Mission planners for aircraft operating under the threat of detection by ground-based radar systems are concerned with the probability of detection. Current path planning methods for such scenarios consider the aircraft pose, radar position, and radar parameters to be deterministic and known. This paper presents a framework for incorporating uncertainty in these quantities into a radar detection model that is used by a path planner. The developed path planner evaluates the radar detection risk in the presence of uncertainties and uses linear covariance analysis to efficiently generate error budgets. The error budgets identify the contribution of each source of uncertainty (e.g., sensor measurement noise, radar position uncertainty) to the overall variability in the probability of detection. The framework is applied to a modified visibility graph path planner that uses the detection risk and its variability to calculate path adjustments to maintain the detection risk below a specified threshold. The results show that the framework is effective at providing actionable information to the mission planner that improves the final planned path and reduces the detection risk.
CeccarelliNEnrightJJFrazzoliE, et al. Micro UAV path planning for reconnaissance in wind. In: American control conference, New York, 9–13 July 2007, pp. 5310–5315. New York: IEEE.
2.
LarsonRPachterMMearsM.Path planning by unmanned air vehicles for engaging an integrated radar network. In: AIAA guidance, navigation, and control conference and exhibit, San Francisco, CA, 15–18 August 2005.
3.
Xiao-weiFZhongLXiao-guangG.Path Planning for UAV in Radar Network Area. In 2010 second WRI global congress on intelligent systems, vol. 3, Wuhan, China, 16–17 December 2010, pp. 260–263. New York: IEEE.
4.
KabambaPTMeerkovSMZeitzFHIII. Optimal path planning for unmanned combat aerial vehicles to defeat radar tracking. J Guid Control Dyn2012; 29: 279–288.
5.
MahafzaBRElsherbeniA.MATLAB simulations for radar systems design. Boca Raton, FL: CRC Press, 2003.
6.
BortoffS.Path planning for UAVs. In: Proceedings of the 2000 American control conference. ACC, vol. 1, Chicago, IL, 28–30 June 2000, pp. 364–368. New York: IEEE.
7.
ChandlerPRasmussenSPachterM.UAV cooperative path planning. In: AIAA guidance, navigation, and control conference and exhibit, Denver, CO, 14–17 August 2000.
8.
PachterMHebertJ. Optimal aircraft trajectories for radar exposure minimization. In: Proceedings of the 2001 American control conference, vol. 3, Arlington, VA, 25–27 June 2001, pp. 2365–2369. New York: IEEE.
9.
MooreF.Radar cross-section reduction via route planning and intelligent control. IEEE Trans Control Syst Technol2002; 10(5): 696–700.
10.
McFarlandMZacheryRTaylorB.Motion planning for reduced observability of autonomous aerial vehicles. In: Proceedings of the 1999 IEEE international conference on control applications, vol. 1, Kohala Coast, HI, 22–27 August 1999, pp. 231–235. New York: IEEE.
11.
JunMD’AndreaR.Path planning for unmanned aerial vehicles in uncertain and adversarial environments. In: ButenkoSMurpheyRPardalosPM (eds) Cooperative control: models, applications and algorithms. Cooperative Systems. Boston, MA: Springer, 2003, pp. 95–110.
12.
SunXCaiCYangJ, et al. Route evaluation for unmanned aerial vehicle based on type-2 fuzzy sets. Eng Appl Artif Intell2015; 39: 132–145.
13.
ErlandssonTNiklassonL.Automatic evaluation of air mission routes with respect to combat survival. Inf Fusion2014; 20: 88–98.
14.
ErlandssonT.Route planning for air missions in hostile environments. J Def Model Simul2015; 12(3): 289–303.
15.
SavagePG.Strapdown analytics. Maple Plain, MN: Strapdown Associates, 2000.
16.
FarrellJ.Aided navigation: GPS with high rate sensors. 1st ed. New York: McGraw-Hill, Inc., 2008.
17.
GrewalMSAndrewsAPBartoneCG.Global navigation satellite systems, inertial navigation, and integration. Hoboken, NJ: John Wiley, 2020.
18.
CostleyAChristensenRLeishmanRC, et al. Sensitivity of single-pulse radar detection to aircraft pose uncertainties. IEEE Trans Aerosp Electron Syst2022; 59: 2286–2295.
19.
CostleyAChristensenRLeishmanRC, et al. Sensitivity of the probability of radar detection to radar state uncertainty. IEEE Trans Aerosp Electron Syst2023; 59: 9740–9747.
20.
CostleyAChristensenRSLeishmanR, et al. Analytical aircraft state and IMU signal generator from smoothed reference trajectory. IEEE Trans Aerosp Electron Syst2021; 58: 2517–2530.
21.
BeardRMcLainT.Small unmanned aircraft theory and practice. Princeton, NJ: Princeton University Press, 2012.
22.
ScheuerAFraichardT. Continuous-curvature path planning for car-like vehicles. In: Proceedings of the 1997 IEEE/RSJ international conference on intelligent robot and systems. Innovative robotics for real-world applications, vol. 2, Grenoble, 11 September 1997, pp. 997–1003. New York: IEEE.
23.
MaybeckPS.Stochastic models, estimation, and control, vol. 1. New York: Navtech Book and Software Store, 1994.
24.
ZanettiR.Rotations, transformations, left quaternions, right quaternions?J Astronaut Sci2019; 66(3): 361–381.
25.
CarpenterJRD’SouzaCN.Navigation filter best practices. NASA technical report, National Aeronautics and Space Administration, Hampton, VA, 2018.
26.
LearW.Kalman filtering techniques. NASA Technical Report JSC-20688, NASA Johnson Space Center, Houston, TX, 1985.
27.
ChristensenRSGellerD.Linear covariance techniques for closed-loop guidance navigation and control system design and analysis. Proc Insti Mech Eng, Part G J Aero Eng2014; 228(1): 44–65.
28.
ChristensenRSDrogeGLeishmanRC.Closed-loop linear covariance framework for path planning in static uncertain obstacle fields. J Guid Control Dyn2022; 45(4): 669–683.
29.
MarkleyFLCarpenterJR.Generalized linear covariance analysis. J Astronaut Sci2009; 57(1): 233–260.
30.
DijkstraE.A note on two problems in connexion with graphs. Numer Math1959; 1(1): 269–271.
31.
HartPENilssonNJRaphaelB.A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Sys Sci Cybern1968; 4(2): 100–107.
32.
BlancoJL.A tutorial on SE (3) transformation parameterizations and on-manifold optimization, Technical report University of Malaga, Málaga, 2010.
