Preface

Gyroscopes have been part of our lives for a long time. They have been used as toys in our childhood, and as navigation tools to equip our spacecraft, aircraft, vehicles, vessels, and even our smartphones to make our lives safe and comfortable. Stone tops have been excavated from the Neolithic sites in Xia County, Shanxi, China. It can be seen that gyroscopes have a history of at least four or five thousand years. A top belongs to the mechanical gyroscope, which is the most common or familiar type of gyroscope. A mechanical gyroscope spins on a point when it is turned around very quickly. However, the name "gyroscope" did not appear until in the middle of the nineteenth century. It was created by a French physicist, Jean-Bernard-Léon Foucault, by joining two Greek roots: gyros meaning "circle or rotation" and skopeein meaning "to see." Since then the field of gyroscopes has been maintaining a momentum of vigorous development and expansion, influenced by new applications of the latest scientific and technological innovations. New types of gyroscopes and new applications are springing up like mushrooms.

This book reviews recent topics on gyroscopes. Chapter 1 briefly introduces the history of gyroscopes, and presents a concise analysis of four main types of gyroscope: mechanical gyroscope, ring laser gyroscope, fiber-optic gyroscope (FOG), and MEMS (microelectromechanical systems) gyroscope. The dynamic future of new gyroscopes based on new principles and technologies is also presented.

Chapter 2 analyzes the classical structure and main performance parameters of the interferometric fiber-optic gyroscope (IFOG) and the integrated optics passive-resonator gyroscope (IORG). The main advanced models and performance parameters of these two types of inertial sensors are described and the design trends of both types are forecast. The chapter demonstrates that IFOGs have higher resolution performance than resonant fiber-optic gyroscopes and IORGs. IORG technology has experienced a vigorous development and refinement, and yet its performance is still at least one order of magnitude worse than that demanded by navigation applications. An improvement in this kind of gyroscope is needed to realize a significant impact on the market.

Chapter 3 reviews the developmental progress of FOGs, and also introduces their basic principles and application areas. The authors analyze the characteristics of the three classical types of FOGs: interferometric FOGs, resonant FOGs, and stimulated Brillouin scattering FOGs. The chapter presents a comparative analysis of the development and research situation of FOGs in the United States, Japan, France, and other major developing countries, and compares the application of FOGs in various international companies. The developmental trends and key technological breakthroughs of FOGs are also forecast.

In Chapter 4, low-cost MEMS gyroscope noise behavior is characterized using an ARMA autoregressive-moving-average (ARMA) model. A linear Sage Husa adaptive fading Kalman filter based on an ARMA (2, 1) model with adaptive transitive factors is introduced to reduce the drift and random noise of MEMS gyroscopes.

The proposed method consists of two stages. In the first stage, the predicted state vector is modified by an adaptive transitive factor. In the second stage, the measurement noise covariance matrix is modified by another adaptive factor based on the residual vector. The performance of the suggested algorithm is analyzed in AV analysis and also with the conventional Kalman filter and a single transitive factor-based SHAFKF algorithm. It was testified that the SHAFKF algorithm was a suitable linear adaptive KF for minimizing drift and random noise of MEMS gyro signals in the static case.

To achieve agility and large-angle attitude maneuvers of spacecraft, Chapter 5 proposes a discrete-time nonlinear attitude tracking control in which the amplitude of the control input does not depend on the sampling period. The chapter considers discrete-time nonlinear attitude tracking control problems of spacecraft and derived a Euler approximation system with respect to tracking error; then a discrete-time nonlinear attitude tracking controller is introduced and the exact discrete-time system with a derived controller is analyzed. The effectiveness of the proposed control method is verified by numerical simulations.

Chapter 6 demonstrates that the MEMS gyroscope could be used as an effective tool for gait analysis. It could help to cut the cost of revealing underlying pathologies manifested by gait abnormalities. The chapter gives a close examination of human gait patterns (normal and abnormal) using gyroscope-based wearable technology, and experimental results show that foot-mounted gyroscopes could assess gait abnormalities in both temporal and spatial domains. Gait analysis systems based on MEMS gyroscopes are economical, convenient, and suitable to use in both the clinic and at home.

> **Xuye Zhuang** Department of Instrument Science and Technology, School of Mechanical Engineering, Shandong University of Technology, China
