Journal of Intelligent & Robotic Systems

, Volume 97, Issue 1, pp 141–154 | Cite as

Multi-UAV Trajectory Optimization Utilizing a NURBS-Based Terrain Model for an Aerial Imaging Mission

  • Youngjun ChoiEmail author
  • Mengzhen Chen
  • Younghoon Choi
  • Simon Briceno
  • Dimitri Mavris


Trajectory optimization precisely scanning an irregular terrain is a challenging problem since the trajectory optimizer needs to handle complex geometry topology, vehicle performance, and a sensor specification. To address these problems, this paper introduces a novel framework of a multi-UAV trajectory optimization method for an aerial imaging mission in an irregular terrain environment. The proposed framework consists of terrain modeling and multi-UAV trajectory optimization. The terrain modeling process employs a Non-Uniform Rational B-Spline (NURBS) surface fitting method based on point cloud information resulting from an airborne LiDAR sensor or other sensor systems. The NURBS-based surface model represents a computationally efficient terrain topology. In the trajectory optimization method, the framework introduces a multi-UAV vehicle routing problem enabling UAV to scan an entire area of interest, and obtains feasible trajectories based on given vehicle performance characteristics, and sensor specifications, and the approximated terrain model. The proposed multi-UAV trajectory optimization algorithm is tested by representative numerical simulations in a realistic aerial imaging environment, namely, San Diego and Death Valley, California.


Multi-UAV trajectory optimization Aerial imaging Non-Uniform Rational B-Spline (NURBS) Terrain modeling Vehicle routing problem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This paper is a major enhancement of the ICUAS 2018 accepted paper.


