随着宇航推进技术的不断发展，高效的连续电推进逐渐受到广泛关注，在多次空间探测任务中成功应用。连续电推进轨道的设计与优化是未来实施低消耗、高回报探测任务的关键技术手段。然而，连续推力作用时间长、轨迹优化难度大、在大行星附近的飞行圈数多等特点使得相应的轨迹优化问题难以快速求解，限制了进一步的任务设计。为了提升连续推力轨迹优化效率，本文研究间接法的协态初值估计与同伦延拓方法。 首先，为解决间接法的初值猜测难题，研究了协态变量和标称轨道之间的映射关系。对所有一阶必要条件是否为协态变量的线性函数进行分析和归纳，给出了关于协态变量的线性等式约束条件。在已知标称轨道的基础上，构造以协态变量初始值和哈密顿函数为变量的线性方程组，分析了方程组对协态初值估计的限制作用。采用最小二乘法提出了解析协态初值估计方法，成功求解时间/能量最优行星际交会问题和燃料最优月球软着陆问题。 随后，针对间接法中同伦延拓方法的初始化难题，研究了由两个子系统（优化问题）组成的混合系统的同伦延拓方法。通过将同伦方法和混合系统相结合，使同伦过程与初始问题的设计更普适，提出了新的带同伦参数的子系统间耦合函数形式及其对应的一阶必要条件。以燃料最优问题为例，讨论了初始问题解析求解和原问题的数值求解。在求解地球至具有大椭圆、较大倾角轨道小行星的燃料最优交会时，该方法能够快速初始化，具有100%的收敛率。 最后，应用间接法求解地球附近多圈轨迹优化问题，研究了高精度模型下时间/燃料最优转移和交会问题的快速求解方法。根据连续推力远小于地球引力的特点，构建多圈轨迹优化近似动力学模型，给出了它和高精度模型之间的同伦延拓方法，提出了Sundman自变量变换对应的协态变量映射。考虑到多圈问题多局部解的特点，提出了具有固定末端真经度的近似模型下优化问题，分析了最优转移和交会结果随圈数变化的规律。针对时间最优交会问题，提出了基于割线法的交会点快速求解算法；对于燃料最优问题，给出了末端时间约束同伦方法。采用混合系统同伦延拓方法，实现了解析协态初值估计。应用于地球同步转移轨道至地球同步轨道的时间和燃料最优交会问题，以100%的收敛率和分钟量级的计算效率实现了数百圈问题的快速优化。

In the past two decades, low-thrust propulsion systems have gained much attention due to their high propulsion efficiency and successful application to various exploration missions. The continuous low-thrust trajectory optimization plays an important role in decreasing the propellant consumption and increasing the mission rewards. However, the trajectory optimization problem is difficult to solve quickly because of the long-acting time of continuous thrust, complicated optimization algorithms, and many revolutions around the planets. To improve the optimization efficiency, we study the indirect method with suitable initial costate estimation and fast homotopy method in this paper. Firstly, to overcome the obstacle of initial guesses for the indirect method, the mapping relationship between the initial costate values and the reference trajectory is investigated. The Hamiltonian function is generally linear with respect to the costates, and all the first-order optimality necessary conditions are therefore analyzed and classified according to their inherent properties. Meanwhile, some linear conditions with respect to the costates are obtained, and the linear algebraic equations are derived, under the assumption that the spacecraft moves along a near-optimal reference trajectory. The limitation of these equations on the initial costates is analyzed, and a least-squares method is used to obtain the initial costates when the corresponding coefficient matrix is invertible. Three examples of typical optimal control problems comprised of a minimum-energy interplanetary rendezvous, a minimum-time interplanetary rendezvous, and a minimum-propellant pinpoint landing are studied to demonstrate the advantage of the proposed estimation method. Secondly, to provide a warm start for the homotopy process of the indirect method, the trajectory optimization of a switched system is investigated in combination with the homotopy method. The basic idea is to embed the trajectory optimization model into the switched system, which embeds different types of dynamics and/or performance indexes, such that the embedded dynamics and/or performance index can be more generally designed to obtain the initial costates analytically. The embedding function of the switched system is designed by incorporating a homotopy parameter to connect the analytical initial costates with the optimal solution to the low-thrust trajectory optimization problem. A new embedding function is formulated, and the corresponding first-order optimality conditions are derived. The numerical solving algorithm with analytical initial costates is presented for the minimum-propellant problem. The proposed method can be quickly initialized to solve the interplanetary rendezvouses with multi-revolution, elliptical, and inclined transfer trajectories, and all the cases tested in this paper converge. Finally, the indirect method is applied to solve the many-revolution problems around the Earth. Two fast solution methods are proposed to solve the minimum-time and minimum-propellant many-revolution trajectory optimization problems. Since the continuous thrust magnitude is high-order small compared to the Earth's gravity, an approximate dynamics model is conducted, and the homotopy method is used to link the approximate model with the high-fidelity model. Then, the costate relationship between the optimal control problems before and after the Sundman transformation is proposed. Considering that the many-revolution problem has numerous locally optimal solutions, we formulate the optimal control problem with fixed final true longitude subject to the approximate model, to analyze the optimal solutions of different final true longitudes. For the minimum-time problem, the secant method is used to satisfy the rendezvous condition. Besides, the homotopy method of adjusting the final time is used to solve the minimum-propellant problem. The analytical initialization is achieved by the proposed warm-start homotopy method. Several minutes are utilized to solve the minimum-time and minimum-propellant rendezvouses from geostationary transfer orbit to the geostationary orbit with hundreds of revolutions, and all the tested cases converge.