航天器集群构形控制的虚拟弹簧阻尼网络方法

针对航天器集群质心相对运动构形控制问题，提出了一种基于虚拟弹簧阻尼网络的分布式控制方法。航天器间以虚拟的弹簧阻尼器相互连接，弹簧的原长根据期望的相对运动构形来设定。各航天器的控制输入是与其相连的所有弹簧阻尼器的合力。在线性动力学模型和拓扑结构连通且固定的假设下，基于代数图论的方法推导出了闭环系统稳定性条件。对近地轨道上100个航天器形成格点相对运动构形和20个航天器形成时变距离的椭圆构形的实例进行了仿真，考虑了轨道摄动的影响，结果表明，集群通过虚拟弹簧阻尼网络控制可实现期望构形，并能达到厘米量级的构形保持控制精度。该控制方法不改变集群的质心，只需施加很小的控制加速度；仅基于局部的邻居交互，能够适应大规模集群对分布式控制的要求。

Virtual Spring Damper Mesh Method for Formation Control of Spacecraft Swarm

A method based on a virtual spring-damper mesh is proposed for formation control of spacecraft swarms. Spacecrafts are interconnected virtually by spring-damper pairs. The natural lengths of the springs are set according to the geometrical requirements for the desired formation. The control input to each spacecraft is the resultant of the forces generated by the virtual spring-damper pairs connected to the spacecraft. Under the assumption of linear translational dynamics and that the mesh topology is fixed and connected, the stability condition of the virtual spring-damper mesh controlled closed-loop relative motion system are derived by using the algebraic graph theory. Simulations of a lattice formation of 100 spacecrafts and an elliptical, time-varying formation of 20 spacecrafts are presented. Orbit perturbations are included in the simulation. The results show that the desired formations can autonomously evolve from random initial states and that the formation-keeping errors are in the order of centimeter. The method won’t change the mass center of the swarm, and only small control accelerations are required. The distributed nature of the interactions makes the method desirable for formation control of large swarms.