stabilization, traction control, and roll‐over detection;
Gesture recognition and localization in gaming and mobile devices;
Optical image stabilization (OIS) of cameras;
Head tracking in Augmented Reality (AR) and Virtual Reality (VR);
Autonomous vehicles, such as self‐driving cars and Unmanned Aerial Vehicles (UAVs).
1.1 Types of Coriolis Vibratory Gyroscopes
CVGs can be divided into two broad categories based on the gyroscope's mechanical element [1]: degenerate mode (i.e.
Figure 1.1 Coriolis Vibratory Gyroscopes, in their simplest form, consist of a vibrating element with two or more mechanically coupled vibratory modes. Illustration shows a
1.1.1 Nondegenerate Mode Gyroscopes
Nondegenerate mode CVGs are currently being used in a variety of commercial applications due to ease of fabrication and lower cost. Most common implementations utilize two to four vibratory modes for sensing angular velocity along one to three axes. This is commonly achieved by forcing a proof mass structure into oscillation in a so‐called “drive” mode and sensing the oscillation on one or more “sense” modes. For example, the
Resonance frequency of sense modes are typically designed to be several hundreds to a few thousand hertzs away from the drive frequency. The existence of this so‐called drive‐sense separation (
Nondegenerate mode gyroscopes are typically operated using open‐loop mechanization. In open‐loop mechanization, “drive” mode oscillation is sustained via a positive feedback loop. The amplitidue of “drive” mode oscillations are controlled via the so‐called Amplitude Gain Control (AGC) loop. No feedback loop is employed on the “sense” mode, which leaves “sense” mode proof mass free to oscillate in response to the angular rate input.
1.1.2 Degenerate Mode Gyroscopes
Degenerate mode gyroscopes utilize two symmetric modes for detecting angular rotation. For an ideal degenerate mode gyroscope, these two modes have identical stiffness and damping; for this reason typically an axisymmetric or
In FTR mechanization, an external force is applied to the vibratory element that is equal and opposite to the Coriolis force being generated. This is a rate measuring gyroscope implementation, where the magnitude of externally applied force can be used to detect angular velocity. The main benefit of this mode of operation is to boost the mechanical bandwidth of the resonator, which would otherwise be limited by the close to zero drive‐sense separation (
In the whole‐angle mechanization, the two modes of the gyroscope are allowed to freely oscillate and external forcing is only applied to null the effects of imperfections such as damping and asymmetry. In this mode of operation the mechanical element acts as a “mechanical integrator” of angular velocity, resulting in an angle measuring gyroscope, also known as a Rate Integrating Gyroscope (RIG).
Whole‐angle gyroscope architectures can be divided into three main categories based on the geometry of the resonator element: (i) lumped mass systems, (ii) ring/disk systems, and (iii) micro‐wineglasses. Ring/disk systems are further divided into three categories: (i) rings, (ii) concentric ring systems, and (iii) disks. Whereas, micro‐wineglasses are divided into two categories according to fabrication technology: surface micro‐machined and bulk micro‐machined wineglass gyroscope architectures, Figure 1.2 [2].
String and bar resonators can also be instrumented to be used as whole‐angle gyroscopes, even though these types of mechanical elements are typically not used at micro‐scale due to limited transduction capacity. In principle, any axisymmetric elastic member can be instrumented to function as a whole‐angle gyroscope.
1.2 Generalized CVG Errors
Gyroscopes are susceptible to a variety of error sources caused by a combination of inherent physical processes
