A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within the overlapping spheres, with user-defined radii, centered around multiple cooperative satellites wit...
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A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within the overlapping spheres, with user-defined radii, centered around multiple cooperative satellites within a constrained time. The differential correction algorithm develops and utilizes the state transition matrix along with the equations of motion and multiple satellites' state information to determine the optimum trajectory to achieve the desired results. The results from the algorithm are presented for prograde orbits. The results are presented in order to allow for mission design trade-offs, including satellite separation distance and required V based on the satellites' initial inclinations. The results also provide empirical methods to determine the miss distance and optimum V solutions for the provided problem. This work ultimately provides the framework for applying the algorithm to a unique user defined responsive space scenario.
A method for performing bearings-only initial relative orbit determination of a nearby space object in the absence of any information regarding the space object's geometry and relative orbit is presented. To resol...
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A method for performing bearings-only initial relative orbit determination of a nearby space object in the absence of any information regarding the space object's geometry and relative orbit is presented. To resolve the range ambiguity characteristic of a single optical sensor system, a second optical sensor is included at a known baseline distance on the observing spacecraft. To formulate an initial estimate of the space object's relative orbit and its associated uncertainty, the angle measurements from both sensors are used to bound a region for all possible relative positions of the space object. A parameterized probability distribution in relative position that reflects uniform relative range uncertainty across the bounded region is constructed at two unique times. Linkage of the positional distributions is performed using a second-order relative lambert solver to formulate a full-state probability density function in relative position and velocity, which can be further refined through processing subsequent measurement data in a Bayesian framework.
A study was conducted to demonstrate the formulation of the new lambert algorithm using the Hamilton-Jacobi-Bellman Equation (HJB). The two-point boundary-value problem (TPBVP) of the Hamiltonian system was treated as...
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A study was conducted to demonstrate the formulation of the new lambert algorithm using the Hamilton-Jacobi-Bellman Equation (HJB). The two-point boundary-value problem (TPBVP) of the Hamiltonian system was treated as an optimal control problem where the Lagrangian function played a role as a performance index. The approach demonstrated in the study was based on the expansion of the value function in the Chebyshev series with unknown coefficients, considering the computational advantages of the use of Chebyshev polynomials. The differential expressions that arose in the HJB equation were expanded in Chebyshev series with the unknown coefficients. The new algorithm had the potential to provide a solution to the TPVBP using the spectral information about the gravitation potential function and was applicable to the problem under a higher-order perturbed potential function without any modification.
A classic result for the two-point boundary value problem in the framework of Keplerian motion allows the derivation of a novel parametrization of orbits passing through two arbitrary points in space. In particular, i...
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A classic result for the two-point boundary value problem in the framework of Keplerian motion allows the derivation of a novel parametrization of orbits passing through two arbitrary points in space. In particular, it is shown that these orbits *** unambiguously identified in terms of their eccentricity vector component in the direction perpendicular to the chord connecting the two points. The parametrization, in terms of transverse eccentricity component, lends itself to an efficient and intuitive solution algorithm for the classical lambert problem, that is, the determination of the orbit that connects two points in space in a prescribed time. Although, from the computational point of view, the resulting numerical procedure does not provide advantages over the elegant Battin's method, its derivation is considerably less demanding from the mathematical standpoint and physically more intuitive.
THIS Engineering Note follows a previous paper in which Avanzini [1] presented a transverse-eccentricity-vector-based algorithm to solve the classical lambert problem: that is, the determination of a transfer orbit ha...
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THIS Engineering Note follows a previous paper in which Avanzini [1] presented a transverse-eccentricity-vector-based algorithm to solve the classical lambert problem: that is, the determination of a transfer orbit having a specified flight time and connecting two position vectors [2]. In Avanzini's [1] paper, the eccentricity vector of the transfer orbit can be decomposed into a constant component parallel to the chord connecting the two points and a variable transverse component in the direction perpendicular to it on the orbit plane. Given the two fixed position vectors, the transfer time can be expressed as a function of the transverse eccentricity e(T). Compared with the elegant Battin's method, the derivation of this simple lambert algorithm seems to be considerably less demanding from the mathematical standpoint and physically more intuitive [1]. However, with the only consideration of direct-transfer arcs, neither the explicit expression of the derivative of the transfer time with respect to the transverse eccentricity nor the multiple-revolution solutions based on the novel method were given in [1].
Recently, it has been shown that taking the total velocity characteristic, the time of flight, and the trajectory safety into consideration and constructing a multi-objective optimization problem is an attractive and ...
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Recently, it has been shown that taking the total velocity characteristic, the time of flight, and the trajectory safety into consideration and constructing a multi-objective optimization problem is an attractive and realistic proposition for rendezvous trajectory design. Luo et al. [1] formulated the multi-objective linearized rendezvous optimization problem and solved it through the multi-objective genetic algorithm NSGA-II. It was shown that the tradeoffs between time of flight, propellant cost, and trajectory safety are quickly established using NSGA-II. In recognition of the drawbacks associated with linearized rendezvous equations, this study was expanded to a nonlinear two-body rendezvous by using NSGA-II and a lambert algorithm. The nonlinear two-body multi-objective model is more accurate and suitable for more problems in comparison with linearized rendezvous models, which are limited to circular and near-rendezvous. However, the two-body model still does not take into account trajectory perturbations, such as nonspherical perturbations and atmospheric drag, which exist in real operational missions. Thus, it is desirable to be able to obtain Pareto-optimal solutions for perturbed rendezvous trajectories.
DE and PSO proved robust given their reliability record in the random seedanalysis, and they were able to locate the optimum in relatively few function ***, both DE and PSO proved to be viable tools for solving the in...
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DE and PSO proved robust given their reliability record in the random seedanalysis, and they were able to locate the optimum in relatively few function ***, both DE and PSO proved to be viable tools for solving the interplanetary trajectoryproblem for these scenarios, as each was able to identify candidate trajectories without anexcessive computational cost. Granted, the use of a single gravity assist in an interplanetarytrajectory problem is not considered a daunting task. DE's performance in this case makes it anattractive means to minimize Δv on more involved multiple gravity-assist problems requiring n-bodygravity fields. Although this work uses an epoch of 01 January 2005 00:00 UT, this epoch was chosenarbitrarily. Upon inspection of the final results, it is the author's opinion that this analysiswould hold up for any other chosen epoch time.
For human missions to Mars, the top priority is a safe return of the crew to Earth. In the case of an emergency, trajectories that naturally return to the Earth with no intervention are preferred. We use automated des...
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For human missions to Mars, the top priority is a safe return of the crew to Earth. In the case of an emergency, trajectories that naturally return to the Earth with no intervention are preferred. We use automated design software to compute all possible Mars free return trajectories from 1995 to 2020, given constraints on the total time of Right and on the launch energy. The resulting data file contains all of the previously known types of returns. Because Earth and Mars return to the same inertial positions every 15 years, these results are representative of all Mars free returns. Of particular interest are two families of fast free returns (having times of flight of about 1.4 years) that occur in 2000 and 2002 and repeat in 2015 and 2017.
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