基于Tersoff-Brenner势的航天器群图形编队研究

从分子动力学模拟角度提出了一种分布式航天器群导航控制方法，可使行星中心开普勒轨道上的航天器群在有限的感知信息条件下自发实现图形编队.该法基于人工势场技术，主要分为两个部分：改造自C-W方程的外围全局汇聚势场和基于Tersoff-Brenner势的局部塑形势场.前者将各航天器导引至预设汇聚点附近，后者进一步使各航天器自我调整彼此相对位置，最终编成期望构型.此外，引入一速度依赖型耗散项以确保任意初始分布条件下图形编队均收敛.通过地球同步轨道上航天器群正四面体构型（含中心，即金刚石结构单元）编队仿真，验证了所提方法的有效性和优越性.将编队脚本简单修改，该法还可方便用于其它类碳元素同素异形体构型的塑造，如石墨晶体结构单元正六边形等.

On Pattern Formation of Swarming Spacecrafts based on Tersoff-Brenner Potential Field

From the perspective of molecular dynamics simulation, we present a distributed control strategy that lets a swarm of spacecraft autonomously form a lattice in orbits around a planet, just making use of limited local sensory information. The strategy is based on the artificial potential field approach, which divides the artificial field into two parts: a global artificial potential field mainly based on the famous C-W equations that gathers the spacecraft around a predefined meeting point, and a local term exploiting the well-known Tersoff-Brenner potential that allows a spacecraft to place itself in the correct position relative to its closest neighbors. Moreover, in order to ensure convergence for all initial distributions of the spacecrafts, a dissipation term depending on the velocity of the agent is introduced. The new methodology is demonstrated in the problem of forming a regular tetrahedron lattice (include the center), i.e., the structure unit of diamond. By slightly changing the scenario, our method can be easily applied to shape other configurations similar to the structures of allotropes of carbon, e.g., a regular hexagon(i.e., the structure unit of graphite) etc.