基于测地线的航天器集群隐蔽机动轨迹规划

Covert Maneuver Trajectory Planning of Spacecraft Cluster Based on Geodesic

针对航天器集群隐蔽机动问题,提出一种基于测地线的航天器集群轨迹规划方法。该方法将轨迹规划问题抽象到微分流形拓扑空间中,通过数学定义赋予空间结构度量。首先将集群的运动约束、避撞约束以及隐蔽构型约束等非凸约束集成到度量中,避免增加系统维度的同时无需进行约束凸化处理。进一步定义了一个依赖于流形度量的目标泛函,利用同伦变换将泛函局部极值问题转为偏微分方程求解问题。数值仿真结果表明,相比于模型预测-序列凸规划算法,该方法在解决了隐蔽机动非凸多约束问题的同时,具有不依赖于初始猜想、集群内部隐蔽覆盖性高和系统控制输入小的特点,能够为航天器集群提供有效的隐蔽机动轨迹。

Aiming at the spacecraft cluster covert maneuvering problem,a spacecraft cluster trajectory planning method based on geodesic is proposed.This method abstracts the trajectory planning problem into the differential manifold topological space and calculates the spatial structure through mathematical definition.Firstly,non-convex constraints such as motion constraints,collision avoidance constraints,and covert configuration constraints of the cluster are integrated into the metric to avoid increasing the system dimension without the need for constraint convexization.Furthermore,an objective functional dependent on manifold metrics is defined,and the local extremum problem of the functional is transformed into a partial differential equation solving problem by using homotopy transformation.The numerical simulation results show that compared with the model predictive control sequential convex programming,the proposed method solves the non-convex multi-constraint problem of covert maneuver and has the characteristics of not relying on the initial guess,high covert accuracy,and small system control input,which can provide effective covert maneuver trajectory for spacecraft cluster.