Using Low-Thrust Exhaust-Modulated Propulsion Fuel-Optimal Planar Earth-Mars Trajectories

Vadali, Srinivas R.; Nah, Ren Sang; Braden, Ellen; Johnson, I. L.

doi:10.2514/2.4553

Cited by 36 publications

(3 citation statements)

References 8 publications

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“…Because guesses for the initial costates are so often problematic in solving a TPBVP, multiple shooting [19,20] was introduced as a means to decompose a trajectory into a series of segments and partition the sensitivities over many nodes. This method has been successfully demonstrated in several low-thrust problems [21,22]. Multiple shooting also allows the addition of kinematic constraints to the nodes joining each trajectory segment.…”

mentioning

confidence: 96%

Low-Thrust Transfers in the Earth-Moon System, Including Applications to Libration Point Orbits

Ozimek

Howell

2010

Journal of Guidance, Control, and Dynamics

104

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Preliminary designs of low-thrust transfer trajectories are developed in the Earth-moon three-body problem with variable specific impulse engines and fixed engine power. The solution for a complete time history of the thrust magnitude and direction is initially approached as a calculus of variations problem to locally maximize the final spacecraft mass. The problem is then solved directly by sequential quadratic programming, using either single or multiple shooting. The coasting phase along the transfer exploits invariant manifolds and, when possible, considers locations along the entire manifold surface for insertion. Such an approach allows for a nearly propellant-free final coasting phase along an arc selected from a family of known trajectories that contract to the periodic libration point orbit. This investigation includes transfer trajectories from an Earth parking orbit to some sample libration point trajectories, including L 1 halo orbits, L 1 and L 2 vertical orbits, and L 2 butterfly orbits. Given the availability of variable specific impulse engines in the future, this study indicates that fuel-efficient transfer trajectories could be used in future lunar missions, such as south pole communications satellite architectures. Nomenclature c = constraint vector G = endpoint function H = Hamiltonian I sp = engine specific impulse i = instantaneous inclination angle m = total spacecraft mass P = engine power magnitude R = rotation matrix r, v = position and velocity vectors, Earth-moon rotating frame S = design variable vector T = engine thrust magnitude t = time U = pseudopotential function u c = control vector u T = thrust direction unit vector X = uncontrolled state vector, Earth-moon rotating framê = eigenvector at a fixed point on a periodic orbit = control constraint Lagrange multiplier vector = instantaneous argument of latitude M = anglelike manifold parameter = costate vector M = timelike manifold parameter = state transition matrix = kinematic boundary condition vector = instantaneous right ascension angle $, = kinematic boundary condition Lagrange multiplier vectors Subscripts c = control variable f = final condition FP = fixed point condition MS = multiple shooting phase p = powered phase PO = parking orbit condition s = stable manifold SS = single shooting phase u = unstable manifold 0 = initial condition

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mentioning

confidence: 96%

Low-Thrust Transfers in the Earth-Moon System, Including Applications to Libration Point Orbits

Ozimek

Howell

2010

Journal of Guidance, Control, and Dynamics

104

View full text Add to dashboard Cite

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“…The overall trajectory is divided in a sequence of problems, each of them expressed in the primary body reference frame; different segments are then patched together, through boundary constraints at the edge of each segment (direct methods), or through conditions on states and costates (indirect methods). Many applications have been presented, making use of direct methods (Tang and Conway 1995;Herman and Spencer 2002;, indirect methods (Guelman 1995;Vadali et al 2000;Nah et al 2001;Ranieri and Ocampo 2005), or hybrid methods (Pierson and Kluever 1994;Kluever and Pierson 1995).…”

mentioning

confidence: 99%

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

Colombo

Vasile

Radice

2009

Celest Mech Dyn Astr

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In this paper an optimisation algorithm based on Differential dynamic programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution. © Springer Science+Business Media B.V. 2009

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“…In fact, the propulsive acceleration of a spacecraft of total mass m s , equipped with an electric thruster of constant specific impulse I sp , can be written as (Kechichian, 1995;Vadali et al, 2000;Mengali and Quarta, 2005) …”

Section: Power Radial Thrustmentioning

confidence: 99%

Artificial equilibrium points for a generalized sail in the circular restricted three-body problem

Aliasi

Mengali

Quarta

2011

Celest Mech Dyn Astr

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This paper introduces a new approach to the study of artificial equilibrium points in the circular restricted three-body problem for propulsion systems with continuous and purely radial thrust. The propulsion system is described by means of a general mathematical model that encompasses the behavior of different systems like a solar sail, a magnetic sail and an electric sail. The proposed model is based on the choice of a coefficient related to the propulsion type and a performance parameter that quantifies the system technological complexity. The propulsion system is therefore referred to as generalized sail. The existence of artificial equilibrium points for a generalized sail is investigated. It is shown that three different families of equilibrium points exist, and their characteristic locus is described geometrically by varying the value of the performance parameter. The linear stability of the artificial points is also discussed.

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Using Low-Thrust Exhaust-Modulated Propulsion Fuel-Optimal Planar Earth-Mars Trajectories

Cited by 36 publications

References 8 publications

Low-Thrust Transfers in the Earth-Moon System, Including Applications to Libration Point Orbits

Low-Thrust Transfers in the Earth-Moon System, Including Applications to Libration Point Orbits

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

Artificial equilibrium points for a generalized sail in the circular restricted three-body problem

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