The optimal stabilization of a rigid body motion without angular velocity measurements is considered with the help of three internal rotors that effected by internal frictions. In this paper, the orientation of the bo...The optimal stabilization of a rigid body motion without angular velocity measurements is considered with the help of three internal rotors that effected by internal frictions. In this paper, the orientation of the body will be described in terms of the Modified Rodrigues parameters (MRPs). The optimal control law which stabilizes asymptotically this motion and minimizes the require like-energy cost is obtained in terms of the MRPs. Numerical study and simulation are introduced.展开更多
There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude ...There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator （MEAE）, whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator （SEAE）, whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE, and simulation results demonstrate the efficacy of the presented algorithm.展开更多
文摘The optimal stabilization of a rigid body motion without angular velocity measurements is considered with the help of three internal rotors that effected by internal frictions. In this paper, the orientation of the body will be described in terms of the Modified Rodrigues parameters (MRPs). The optimal control law which stabilizes asymptotically this motion and minimizes the require like-energy cost is obtained in terms of the MRPs. Numerical study and simulation are introduced.
基金National Natural Science Foundation of China (10572114)
文摘There are two attitude estimation algorithms based on the different representations of attitude errors when modified Rodrigues parameters are applied to attitude estimation. The first is multiplicative error attitude estimator （MEAE）, whose attitude error is expressed by the modified Rodrigues parameters representing the rotation from the estimated to the true attitude. The second is subtractive error attitude estimator （SEAE）, whose attitude error is expressed by the arithmetic difference between the true and the estimated attitudes. It is proved that the two algorithms are equivalent in the case of small attitude errors. It is possible to describe rotation without encountering singularity by switching between the modified Rodrigues parameters and their shadow parameters. The attitude parameter switching does not bring disturbance to MEAE, but it does to SEAE. This article introduces a modification to eliminate the disturbance on SEAE, and simulation results demonstrate the efficacy of the presented algorithm.
文摘研究了刚性航天器的时延姿态稳定控制问题。首先建立了基于修正罗德里格斯参数(modified rodrigues parameters,MRPs)的航天器非线性状态模型,具有确定上界的时延项在状态反馈控制律中体现。通过构造Lyapunov-Krasovskii泛函进行稳定性分析,由此得到保证系统渐近稳定的线性矩阵不等式,依此设计状态反馈控制系数矩阵。考虑到航天器三轴间的耦合非线性项,利用扩张状态观测器(extended state observer,ESO)方法,设计了二阶非线性扩张状态观测器,以获得航天器系统内部状态向量并用于状态反馈控制律。为便于工程实际应用,仿真中将MRPs响应输出转换为欧拉角响应,仿真结果表明,本文所设计的控制系统能保证航天器三轴姿态稳定。
