常值推力下面内轨道优化的一种改进间接法

针对常值推力下航天器面内轨道转移燃耗最省的轨道优化问题,利用极大值原理导出了最优轨迹下推力方向角应满足的控制方程,结合动力学方程建立了一种求解航天器面内最优转移轨道的改进间接法,及其在推力方向角调节能力受限条件下的应用方法。由于避免了协态变量微分方程组的求解,改进间接法相对于传统间接法降低了初值猜测的难度和计算量;与采用Gauss伪谱法求解相比,所建立的改进间接法求解结果精度更高,数值光滑性更好。仿真算例表明:推力方向角调节能力受限会改善推力方向角变化规律,降低推力方向角变化范围;就燃耗而言,推力越大燃耗越多,优化轨道节省燃耗更加显著。

An improved indirect method for in plane orbit optimization under constant thrust

The transfer of a spacecraft between coplanar orbits under continuous constant thrust with minimum fuel consumption was investigated.A control equation of the optimal trajectory,which the steering angle must satisfy,was derived by using maximum principle.Combining the control equation with dynamic equations,we establish an improved indirect method to design optimal coplanar transfer orbit and propose an approximate application method for the condition when thrust direction adjustment ability was limited.Due to avoiding solving the Lagrange costate differential equations,the improved indirect method reduces difficulty of initial value estimation and calculation a lot than traditional indirect method.Compared with Gauss pseudospectral method,the improved indirect method can get higher precision and better numerical smoothness.Simulations show that a limitation on the magnitude of the second derivative of thrust angle can improve change law of thrust angle and reduce change range of thrust angle;as to the fuel consumption,the greater the thrust magnitude is,the more the fuel consumption is,and the optimal transfer orbit can save fuel consumption a lot under a certain large magnitude of thrust.