在航太任務的前期規劃中，軌跡最佳化扮演了很重要的角色，得以在任務開始前規劃達成某項衡量標準的最大或最小化之飛行路徑，這類型的問題可以表示為一連續時間的最佳化控制問題。近年來有更多的太空任務選擇使用電能推進進行軌道轉換，而此推進系統被歸類為低推力推進系統，低推力軌道轉換問題是一種難以解決的問題。相較於高推力飛行器，低推力引擎需要更長的時間完成任務，使得數學上很難精準計算出各個時間點的飛行器之狀態，本文主要是研究如何將full-space Lagrange-Newton method 平行化，讓此演算法得已更快速的計算以解決低推力軌道轉換問題。計算KKT 系統時，不同於大多數將稠密矩陣平均分割的方式，本文將資料以稀疏矩陣的方式儲存，並透過將狀態變數與拉格朗日乘子分別平均分配至各個計算核心的方式，減少該演算法的資料傳輸次數，讓數值求解器可以大幅的減少計算時間。我們以數個二維座標的衛星低推力軌道轉換問題為範例，檢驗此演算法在低推力問題運用的可行性。

In the planning stage of space missions, trajectory optimization plays an important role in planning the flight path that maximum or minimum some quanitities before the mission begins. This type of mathematically problem can be expressed as a continuous time optimal control problem. In recent years, more space missions choose to use electric propulsion for orbital operations. However, this propulsion system is classified into the low thrust propulsion system. The problem of low thrust orbit transition is a difficult problem. Compared with the high thrust spacecraft, the low thrust engine takes more time to complete the mission, and this is the reason that it is difficult to accurately calculate the state of the spacecraft at each time point in mathematical. This thesis is to study how to parallelize the full-space Lagrange-Newton method, to make this algorithm can compute faster for solving the problem of low thrust trajectory problem. When computing KKT systems, different from most methods that dividing the dense matrix evenly, we store the data in a sparse matrix and reduce it by respectively dividing the state variables and the Lagrange multipliers into each computational cores. Reducing the number of data transfers for this algorithm allows the numerical solver to significantly reduce computational time. We take a few two-dimensional low-thrust orbit transfer trajectory optimization problems like the examples to test the feasibility of this algorithm in the application of low thrust transfer.

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