基于傅里叶级数的小推力航天器快速轨迹设计

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%.

Rapid Design of Low-thrust Rendezvous Trajectory with Fourier Series

Trajectory design with low-thrust propulsion needs a method for quickly approximating the spacecraft's trajectory during the preliminary stage phase. To address this requirement, a 3D rendezvous trajectory design model is proposed based on the shape-based theory, by which the trajectory design problem is simplified into solving the coefficients of Fourier series. In the process of solving coefficients, thrust constraint is considered, and the existence conditions of the coefficients are qualitatively analyzed. Finally, the correctness and feasibility of this approach are verified through a numerical example. Results show that the proposed method can not only satisfy the boundary conditions and thrust constraint, but also has a good computational efficiency. Its computation time is only 0.67% of that of the Gauss pseudospectral method.