为了满足小推力航天器交会轨迹的快速性设计需求,基于形状逼近理论,设计了一种三维轨迹模型.将轨迹设计问题转换为求解傅里叶级数的系数问题,避免了轨迹运动方程非线性强、难以求解的难题,极大地提高了计算效率.考虑到推力加速度的限制,建立了加速度约束方程,并结合轨迹的运动方程,给出了傅里叶级数的求解过程.同时根据边界条件和最大推力加速度值,定性地分析了傅里叶系数的存在条件.仿真验证了该方法的正确性和可行性,并从计算效率上与高斯伪谱法进行了对比,结果表明本文的方法计算耗时仅为高斯伪谱法的0.67%. In order to meet the requirement of rapid design of intersection trajectory of small thrust spacecraft, a three-dimensional trajectory model is designed based on the shape approximation theory.The trajectory design problem is transformed into the problem of solving the Fourier series coefficient to avoid the non-linearity of trajectory equation Strong and difficult to solve, which greatly improves the computational efficiency.According to the limitation of thrust acceleration, the acceleration constraint equation is established and the solving procedure of Fourier series is given in conjunction with the trajectory equation of motion.At the same time, according to the boundary conditions And the maximum thrust acceleration, the existence conditions of Fourier coefficients are qualitatively analyzed.The simulation results verify the correctness and feasibility of the proposed method and compare it with the Gaussian pseudospectral method. The results show that the proposed method Time-consuming only 0.67% Gaussian pseudospectral method.