连续推力机动轨道优化设计的贝塞尔曲线法

A Novel Bezier Method for Continuous Thrust Maneuver Orbit Optimal Design

提出一种基于贝塞尔曲线的平面机动轨道设计方法。该方法将贝塞尔曲线方程与轨道形状方程相结合,利用得到的复合函数作为轨道方程来对机动轨道进行数学描述;通过约束条件获得可行的机动轨道族,由控制点设计给出具体的优化变量,将累积速度增量作为优化指标函数;并利用优化算法完成参数优化,从而得到最优机动轨道。最后针对设计的机动轨道推力峰值较大的问题,进一步提出了分段贝塞尔曲线法,在降低推力峰值的同时,可进一步降低燃料消耗,并在平面机动转移轨道设计的基础上,通过梯度下降对自由控制点进行修正,解决了考虑时间约束的平面轨道交会问题。

A planar maneuver orbit design method based on the Bezier curve is proposed.The method combines the Bezier curve equation with the orbital shape equations,uses the obtained composite function as the transfer orbit equation to describe the maneuver orbit,obtains the feasible maneuver orbit family through the constraint condition,and gives the specific optimization variable through the control point design.Through the calculation of the accumulated velocity pulse,the optimal index function is given and the SA-DE-RM algorithm is used to complete the orbit optimization.A segmented improvement is adopted to reduce the peak value of the thrust and the fuel consumption is further reduced as well.The rendezvous problem is solved by introducing a gradient descent algorithm.