Abstract
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.
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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)
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)
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)
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)
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)
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)
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)
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)
Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6(1), 80–91 (1959)
Dierckx, P.: Curve and Surface Fitting with Splines. Oxford University Press, London (1995)
Farin, G., et al.: Fairing cubic b-spline curves. Comput. Aided Geom. Des. 4(1-2), 91–103 (1987)
Galceran, E., Carreras, M.: A survey on coverage path planning for robotics. Robot. Auton. Syst. 61(12), 1258–1276 (2013)
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)
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)
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)
Kjellander, J.A.: Smoothing of cubic parametric splines. Comput. Aided Des. 15(3), 175–179 (1983)
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)
Lyche, T., Mørken, K.: Knot removal for parametric b-spline curves and surfaces. Comput. Aided Geom. Des. 4(3), 217–230 (1987)
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)
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)
Piegl, L., Tiller, W.: The NURBS Book. Springer Science & Business Media, Berlin (2012)
Sederberg, T.W., et al.: T-spline simplification and local refinement. ACM Trans. Graphics 23(3), 276–283 (2004)
Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods. Oxford University Press, London (1985)
Tiller, W.: Knot-removal algorithms for curves and surfaces. Comput. Aided Des. 24(8), 445–453 (1992)
Titsias, M.: Variational learning of inducing variables in sparse Gaussian processes. In: Artificial Intelligence and Statistics, pp. 567–574 (2009)
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)
Vasudevan, S., Ramos, F., Nettleton, E., Durrant-Whyte, H.: Gaussian process modeling of large-scale terrain. J. Field Rob. 26(10), 812–840 (2009)
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)
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)
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)
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This paper is a major enhancement of the ICUAS 2018 accepted paper.
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Choi, Y., Chen, M., Choi, Y. et al. Multi-UAV Trajectory Optimization Utilizing a NURBS-Based Terrain Model for an Aerial Imaging Mission. J Intell Robot Syst 97, 141–154 (2020). https://doi.org/10.1007/s10846-019-01027-9
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DOI: https://doi.org/10.1007/s10846-019-01027-9