Although global navigation satellite systems(GNSS)have been routinely applied to determine attitudes,there exists no literature on determining angular velocity and/or angular acceleration from GNSS.Motivated by the invention of computerized accelerometers of the correspondence author and following the success of accurately recovering translational velocity and acceleration waveforms from very high-rate GNSS precise positioning by Xu and his collaborators in 2021,we propose the concept of GNSS gyroscopes and reconstruct angular velocity and acceleration from very high-rate GNSS attitudes by applying regularization under the criterion of minimum mean squared errors.The major results from the experiments can be summarized in the following:(i)angular velocity and acceleration waveforms computed by applying the difference methods to high-rate GNSS attitudes are too noisy and can be physically not meaningful and numerically incorrect.The same can be said about inertial measurement unit(IMU)attitudes,if IMU gyros are not of very high accuracy;(ii)regularization is successfully applied to reconstruct the high-rate angular velocity and acceleration waveforms from 50 Hz GNSS attitudes and significantly outperforms the difference methods,validating the proposed concept of GNSS gyroscopes.By comparing the angular velocity and acceleration results by using the difference methods and regularization,we find that the peak values of angular velocity and acceleration by regularization are much smaller by a maximum factor of 1.57 in the angular velocity to a maximum factor of 8662.53 times in the angular acceleration in the case of high-rate GNSS,and by a maximum factor of 1.26 in the angular velocity to a maximum factor of 2819.85 times in the angular acceleration in the case of IMU,respectively;and(iii)the IMU attitudes apparently lead to better regularized angular velocity and acceleration waveforms than the high-rate GNSS attitudes,which can well be explained by the fact that the former is of better accuracy than the latter.As
为提高敏捷挠性航天器在轨连续机动的快速性和高稳定性,应用变速控制力矩陀螺(variable speed control moment gyroscopes,VSCMGs)作为姿态控制执行机构,提出了一种将观测器与自适应控制结合的姿态控制律与VSCMGs复合操纵律。考虑到机动过程中挠性模态及精确惯量不可知,采用模态观测器和转动惯量估计器对不可测的状态或参数进行辨识,辨识结果用于精确估计前馈补偿力矩,利用Lyapunov分析方法证明了闭环控制系统的稳定性。鉴于VSCMGs实际使用的力矩分配能力、避奇异能力、轮速平衡能力与末态框架角定位能力,分别设计了加权伪逆操纵律与3种对应的零运动。基于雅可比矩阵条件数提出了末态框架角的优选方法,给出了VSCMGs零运动在机动过程不同阶段的部署方案。结果表明:通过连续姿态机动数值仿真验证了所提算法的有效性;VSCMGs在连续机动过程中平滑切换模式,在不同的机动阶段实现了相应功能。模态观测值和惯量估计值在多次机动后收敛至真值附近,经过参数辨识后的控制器使航天器在机动末端更快更稳地达到指向精度要求。
The field of levitated optomechanics has experienced significant advancements in manipulating the translational and rotational dynamics of optically levitated particles and exploring their sensing applications.The concept of using optically levitated particles as gyroscopes to measure angular motion has long been explored but has not yet been proven either theoretically or experimentally.In this study,we present the first rotor gyroscope based on optically levitated high-speed rotating particles.The gyroscope is composed of a micrometer-size ellipsoidal vaterite particle that is driven to rotate at MHz frequencies in a vacuum environment.When an external angular velocity is input,the optical axis deviates from its initial position,resulting in changes in the frequency and amplitude of the rotational signal.By analyzing these changes,the angular velocity of the input can be accurately detected,making it the smallest rotor gyroscope in the world.The angular rate bias instability of the gyroscope is measured to be 0.08°/s and can be further improved to as low as 10^(−9)°/h theoretically by cooling the motion and increasing the angular moment of the levitated particle.Our work opens a new application paradigm for levitated optomechanical systems and may pave the way for the development of quantum rotor gyroscopes.
Kai ZengXiangming XuYulie WuXuezhong WuDingbang Xiao
