This dissertation contributes three general steps of space transfer problem. As the first step, t... more This dissertation contributes three general steps of space transfer problem. As the first step, this problem is mathematically modelled. Fortunately, it is not an untouched problem, and has been one of the most well-known and challenging problems in mathematics, physics and engineering. Actually, it is known as the Multi-Body System, since 18th century till now. During the first step, lots of transfer problem's elements have to be determined. The position, velocity and timing of the start maneuver, the restrictions on position and velocity in the space, especially in the vicinity of the Earth, limits on facilities, etc. are crucial in the mathematical modeling. On the other hand, since the main problem is an interplanetary problem, thus the determination of the final condition is also very important to be exactly understood and obtained. The second step of the space transfer problem is analysis the mathematical model achieved in the first step. It will be discussed that the system is classified as a chaotic system. After analyzing the behaviour of the system, we would like to control its chaotic behaviour such that some favourite goals are successfully achieved. This step of the study is namely the control of the system. To this end, a new approach is selected which model the transfer problem as an optimal control problem. There are a lot of methods to solve an optimal control problem. Among different classes of solution methods, the direct method is selected which has its own advantages and disadvantages. Its most important advantage is the ability of using the well developed theory of nonlinear programming problem which has been investigated for many decades. The direct method discretizes the transfer optimal control problem and transcribes it into a nonlinear programming problem. Solving the nonlinear programming problem leads to the optimal solutions, i.e. the optimal trajectory and control. After achieving the optimal solutions, the presented method uses the parametric sensitivity analysis of the discretized nonlinear programming problem and investigates the sensitivity of the optimal solutions with respect to the perturbations. At last, this method contributes a real-time control to correct the violations during the mission. The numerical results regarding an extensive collection of transfer examples show the applicability of the presented method
In this article, after describing a procedure to construct trajectories for a spacecraft in the f... more In this article, after describing a procedure to construct trajectories for a spacecraft in the four-body model, a method to correct the trajectory violations is presented. To construct the trajectories, periodic orbits as the solutions of the three-body problem are used. On the other hand, the bicircular model based on the Sun-Earth rotating frame governs the dynamics of the spacecraft and other bodies. A periodic orbit around the first libration-point L 1 is the destination of the mission which is one of the equilibrium points in the Sun-Earth/Moon three-body problem. In the way to reach such a far destination, there are a lot of disturbances such as solar radiation and winds that make the plans untrustworthy. However, the solar radiation pressure is considered in the system dynamics. To prevail over these difficulties, considering the whole transfer problem as an optimal control problem makes the designer to be able to correct the unavoidable violations from the pre-designed trajectory and strategies. The optimal control problem is solved by a direct method, transcribing it into a nonlinear programming problem. This transcription gives an unperturbed optimal trajectory and its sensitivities with respect perturbations. Modeling these perturbations as parameters embedded in a parametric optimal control problem, one can take advantage of the parametric sensitivity analysis of nonlinear programming problem to recalculate the optimal trajectory with a very smaller amount of computation costs. This is obtained by evaluating a first-order Taylor expansion of the perturbed solution in an iterative process which is aimed to achieve an admissible solution. At the end, the numerical results show the applicability of the presented method.
This dissertation contributes three general steps of space transfer problem. As the first step, t... more This dissertation contributes three general steps of space transfer problem. As the first step, this problem is mathematically modelled. Fortunately, it is not an untouched problem, and has been one of the most well-known and challenging problems in mathematics, physics and engineering. Actually, it is known as the Multi-Body System, since 18th century till now. During the first step, lots of transfer problem's elements have to be determined. The position, velocity and timing of the start maneuver, the restrictions on position and velocity in the space, especially in the vicinity of the Earth, limits on facilities, etc. are crucial in the mathematical modeling. On the other hand, since the main problem is an interplanetary problem, thus the determination of the final condition is also very important to be exactly understood and obtained. The second step of the space transfer problem is analysis the mathematical model achieved in the first step. It will be discussed that the system is classified as a chaotic system. After analyzing the behaviour of the system, we would like to control its chaotic behaviour such that some favourite goals are successfully achieved. This step of the study is namely the control of the system. To this end, a new approach is selected which model the transfer problem as an optimal control problem. There are a lot of methods to solve an optimal control problem. Among different classes of solution methods, the direct method is selected which has its own advantages and disadvantages. Its most important advantage is the ability of using the well developed theory of nonlinear programming problem which has been investigated for many decades. The direct method discretizes the transfer optimal control problem and transcribes it into a nonlinear programming problem. Solving the nonlinear programming problem leads to the optimal solutions, i.e. the optimal trajectory and control. After achieving the optimal solutions, the presented method uses the parametric sensitivity analysis of the discretized nonlinear programming problem and investigates the sensitivity of the optimal solutions with respect to the perturbations. At last, this method contributes a real-time control to correct the violations during the mission. The numerical results regarding an extensive collection of transfer examples show the applicability of the presented method
In this article, after describing a procedure to construct trajectories for a spacecraft in the f... more In this article, after describing a procedure to construct trajectories for a spacecraft in the four-body model, a method to correct the trajectory violations is presented. To construct the trajectories, periodic orbits as the solutions of the three-body problem are used. On the other hand, the bicircular model based on the Sun-Earth rotating frame governs the dynamics of the spacecraft and other bodies. A periodic orbit around the first libration-point L 1 is the destination of the mission which is one of the equilibrium points in the Sun-Earth/Moon three-body problem. In the way to reach such a far destination, there are a lot of disturbances such as solar radiation and winds that make the plans untrustworthy. However, the solar radiation pressure is considered in the system dynamics. To prevail over these difficulties, considering the whole transfer problem as an optimal control problem makes the designer to be able to correct the unavoidable violations from the pre-designed trajectory and strategies. The optimal control problem is solved by a direct method, transcribing it into a nonlinear programming problem. This transcription gives an unperturbed optimal trajectory and its sensitivities with respect perturbations. Modeling these perturbations as parameters embedded in a parametric optimal control problem, one can take advantage of the parametric sensitivity analysis of nonlinear programming problem to recalculate the optimal trajectory with a very smaller amount of computation costs. This is obtained by evaluating a first-order Taylor expansion of the perturbed solution in an iterative process which is aimed to achieve an admissible solution. At the end, the numerical results show the applicability of the presented method.
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