A Low-Cost MEMS Missile-Borne Compound Rotation Modulation Scheme

Rotation modulation (RM) has been widely used in navigation systems to significantly improve the navigation accuracy of inertial navigation systems (INSs). However, the traditional single-axis rotation modulation cannot achieve the modulation of all the constant errors in the three directions; thus, it is not suitable for application in highly dynamic environments due to requirements for high precision in missiles. Aiming at the problems of error accumulation and divergence in the direction of rotation axis existing in the traditional single-axis rotation modulation, a novel rotation scheme is proposed. Firstly, the error propagation principle of the new rotation modulation scheme is analyzed. Secondly, the condition of realizing the error modulation with constant error is discussed. Finally, the original rotation modulation navigation algorithm is optimized for the new rotation modulation scheme. The experiment and simulation results show that the new rotation scheme can effectively modulate the error divergence of roll angle and improve the accuracy of roll angle by two orders of magnitude.

Enhancement of the attitude dynamics capabilities of the spinning spacecraft using inertial morphing

ABSTRACTIn the previous works by the authors, an efficient method of control of the inversion of the spinning spacecraft was proposed. This method was prompted by the Dzhanibekov’s Effect or Tennis Racket Theorem, which are often seen by many as odd or even mysterious. For the spacecraft, initially undergoing periodic flipping motion, proposed method allows to completely stop these flips by transferring the unstable motion into the regular stable spin. Similarly, the method allows activation of the flipping motion of the spacecraft, which is initially undergoing its stable spin. In this paper, spacecraft designs, which have inertial morphing capabilities, are considered and their advantages are further investigated. For general formulation, the ability of the spacecraft to change its inertial properties, associated with all three principal axes of inertia, are assumed. For simulation of these types of spacecraft systems, extended Euler’s equations are used and peculiar dynamics of the spacecraft is illustrated with a several study cases. Complex spacecraft attitude dynamics manoeuvres, using geometric interpretation, employing angular momentum spheres and kinetic energy ellipsoids, are considered in detail. Contributions of the inertial morphing to the changes of the shape of the kinetic energy ellipsoid are demonstrated and are related to the resultant various feature manoeuvres, including inversion and re-orientation. A method of reduction of the compound rotation of the spacecraft into a single stable predominant rotation around one of the body axes was proposed. This is achieved via multi-stage morphing and employing proposed instalment into separatrices. Implementation of the morphing control capabilities are discussed. For the periodic inversion motions, calculation of the periods of the flipping motion, based on the complete elliptic integral of the first kind, is performed. Flipping periods for various combinations of inertial properties of the spacecraft are presented in a systematic way. This paper discusses strategies to the increase or reduction the flipping and/or wobbling motions. A discovered asymmetric ridge of high periods for peculiar combinations of the inertial properties is discussed in detail. Numerous examples are illustrated with animations in virtual reality, facilitating explanation of the analysis and control methodologies to a wide audience, including specialists, industry and students.