﻿ 电磁航天器编队动力学建模与运动规划方法
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Dynamics modeling and motion programming for electromagnetic formation flight
SHAO Longfei, SHI Peng , ZHAO Yushan
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:Based on the mechanism of electromagnetic spacecraft, the relative translational “tethered” dynamics model for two-craft electromagnetic formation flight (EMFF) in low earth orbit was developed by using Lagrange theory. The linearized equations for motion and stability analysis of two-craft radial and along-track formation were investigated. To stabilize the formation structure, the feedback control law was studied. The motion programming of electromagnetic formation could be transformed into a standard optimal problem, which could be perfectly solved by the Gauss pseudospectral method. In order to deal with the reconfiguration maneuver of multi-craft electromagnetic formation, the sequence control strategy was proposed. Then the multi-craft problem was transformed into a multi-phase motion planning problem. Thus, the problem of multi-phase optimal control could be solved by Gauss pseudospectral optimization software (GPOPS). The simulation result shows that the methods of dynamics modeling and motion planning proposed in this paper are valid.
Key words: electromagnetic spacecraft     formation flight     reconfiguration maneuver     sequence control     motion programming

1 电磁航天器编队动力学模型 1.1 电磁系统模型

1.2 双星电磁航天器相对动力学建模

Lto=Lx(β)Ly(α)

 图 1 电磁航天器编队几何关系示意图Fig. 1 Geometric model of EMFF system

L=T-Vg-Ve

A,B相对系统质心位置矢量为l1l2,质量为m1和m2,满足m1l1+m2l2=0,令l=l1-l2;即可得l1l1So系下相对变化率为

2 动力学模型分析 2.1 动力学特性分析

1) 以双星电磁航天器编队构型参数α,β,l为变量,有利于分析编队整体构型的变化规律.由α,β定义,可得双星“绳系”系统相对于So系的角速度为

2) 可用于电磁航天器绳系编队分析.

2.2 模型线性化与稳定性分析

 参数 a/km e i/(°) Ω/(°) ω/(°) θ/(°) 取值 6878.1 0 0 0 0 0

 图 2 电磁编队线性化与非线性动力学模型比较Fig. 2 Comparison between linear and nonlinear dynamics models for EMFF

 图 3 电磁编队构型保持状态误差变化曲线Fig. 3 State parameter error variations of EMFF system
3 电磁航天器编队运动规划< 3.1 基于高斯伪谱法的电磁航天器运动规划

1) 时间性能指标.

2) 重构过程平缓的性能指标.

3) 系统能量性能指标.

 图 4 双星电磁编队构型状态参数变化Fig. 4 State parameter variations of two-craft EMFF reconfiguration

 图 5 电磁编队控制磁矩与电磁控制力Fig. 5 Electromagnetic control(magnetic dipole and force) of two-EMFF reconfiguration
3.2 序列控制

 图 6 构型重构序列控制示意图Fig. 6 Sequence control of multi-reconfiguration maneuver

 图 7 电磁航天器构型重构优化路径示意图Fig. 7 Optimal trajectories of multi-EMFF reconfiguration

 图 8 A,B和C在重构变换过程中坐标变化Fig. 8 Position coordinates of multi-EMFF reconfiguration

 图 9 A和B在重构变换过程中控制磁矩的变化Fig. 9 Histories of magnetic moments in reconfiguration
4 结 论

1) 短时间、小偏差下,偏差线性化模型可以很好地代替原模型,可以简化模型的分析与控制;

2) 通过序列控制策略,利用双星模型可以有效地解决复杂高非线性多星电磁编队控制问题.

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#### 文章信息

SHAO Longfei, SHI Peng, ZHAO Yushan

Dynamics modeling and motion programming for electromagnetic formation flight

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(4): 737-743.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0305