  1. 1.
    Acar, E.U., Choset, H., Rizzi, A.A., Atkar, P.N., Hull, D.: Morse decompositions for coverage tasks. Int. J. Robot. Res. 21(4), 331–344 (2002)CrossRefGoogle Scholar
  2. 2.
    Avellar, G.S., Pereira, G.A., Pimenta, L.C., Iscold, P.: Multi-UAV routing for area coverage and remote sensing with minimum time. Sensors 15(11), 27783–27803 (2015)CrossRefGoogle Scholar
  3. 3.
    Bircher, A., Alexis, K., Burri, M., Oettershagen, P., Omari, S., Mantel, T., Siegwart, R.: Structural inspection path planning via iterative viewpoint resampling with application to aerial robotics. In: 2015 IEEE International Conference On Robotics and Automation (ICRA), pp 6423–6430 (2015)Google Scholar
  4. 4.
    Brujic, D., Ainsworth, I., Ristic, M.: Fast and accurate NURBS fitting for reverse engineering. Int. J. Adv. Manuf. Technol. 54(5–8), 691–700 (2011)CrossRefGoogle Scholar
  5. 5.
    Carr, J.C., Fright, W.R., Beatson, R.K.: Surface interpolation with radial basis functions for medical imaging. IEEE Trans. Med. Imaging 16(1), 96–107 (1997)CrossRefGoogle Scholar
  6. 6.
    Choi, Y., Choi, Y., Briceno, S., Mavris, D.N.: Three-dimensional UAS trajectory optimization for remote sensing in an irregular terrain environment. In: 2018 International Conference on Unmanned Aircraft Systems (ICUAS) (2018)Google Scholar
  7. 7.
    Choi, Y., Jimenez, H., Mavris, D.N.: Two-layer obstacle collision avoidance with machine learning for more energy-efficient unmanned aircraft trajectories. Robot. Auton. Syst. 98, 158–173 (2017)CrossRefGoogle Scholar
  8. 8.
    Choi, Y., Payan, A.P., Briceno, S.I., Mavris, D.N.: A framework for unmanned aerial systems selection and trajectory generation for imaging service missions. In: 2018 Aviation Technology, Integration, and Operations Conference (2018)Google Scholar
  9. 9.
    Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6(1), 80–91 (1959)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dierckx, P.: Curve and Surface Fitting with Splines. Oxford University Press, London (1995)zbMATHGoogle Scholar
  11. 11.
    Farin, G., et al.: Fairing cubic b-spline curves. Comput. Aided Geom. Des. 4(1-2), 91–103 (1987)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Galceran, E., Carreras, M.: A survey on coverage path planning for robotics. Robot. Auton. Syst. 61(12), 1258–1276 (2013)CrossRefGoogle Scholar
  13. 13.
    Hameed, I.A., la Cour-Harbo, A., Osen, O.L.: Side-to-side 3D coverage path planning approach for agricultural robots to minimize skip/overlap areas between swaths. Robot. Auton. Syst. 76, 36–45 (2016)CrossRefGoogle Scholar
  14. 14.
    Iglesias, A., Galvez, A., Avila, A.: Immunological approach for full NURBS reconstruction of outline curves from noisy data points in medical imaging. IEEE/ACM Trans. Comput. Biol. Bioinform. (1), pp. 1–1 (2017)Google Scholar
  15. 15.
    Jing, W., Polden, J., Lin, W., Shimada, K.: Sampling-based view planning for 3d visual coverage task with unmanned aerial vehicle. In: 2016 IEEE/RSJ International Conference On Intelligent Robots and Systems (IROS), pp 1808–1815 (2016)Google Scholar
  16. 16.
    Kjellander, J.A.: Smoothing of cubic parametric splines. Comput. Aided Des. 15(3), 175–179 (1983)CrossRefGoogle Scholar
  17. 17.
    Li, Y., Chen, H., Er, M.J., Wang, X.: Coverage path planning for uavs based on enhanced exact cellular decomposition method. Mechatronics 21(5), 876–885 (2011)CrossRefGoogle Scholar
  18. 18.
    Lyche, T., Mørken, K.: Knot removal for parametric b-spline curves and surfaces. Comput. Aided Geom. Des. 4(3), 217–230 (1987)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Mongus, D., Lukač, N., Zalik, B.: Ground and building extraction from LiDAR data based on differential morphological profiles and locally fitted surfaces. ISPRS ISPRS J. Photogramm. Remote Sens. 93, 145–156 (2014)CrossRefGoogle Scholar
  20. 20.
    Nedjati, A., Izbirak, G., Vizvari, B., Arkat, J.: Complete coverage path planning for a multi-UAV response system in post-earthquake assessment. Robotics 5(4), 26 (2016)CrossRefGoogle Scholar
  21. 21.
    Piegl, L., Tiller, W.: The NURBS Book. Springer Science & Business Media, Berlin (2012)zbMATHGoogle Scholar
  22. 22.
    Sederberg, T.W., et al.: T-spline simplification and local refinement. ACM Trans. Graphics 23(3), 276–283 (2004)CrossRefGoogle Scholar
  23. 23.
    Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford University Press, London (1985)Google Scholar
  24. 24.
    Tiller, W.: Knot-removal algorithms for curves and surfaces. Comput. Aided Des. 24(8), 445–453 (1992)CrossRefGoogle Scholar
  25. 25.
    Titsias, M.: Variational learning of inducing variables in sparse Gaussian processes. In: Artificial Intelligence and Statistics, pp. 567–574 (2009)Google Scholar
  26. 26.
    Torres, M., Pelta, D.A., Verdegay, J.L., Torres, J.C.: Coverage path planning with unmanned aerial vehicles for 3D terrain reconstruction. Expert Syst. Appl. 55, 441–451 (2016)CrossRefGoogle Scholar
  27. 27.
    Vasudevan, S., Ramos, F., Nettleton, E., Durrant-Whyte, H.: Gaussian process modeling of large-scale terrain. J. Field Rob. 26(10), 812–840 (2009)CrossRefGoogle Scholar
  28. 28.
    Vasudevan, S., Ramos, F., Nettleton, E., Durrant-Whyte, H.: Non-stationary dependent Gaussian processes for data fusion in large-scale terrain modeling. In: 2011 IEEE International Conference On Robotics and Automation (ICRA), pp. 1875–1882 (2011)Google Scholar
  29. 29.
    Zelinsky, A., Jarvis, R.A., Byrne, J., Yuta, S.: Planning paths of complete coverage of an unstructured environment by a mobile robot. In: Proceedings of International Conference on Advanced Robotics, vol. 13, pp 533–538 (1993)Google Scholar
  30. 30.
    Zhong, D., Liu, J., Li, M., Hao, C.: Reconstruction of digital terrain for hydropower engineering based on tin model. Prog. Nat. Sci. 18(11), 1409–1415 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Aerospace Systems Design Laboratory, School of Aerospace EngineeringGeorgia Institute of Technology North AvenueAtlantaUSA

Personalised recommendations