Optimization of very-low-thrust trajectories using evolutionary neurocontrol

“…12 shows for a circular orbit (∆i/∆t)(a cr ) for different solar sail temperature limits. For 200 • C ≤ T lim ≤ 260 • C, the optimal orbit cranking semi-major axis can be approximated with an error of less than 1% bỹ a cr,opt ≈ 30 •T −0.897 lim (15) whereã cr,opt = acr,opt 1 AU andT lim = T lim 1 • C . The maximum inclination change rate can be approximated with an error of less than 1% by ( ∆i/∆t) max ≈ 9.26 × 10 −4 •T lim − 5.68 × 10 −2 (16) where ( ∆i/∆t) max = (∆i/∆t)max 1 deg/day .…”

Section: B Variation Of the Hyperbolic Excess Energy For Interplanetmentioning

confidence: 99%

Solar Sail Trajectory Optimization for Intercepting, Impacting, and Deflecting Near-Earth Asteroids

Dachwald

Wie

2005

AIAA Guidance, Navigation, and Control Conference and Exhibit

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A fictional asteroid mitigation problem posed by AIAA assumes that a 200 m near-Earth asteroid (NEA), detected on 04 July 2004 and designated as 2004 WR, will impact the Earth on 14 January 2015. Adopting this exemplary scenario, we show that solar sail spacecraft that impact the asteroid with very high velocity are a realistic near-term option for mitigating the impact threat from NEAs. The proposed mission requires several Kinetic Energy Interceptor (KEI) solar sail spacecraft. Each sailcraft consists of a 160 m × 160 m, 168 kg solar sail and a 150 kg impactor. Because of their large ∆V-capability, solar sailcraft with a characteristic acceleration of 0.5 mm/s 2 can achieve an orbit that is retrograde to the target orbit within less than about 4.5 years. Prior to impacting 2004 WR at its perihelion of about 0.75 AU, each impactor is to be separated from its solar sail. With a relative impact velocity of about 81 km/s, each impactor will cause a conservatively estimated ∆v of about 0.35 cm/s in the trajectory of the target asteroid, largely due to the impulsive effect of material ejected from the newly formed crater. The deflection caused by a single impactor will increase the Earth-miss distance by about 0.7 Earth radii. Several sailcraft will therefore be required for consecutive impacts to increase the total Earthmiss distance to a safe value. In this paper, we elaborate a potential mission scenario and investigate trade-offs between different mission parameters, e.g. characteristic acceleration, sail temperature limit, hyperbolic excess energy for interplanetary insertion, and optical solar sail degradation.

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“…In addition, the trajectory design problem is particularly problematic when the initial and terminal orbits are widely spaced, resulting in a trajectory that requires a large number of orbital revolutions in order to complete the transfer. Then, even if a solution is obtained, it is highly likely that the trajectory is not the global optimal solution [1].…”

Section: Introductionmentioning

confidence: 99%

“…In [1][2][3][4][5][6][7][8], numerical optimization techniques were used to optimize interplanetary space trajectories. In [9], a variation of parameters approach was employed to solve a minimum-fuel timefixed rendezvous problem, whereas in [10], Pontryagin's minimum principle [11,12] was used to determine the optimal thrust acceleration for an orbit maintenance study.…”

Section: Introductionmentioning

confidence: 99%

Minimum-Time Trajectory Optimization of Multiple Revolution Low-Thrust Earth-Orbit Transfers

Graham

Rao

2015

Journal of Spacecraft and Rockets

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The problem of determining high-accuracy minimum-time Earth-orbit transfers using low-thrust propulsion is considered. The optimal orbital transfer problem is posed as a constrained nonlinear optimal control problem and is solved using a variable-order Legendre-Gauss-Radau quadrature orthogonal collocation method. Initial guesses for the optimal control problem are obtained by solving a sequence of modified optimal control problems where the final true longitude is constrained and the mean square difference between the specified terminal boundary conditions and the computed terminal conditions is minimized. It is found that solutions to the minimumtime low-thrust optimal control problem are only locally optimal, in that the solution has essentially the same number of orbital revolutions as that of the initial guess. A search method is then devised that enables computation of solutions with an even lower cost where the final true longitude is constrained to be different from that obtained in the original locally optimal solution. A numerical optimization study is then performed to determine optimal trajectories and control inputs for a range of initial thrust accelerations and constant specific impulses. The key features of the solutions are then determined, and relationships are obtained between the optimal transfer time and the optimal final true longitude as a function of the initial thrust acceleration and specific impulse. Finally, a detailed postoptimality analysis is performed to verify the close proximity of the numerical solutions to the true optimal solution. Nomenclature a = semimajor axis, m e = eccentricity f = second modified equinoctial element g = third modified equinoctial element g e = sea-level acceleration due to Earth gravity, m∕s 2 H = optimal control augmented Hamiltonian h = second modified equinoctial element i = inclination, deg or rad (i r , i θ , i h ) = rotating radial coordinate system J 2 = second zonal harmonic J 3 = third zonal harmonic J 4 = fourth zonal harmonic k = fifth modified equinoctial element L = sixth modified equinoctial element (true longitude), rad or deg m = mass, kg n = mean motion P k = Legendre polynomial of degree k p = first modified equinoctial element (semiparameter), m R e = radius of the Earth, m T = thrust, N t = time, s or day u = control direction u h = normal component of control u r = radial component of control u θ = tangential component of control Δ = spacecraft specific force, m · s −2 λ = optimal control costate μ = optimal control path constraint Lagrange multiplier μ e = Earth gravitational parameter, m 3 · s −2 ν = true anomaly, deg or rad Ω = longitude of ascending node, deg or rad ω = argument of periapsis, deg or rad

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Optimization of very-low-thrust trajectories using evolutionary neurocontrol

Cited by 39 publications

References 8 publications

Main belt asteroid sample return mission using solar electric propulsion

Main belt asteroid sample return mission using solar electric propulsion

Solar Sail Trajectory Optimization for Intercepting, Impacting, and Deflecting Near-Earth Asteroids

Minimum-Time Trajectory Optimization of Multiple Revolution Low-Thrust Earth-Orbit Transfers

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