The public reporting buitlen for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regaiding this burden estimate or any other aspect of this collection of infonnation, including suggestions for reducing this buidcn, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstarrding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 0MB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YY) SPONSORING/MONITORING AGENCY REPORT NUMBER(S)AFRL-VA-WP-TP-2003-303 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESTo be presented at the Conference on Decision and Control, Maui, HI, 9-12 Dec 03. © 2003 IEEE. This work is copyrighted. This work, resulting from Department of Air Force contract number F33615-01-C-3149, has been submitted for publication in the Proceedings of the 2003 IEEE Conference on Decision and Control. If published, IEEE may assert copyright. If so, the United States has for itself and others acting on its behalf an unlimited, nonexclusive, irrevocable, paid-up royalty-free worldwide license to use for its purposes. ABSTRACT (Maximum 200 Words)This paper explores low observablity flight path planning of unmanned air vehicles in the presence of radar detection systems. The probability of detection model of an aircraft near enemy radar depends on aircraft attitude, range, and configuration. A detection model is coupled with a simplified aircraft dynamics model. The Nonlinear Trajectory Generation (NTG) software package developed at Caltech is used. NTG algorithm is a gradient descent optimization method that combines three technologies: Bsplines, output space collocation and nonlinear optimization tools. Implementations are formulated with temporal consfraints that allow periods of high observablity interspersed with periods of low observablity. Illusfrative examples of optimized routes for low observablity are presented. SUBJECT TERMSTrajectory Generation, Path Planning, Low-Observable, UAV, RADAR, Probability of Detection AbstractThis paper explores low observability flight path planning of unmanned air vehicles in the presence of radar detection systems. The probability of detection model of an aircraft near an enemy radar depends on aircraft attitude, range, and configuration. A detection model is coupled with a simplified aircraft dynamics model. The Nonlinear Trajectory Generation (NTG) software package developed at Caltech is used. NTG algorithm is a gradient desce...

The public reporting burden for this coilection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, ABSTRACTDetection of an Unmanned Air Vehicle by radar is dependent on many variables including range, altitude, and relative orientation. Given a radar location and appropriate model for the likelihood of detection, a path plan can be created for an Unmanned Air Vehicle which constrains the probability of detection. In this paper such an approach is taken using a linearized detection model. The detection model and the Unmanned Air Vehicle's dynamics are represented as a linear program subject to mixed integer constraints. This mixed integer linear program (MILP) is then solved with commercial software which has been traditionally used by the Operations Research community. This approach searches for all feasible solutions and produces the best path plan based on the user specified parameters. Mstract-DetecAon of an Unmanned Air Vehicle by radar is dependent on many variables including range, altitude, and relative orientation. Given a radar location and appropriate . model for the lilielihood of detection, a path plan can be created for an Unmanned Air Vehicle which constrains the probability of detection. In this paper such an approach is taken using a linearized detection model. The detection model and the Unmanned Air Veliicle's dynamics are represented as a linear program subject to mixed integer constraints. Tliis mixed integer linear program (MILP) is then solved with commercial software which has l>een traditionally used by the Operations Research community. This approach searches for all feasible solutions and produces the best path plan based on the user specified parameters. SUBJECT TERMS

This paper explores the problem of finding a real-time optimal trajectory for unmanned aerial vehicles to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled using the nonlinear trajectory generation method developed by Milam et al. (Milam, M., Mushambi, K., and Murray, R., "New The paper presents a formulation of the trajectory generation task as an optimal control problem, where temporal constraints allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent radar. The guidance is provided in the form of sampled tabular data. It is then shown that the success of nonlinear trajectory generation on the proposed low-observable trajectory generation problem depends upon an accurate parameterization of the guidance data. In particular, such an approximator is desired to have a compact architecture, a minimum number of design parameters, and a smooth continuously differentiable input-output mapping. Artificial neural networks as universal approximators are known to possess these features, and thus are considered here as appropriate candidates for this task. Comparison of artificial neural networks against B-spline approximators is provided, as well. Numerical simulations on multiple radar scenarios illustrate unmanned air vehicle trajectories optimized for both detectability and time. NomenclatureB j;k i t = B-spline basis function for the output z i C i j = coefficients of the B-splines e ac = aircraft positions along the east axis k i = degree of spline polynomial l i = number of knot intervals m i = number of smoothness conditions at knot points n ac = aircraft positions along the north axis p i = number of coefficients of each output r = slant range s"; = signature function u ac = aircraft positions along the up axis ut = control input xt = state of the system z = differentially flat output = azimuth angle " = elevation angle = heading angle

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