Robust UAV mission planning
Unmanned Aerial Vehicles (UAVs) can provide significant contributions to information gathering in military missions. UAVs can be used to capture both full motion video and still imagery of specific target locations within the area of interest. In order to improve the effectiveness of a reconnaissance mission, it is important to visit the largest number of interesting target locations possible, taking into consideration operational constraints related to fuel usage, weather conditions and endurance of the UAV. We model this planning problem as the well-known orienteering problem, which is a generalization of the traveling salesman problem. Given the uncertainty in the military operational environment, robust planning solutions are required. Therefore, our model takes into account uncertainty in the fuel usage between targets, for instance due to weather conditions. We report results for using different uncertainty sets that specify the degree of uncertainty against which any feasible solution will be protected. We also compare the probability that a solution is feasible for the robust solutions on one hand and the solution found with average fuel usage on the other. These probabilities are assessed both by simulation and by derivation of problem specific theoretical bounds on the probability of constraint feasibility. In doing so, we show how the sustainability of a UAV mission can be significantly improved. Additionally, we suggest how the robust solution can be operationalized in a realistic setting, by complementing the robust tour with agility principles.
KeywordsUAV mission planning Robust optimization Robust orienteering problem Agile planning
In this paper we applied techniques from robust optimization, provided to us in an LNMB course by Prof. A. Ben-Tal and Prof. D. den Hertog. We sincerely thank Prof. A. Ben-Tal and Prof. D. den Hertog for sharing their insights on the applicability of these techniques to our UAV planning problem. Also, we thank the participants of the ORP3 conference for their remarks on a previous version of this research. Finally, we thank the anonymous referees for their valuable comments on previous versions of this paper.
- Ben-Tal, A., Ghaoui, L. E., & Nemirovski, A. (2009). Robust optimization. Princeton and Oxford: Princeton University Press. Google Scholar
- Ben-Tal, A., den Hertog, D., & Vial, J. (2012). Deriving robust counterparts of nonlinear uncertain inequalities. Center discussion paper series no. 2012-053. Google Scholar
- Bertuccelli, L., Alighanbari, M., & How, J. (2004). Robust planning for coupled cooperative UAV missions. In CDC 43rd IEEE conference on decision and control, 2004 (Vol. 14(4), pp. 5–19). Google Scholar
- IBM (2009). IBM ILOG CPLEX V12.1 User Manual for CPLEX. Google Scholar
- Mufalli, F., Batta, R., & Nagi, R. (2010). Simultaneous sensor selection and routing of unmanned aerial vehicles for complex mission plans. Working paper, Department of Industrial and Systems Engineering, University at Buffalo, State University of New, York. Google Scholar
- Poggi, M., Viana, H., & Uchoa, E. (2010). The team orienteering problem: formulations and branch-cut and price. In 10th workshop on algorithmic approaches for transportation modelling, optimization, and systems (ATMOS10) (pp. 142–155). Google Scholar
- Rockafellar, R. (1970). Convex analysis. Princeton: Princeton University Press. Google Scholar
- Royset, J. O., & Reber, D. N. (2010). Optimized routing of unmanned aerial systems for the interdiction of improvised explosive devices. Military Operations Research, 3(4), 2917–2922. Google Scholar
- Sammuelson, D. A. (2010). Changing the war with analytics. OR/MS Today 37, 30–35. Google Scholar
- Zaloga, S. (2008). Unmanned aerial vehicles: robotic air warfare 1917–2007. ???: Osprey Publishing. Google Scholar