSUR 23(3):345–405

    Article  Google Scholar 

  2. Bader M (2012) Space-filling curves: an introduction with applications in scientific computing, vol 9. Springer, Berlin

    MATH  Google Scholar 

  3. Berni JA, Zarco-Tejada PJ, Suárez L, Fereres E (2009) Thermal and narrowband multispectral remote sensing for vegetation monitoring from an unmanned aerial vehicle. IEEE Trans Geosci Remote Sens 47(3):722–738

    Article  Google Scholar 

  4. Bhattacharya P, Gavrilova ML (2007) Voronoi diagram in optimal path planning. In: Voronoi diagrams in science and engineering, 2007. ISVD’07. 4th international symposium, IEEE, pp 38–47

  5. Broderick JA, Tilbury DM, Atkins EM (2014) Optimal coverage trajectories for a ugv with tradeoffs for energy and time. Auton Robots 36(3):257–271

    Article  Google Scholar 

  6. Carlson J, Murphy RR (2005) How UGVs physically fail in the field. IEEE Trans Rob 21(3):423–437

    Article  Google Scholar 

  7. Castro RM (2008) Active learning and adaptive sampling for non-parametric inference. Ph.D. thesis, Rice University

  8. Choset H (2000) Coverage of known spaces: the boustrophedon cellular decomposition. Auton Robots 9(3):247–253

    Article  Google Scholar 

  9. Choset H (2001) Coverage for robotics—a survey of recent results. Ann Math Artif Intell 31(1):113–126

    Article  MATH  Google Scholar 

  10. Crombecq K, Laermans E, Dhaene T (2011) Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling. Eur J Oper Res 214(3):683–696

    Article  Google Scholar 

  11. Deschrijver D, Crombecq K, Nguyen HM, Dhaene T (2011) Adaptive sampling algorithm for macromodeling of parameterized \(s\)-parameter responses. IEEE Trans Microw Theory Tech 59(1):39–45

    Article  Google Scholar 

  12. Deschrijver D, Vanhee F, Pissoort D, Dhaene T (2012) Automated near-field scanning algorithm for the emc analysis of electronic devices. IEEE Trans Electromagn Compat 54(3):502–510

    Article  Google Scholar 

  13. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271

    Article  MathSciNet  MATH  Google Scholar 

  14. Martínez-de Dios J, Merino L, Caballero F, Ollero A, Viegas D (2006) Experimental results of automatic fire detection and monitoring with UAVs. For Ecol Manag 234(1):S232

    Article  Google Scholar 

  15. Gademer A, Mainfroy F, Beaudoin L, Avanthey L, Germain V, Chéron C, Monat S, Rudant JP (2009) Solutions for near real time cartography from a mini-quadrotor UAV. In: SPIE Europe remote sensing, International Society for Optics and Photonics, p 74781G

  16. Galceran E, Carreras M (2013) A survey on coverage path planning for robotics. Robot Auton Syst 61(12):1258–1276

    Article  Google Scholar 

  17. Gorissen D, Couckuyt I, Demeester P, Dhaene T, Crombecq K (2010) A surrogate modeling and adaptive sampling toolbox for computer based design. J Mach Learn Res 11(Jul):2051–2055

    Google Scholar 

  18. Gorissen D, Couckuyt I, Laermans E, Dhaene T (2010) Multiobjective global surrogate modeling, dealing with the 5-percent problem. Eng Comput 26(1):81–98

    Article  Google Scholar 

  19. Han J, Xu Y, Di L, Chen Y (2013) Low-cost multi-UAV technologies for contour mapping of nuclear radiation field. J Intell Robot Syst 70(1–4):401–410

    Article  Google Scholar 

  20. Herceg M, Kvasnica M, Jones C, Morari M (2013) Multi-parametric toolbox 3.0. In: Proc. of the European control conference, Zurich, pp 502–510. http://control.ee.ethz.ch/~mpt. Accessed 7 Nov 2017

  21. Hilbert D (1891) Ueber die stetige abbildung einer line auf ein flächenstück. Math Ann 38(3):459–460

    Article  MathSciNet  MATH  Google Scholar 

  22. Huang WH (2001) Optimal line-sweep-based decompositions for coverage algorithms. In: IEEE international conference on robotics and automation, 2001. Proceedings 2001 ICRA, vol 1. IEEE, pp 27–32

  23. Johnson ME, Moore LM, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plan Infer 26(2):131–148

    Article  MathSciNet  Google Scholar 

  24. Judd K, McLain T (2001) Spline based path planning for unmanned air vehicles. In: AIAA guidance, navigation, and control conference and exhibit, Montreal, Canada, p 4238

  25. Kennard RW, Stone LA (1969) Computer aided design of experiments. Technometrics 11(1):137–148

    Article  MATH  Google Scholar 

  26. King DW, Bertapelle A, Moses C (2005) UAV failure rate criteria for equivalent level of safety. In: International helicopter safety symposium, Montreal, p 9

  27. Kleijnen JP (2008) Design and analysis of simulation experiments, vol 20. Springer, Berlin

    MATH  Google Scholar 

  28. Montgomery DC (2017) Design and analysis of experiments. Wiley, Hoboken

    Google Scholar 

  29. Nex F, Remondino F (2014) Uav for 3d mapping applications: a review. Appl. Geomat. 6(1):1–15

    Article  Google Scholar 

  30. Spires S, Goldsmith S (1998) Exhaustive geographic search with mobile robots along space-filling curves. In: Drogoul A, Tambe M, Fukuda T (eds) Collective robotics. Springer, Berlin, Heidelberg, pp 1–12

    Google Scholar 

  31. Spires SV (2003) Exhaustive search system and method using space-filling curves. US Patent 6,636,847

  32. Valente J, Sanz D, Del Cerro J, Barrientos A, de Frutos MÁ (2013) Near-optimal coverage trajectories for image mosaicing using a mini quad-rotor over irregular-shaped fields. Precis Agric 14(1):115–132

    Article  Google Scholar 

  33. Viana FA, Venter G, Balabanov V (2010) An algorithm for fast optimal latin hypercube design of experiments. Int J Numer Meth Eng 82(2):135–156

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Ghent University-imec, IDLab, Technologiepark-Zwijnaarde 15, 9052, Gent, Belgium

    Tom Van Steenkiste, Joachim van der Herten, Dirk Deschrijver & Tom Dhaene

Authors
  1. Tom Van Steenkiste
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Joachim van der Herten
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Dirk Deschrijver
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Tom Dhaene
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Tom Van Steenkiste.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Van Steenkiste, T., van der Herten, J., Deschrijver, D. et al. ALBATROS: adaptive line-based sampling trajectories for sequential measurements. Engineering with Computers 35, 537–550 (2019). https://doi.org/10.1007/s00366-018-0614-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-018-0614-6

Keywords