Landing Footprint Computation for Entry Vehicles

Saraf, Amitabh; Leavitt, J. A.; Mease, Kenneth D.; Ferch, Mark

doi:10.2514/6.2004-4774

Cited by 44 publications

(29 citation statements)

References 7 publications

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“…Through the simplification of the vehicle's dynamics, approximate solutions of the original optimal control problems are derived by some researchers [1-3], in which path constraints are ignored, and the Earth's rotation is omitted, resulting in less accurate and reliable. Saraf [4] provides a rapid landing footprint computation algorithm, which builds an acceleration-based trajectory planner. It also proposes a near-optimal angle of attack control law, while the footprint is not accurate either and the far-side of the boundary is far from the real footprint.…”

Section: A Methods For Entry Vehicle's Maneuver Capacity Analysis and mentioning

confidence: 99%

A method for entry vehicle's maneuver capacity analysis and evaluation

Wei

Wang

Liu

et al. 2014

Proceedings of 2014 International Conference on Modelling, Identification &Amp; Control

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Maneuver capacity provides crucial information for mission planning of entry vehicles. This paper proposes a method to generate the reachable area at the end points of the entry phase which describes the full directional maneuver capacity of the entry vehicles. This method utilizes the parallel characteristics of differential evolution (DE) and the high accuracy of Chebyshev polynomial interpolation to generate one side of the boundary of the reachable area, while conventional methods only generate one point of the boundary in each run.Furthermore, in order to assess the influence of the vehicle's design parameters on the maneuver capacity, a scoring method with analytic hierarchy process (AHP), which can greatly reduce the evaluation effort, is developed.Index Terms-maneuver capacity, entry vehicle, differential evolution, trajectory optimization, analytic hierarchy process. NOMENCLA TURE CL, CD = lift and drag coefficients, respectively L, D = lift and drag acceleration, respectively, m/s 2 g = gravitational acceleration, m/s 2 m = vehicle's mass, kg r = radial distance from Earth's center to the vehicle, m S = reference area, m 2 v = Earth-relative velocity, m/s Vs = velocity of sound, m/s a, (J = angle of attack and bank angle, respectively, rad y = flight-path angle, rad e, ¢ = longitude and latitude, respectively, rad fJ = gravitational constant, m 3 /s 2 p = density of atmosphere, kg/m 3 If! = velocity heading angle, rad We = self-rotation angular velocity of Earth, rad/s I. INTRODUCTlONT he maneuver capacity of entry vehicles provides critical information in mission planning and the evaluation of vehicle design. There are two types of maneuver for entry vehicles: longitude maneuver and lateral maneuver, which indicate the vehicle's ability to fly in the longitude plane and deviate from the longitude plane, respectively. Reachable the end of the entry phase (also called landing footprint) describes the full directional maneuver capacity of the entry vehicles, i.e., lateral maneuver capacity is depicted at each potential longitude maneuver level in landing footprint.To obtain the boundary of the landing footprint, a series of trajectory optimization problems which have similar formula tions need to be solved. The optimal goal is to maximize the terminal crossrange at each downrange under the path constraints and terminal state constraints. However, the severe nonlinearity on the vehicle's dynamics and various constraints make it unlikely to get the accurate solutions of these problems. Through the simplification of the vehicle's dynamics, approximate solutions of the original optimal control problems are derived by some researchers [1][2][3], in which path constraints are ignored, and the Earth's rotation is omitted, resulting in less accurate and reliable. Saraf[4] provides a rapid landing footprint computation algorithm, which builds an acceleration-based trajectory planner. It also proposes a near-optimal angle of attack control law, while the footprint is not accurate either and the far-side of the boun...

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Section: A Methods For Entry Vehicle's Maneuver Capacity Analysis and mentioning

confidence: 99%

A method for entry vehicle's maneuver capacity analysis and evaluation

Wei

Wang

Liu

et al. 2014

Proceedings of 2014 International Conference on Modelling, Identification &Amp; Control

View full text Add to dashboard Cite

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“…In 2004, Saraf et al constructed the footprint boundaries from the end points of feasible reentry trajectories [96]. The method is built around the developed trajectory planner in EA-GLE that can generate the footprints with fixed and varying AOA profiles, respectively.…”

Section: Fig 9 Illustrations Of Footprintsmentioning

confidence: 99%

Progress in reentry trajectory planning for hypersonic vehicle

Zhao

Zhou

Jin

2014

J. of Syst. Eng. Electron.

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The reentry trajectory planning for hypersonic vehicles is critical and challenging in the presence of numerous nonlinear equations of motion and path constraints, as well as guaranteed satisfaction of accuracy in meeting all the specified boundary conditions. In the last ten years, many researchers have investigated various strategies to generate a feasible or optimal constrained reentry trajectory for hypersonic vehicles. This paper briefly reviews the new research efforts to promote the capability of reentry trajectory planning. The progress of the onboard reentry trajectory planning, reentry trajectory optimization, and landing footprint is summarized. The main challenges of reentry trajectory planning for hypersonic vehicles are analyzed, focusing on the rapid reentry trajectory optimization, complex geographic constraints, and cooperative strategies.

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“…Significant steps in this direction have already been performed. Saraf 17 uses interpolation schemes applied to extremal drag-energy profiles for generating landing footprints for entry missions. Lockner 18 developed a more extensive approach based on Tensor Product Splines, 19 which perform excellent for the Lunar Landing problem.…”

Section: -16mentioning

confidence: 99%

“…(16) B i,k denotes the i th B-spline of order k for a given non-decreasing knot vector t = (t i ) (17) are computed, such that the resulting tensor product spline fulfills the interpolation condition, that is…”

Section: Low-density Multivariate Interpolationmentioning

confidence: 99%