基于弹载捷联惯性导航系统精确导航的双欧拉全姿态方法
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摘要
垂直发射的地空导弹在大机动飞行时,其四元数法姿态角输出存在奇异性。为解决该问题,提出了正、反欧拉角微分方程切换的双欧拉全姿态解算方法。对正、反欧拉角微分方程进行了详细推导,论述了正、反欧拉角微分方程精华区与奇异区的倒置关系。在此基础上,建立了正、反欧拉角的转换公式。根据正欧拉角的俯仰角对正、反欧拉角无缝切换,有效解决了俯仰角在±90°附近时姿态奇异性问题。仿真和半物理试验的结果表明:双欧拉全姿态算法解算的实际姿态与理论姿态保持一致,在奇异点附近的姿态角仍能正常输出,未出现突变现象,该方法得出的导航精度比四元数法得出的导航精度提高了9.81%。
When vertically launched surface-to-air missiles are in high maneuvering flight, attitude angle outputs of the quaternion method may have the singularity problem. To solve this problem, a dual-Euler whole attitude solving method that switches between the positive and reverse Euler angle differential equations is proposed. The positive and reverse Euler angle differential equations are derived in detail, and the inverse relationships between essence areas and singular areas of the positive and reverse Euler angle differential equations are discussed. The transformation formula between the positive and reverse Euler angles is established, enabling the positive and reverse Euler angles to be switched seamlessly based on the value of positive Euler angle's pitch angle, and therefore the singularity problem is effectively solved when the pitch angle is close to ±90°. To verify the dual-Euler whole attitude solving method, the simulation and semi-physical experiments are conducted. The results show that by using the dual-Euler whole attitude solving method, actual attitudes and theoretical attitudes are consistent, and outputs of attitude angles are normal near the singular point without abrupt changes. Compared with the quaternion method, the dual-Euler whole attitude solving method can improve the navigation accuracy by more than 9.81%.
When vertically launched surface-to-air missiles are in high maneuvering flight, attitude angle outputs of the quaternion method may have the singularity problem. To solve this problem, a dual-Euler whole attitude solving method that switches between the positive and reverse Euler angle differential equations is proposed. The positive and reverse Euler angle differential equations are derived in detail, and the inverse relationships between essence areas and singular areas of the positive and reverse Euler angle differential equations are discussed. The transformation formula between the positive and reverse Euler angles is established, enabling the positive and reverse Euler angles to be switched seamlessly based on the value of positive Euler angle's pitch angle, and therefore the singularity problem is effectively solved when the pitch angle is close to ±90°. To verify the dual-Euler whole attitude solving method, the simulation and semi-physical experiments are conducted. The results show that by using the dual-Euler whole attitude solving method, actual attitudes and theoretical attitudes are consistent, and outputs of attitude angles are normal near the singular point without abrupt changes. Compared with the quaternion method, the dual-Euler whole attitude solving method can improve the navigation accuracy by more than 9.81%.
引文
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[12] 陈廷楠, 张登成. 双欧法与四元数法的应用比较[J]. 飞行力学, 1996, 14(4): 59-64.
[2] 王业卿, 黄建新, 杨雨, 等. 红外旋转弹导引头捷联惯导系统的姿态算法研究[J].上海航天, 2016, 33(3): 36-42.
[3] 赵忠. 关于捷联惯性系统全姿态计算[J]. 中国惯性技术学报, 1994 (2): 20-21.
[4] 刘腾骏, 林荣峰, 朱晏庆, 等. 基于波门预估递推剔除大跳动星点快速求解姿态算法研究[J]. 上海航天, 2017, 34(3):116-121.
[5] 杜宁, 尹海宁, 朱文山, 等. 卫星机动过程成像的姿态规划与控制研究[J]. 上海航天,2017,34(6):13-19.
[6] 黄雪樵. 克服欧拉方程奇异性的双欧法[J].飞行力学, 1994, 12(4): 28-37.
[7] 许毛跃, 张登成, 李嘉林. 四元数在欧拉方程中的应用研究[J].飞行力学, 2002, 20 (1): 67-70.
[8] 周伟, 张晓今, 寇保华, 等. 双欧法在克服伞-弹系统欧拉方程奇异性中的应用[J]. 航天返回与遥感, 2003, 24(3): 4-8.
[9] 熊志斌, 刘喜斌.克服欧拉方程奇异性的方法研究[J]. 岳阳师范学院学报(自然科学版), 2000, 13(4): 60-62.
[10] YOON S. A study on optimal switching angles in Dual-Euler method[C]// AIAA Modeling & Simulation Technologies Conference & Exhibit. 2002: 156-159.
[11] SINGLA P, MORTARI D, JUNKINS J L. How to avoid singularity for Euler angle set[C] // Proceedings of the AAS/AIAA 14th Space Flight Mechanics Meeting. Maui County, HI, USA, 2004: 1409-1426.
[12] 陈廷楠, 张登成. 双欧法与四元数法的应用比较[J]. 飞行力学, 1996, 14(4): 59-64.