Aircraft routing under the risk of detection

The deterministic problem for finding an aircraft's optimal risk trajectory in a threat environment has been formulated. The threat is associated with the risk of aircraft detection by radars or similar sensors. The model considers an aircraft's trajectory in three‐dimensional (3‐D) space and represents the aircraft by a symmetrical ellipsoid with the axis of symmetry directing the trajectory. Analytical and discrete optimization approaches for routing an aircraft with variable radar cross‐section (RCS) subject to a constraint on the trajectory length have been developed. Through techniques of Calculus of Variations, the analytical approach reduces the original risk optimization problem to a vectorial nonlinear differential equation. In the case of a single detecting installation, a solution to this equation is expressed by a quadrature. A network optimization approach reduces the original problem to the Constrained Shortest Path Problem (CSPP) for a 3‐D network. The CSPP has been solved for various ellipsoid shapes and different length constraints in cases with several radars. The impact of ellipsoid shape on the geometry of an optimal trajectory as well as the impact of variable RCS on the performance of a network optimization algorithm have been analyzed and illustrated by several numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

[1]  S. Brendle,et al.  Calculus of Variations , 1927, Nature.

[2]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .

[3]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .

[4]  Gabriel Y. Handler,et al.  A dual algorithm for the constrained shortest path problem , 1980, Networks.

[5]  J. Vian,et al.  Trajectory Optimization with Risk Minimization for Military Aircraft , 1987 .

[6]  M. Desrochers,et al.  A Generalized Permanent Labelling Algorithm For The Shortest Path Problem With Time Windows , 1988 .

[7]  Nicos Christofides,et al.  An algorithm for the resource constrained shortest path problem , 1989, Networks.

[8]  Alan R. Washburn,et al.  Continuous Autorouters, with an Application to Submarines. , 1990 .

[9]  James N. Eagle,et al.  An Optimal Branch-and-Bound Procedure for the Constrained Path, Moving Target Search Problem , 1990, Oper. Res..

[10]  Refael Hassin,et al.  Approximation Schemes for the Restricted Shortest Path Problem , 1992, Math. Oper. Res..

[11]  J. Tsitsiklis,et al.  Efficient algorithms for globally optimal trajectories , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  James N. Eagle,et al.  Criteria and approximate methods for path‐constrained moving‐target search problems , 1995 .

[13]  John N. Tsitsiklis,et al.  Implementation of efficient algorithms for globally optimal trajectories , 1998, IEEE Trans. Autom. Control..

[14]  Mark B. Milam,et al.  A new computational approach to real-time trajectory generation for constrained mechanical systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[15]  Meir Pachter,et al.  COOPERATIVE CONTROL OF UAVs , 2001 .

[16]  I. Dumitrescu,et al.  Algorithms for the Weight Constrained Shortest Path Problem , 2001 .

[17]  Jonathan P. How,et al.  Aircraft trajectory planning with collision avoidance using mixed integer linear programming , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[18]  P. Pardalos,et al.  Optimal Risk Path Algorithms , 2002 .

[19]  J. Hespanha,et al.  Discrete approximations to continuous shortest-path: application to minimum-risk path planning for groups of UAVs , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[20]  Natashia Boland,et al.  Improved preprocessing, labeling and scaling algorithms for the Weight‐Constrained Shortest Path Problem , 2003, Networks.

[21]  R. D'Andrea,et al.  Low observability path planning for an unmanned air vehicle using mixed integer linear programming , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[22]  R.M. Murray,et al.  Nonlinear trajectory generation for unmanned air vehicles with multiple radars , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).