Abstract
An autonomous aerial inspection using unmanned aerial vehicles (UAVs) requires effective and nearly optimal algorithms for scheduling UAVs. A UAV performing aerial inspection does not need to take photos of inspected objects from exact given points in space. For every inspected object, there is a feasible area (or point) from which clear photos can be taken. The optimization problem is to find points from these areas from which UAV should take photos of objects. These points should be chosen in such a way that the scheduling algorithm, which takes these points as its input, will produce a valuable solution. In this work, for the given feasible areas we find the sequence of visiting these areas and points, to minimize the length of the Hamiltonian cycle consisting of chosen points in a determined sequence.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aarts, E.H.L., van Laarhoven, P.J.M.: Simulated annealing: a pedestrian review of the theory and some applications. In: Devijver P.A., Kittler J. (eds.) Pattern Recognition Theory and Applications. NATO ASI Series (Series F: Computer and Systems Sciences), vol. 30. Springer, Berlin (1987)
Bożejko, W., Wodecki, M.: Parallel evolutionary algorithm for the traveling salesman problem. J. Numer. Anal. Ind. Appl. Math. 2(3–4), 129–137 (2007)
Byrd, R.H., Lu, P., Nocedal, J.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5), 1190–1208 (1995)
Croes, G.A.: A method for solving traveling-salesman problems. Oper. Res. 6(6), 791–812 (1958)
Englert, M., Röglin, H., Vöcking, B.: Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP. Algorithmica 68(1), 190–264 (2014)
Imeson, F., Smith, S.L.: Multi-robot task planning and sequencing using the SAT-TSP language. In: IEEE International Conference on Robotics and Automation, pp. 5397–5402 (2015)
Ke-Lin, D., Swamy, M.N.S.: Search and optimization by metaheuristics, pp. 29–36. Springer, New York City (2016)
Kraft D.: A software package for sequential quadratic programming. Forschungsbericht- Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt (1988)
Mathew, N., Smith, S.L., Waslander, S.L.: Multirobot rendezvous planning for recharging in persistent tasks. IEEE Trans. Robot. 31(1), 128–142 (2015)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)
Powell, M.J.D.: An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 7(2), 155–162 (1964)
Snyder, L., Daskin, M.: A random-key genetic algorithm for the generalized traveling salesman problem. Eur. J. Oper. Res. 17(1), 38–53 (2006)
Wolff, E.M., Topcu, U., Murray, R.M.: Optimal control of non-deterministic systems for a computationally efficient fragment of temporal logic. In: IEEE Conference on Decision and Control, pp. 3197–3204 (2013)
Zhu, C., Byrd, R.H., Lu, P., Nocedal, J.: Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Softw. (TOMS) 23(4), 550–560 (1997)
Acknowledgments
This work is partially supported by the National Science Centre of Poland, grant OPUS no. DEC 2017/25/B/ST7/02181 and by the grant no. POIR.01. 01.01-00-1176/15.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Grymin, R., Bożejko, W., Pempera, J. (2020). A Numerical Approach to Solving the Aerial Inspection Problem. In: Klempous, R., Nikodem, J. (eds) Smart Innovations in Engineering and Technology. ICACON APCASE 2017 2017. Topics in Intelligent Engineering and Informatics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-32861-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-32861-0_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32860-3
Online ISBN: 978-3-030-32861-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)