Angular Rate Measurements Research Articles

Systematic calibration method based on acceleration and angular rate measurements for fiber-optic gyro SINS.

A simple systematic calibration method based on acceleration and angular rate measurements is introduced for the fiber-optic gyro strapdown inertial navigation system in this paper. Meanwhile, a unified mathematical framework and an iterative calculation method are designed for the systematic calibration method. Using this method, one can estimate the fiber-optic gyro inertial measurement unit (FOG IMU) parameters both at a manufacturer's facility and in the field. In order to get all FOG IMU parameters, a procedure adopted based on this approach consists of two stages: First, FOG IMU raw data (accelerometer and gyro readouts) are accumulated in 19 specified FOG IMU positions. Second, the accumulated data are processed by special software to estimate all FOG IMU parameters. In addition, observability analysis of the method in 19 specified FOG IMU positions is done without the limitation of FOG IMU's initial orientation, and this analysis provides theoretical support for the application in a complex terrain. Moreover, the influence of gravity disturbance is analyzed for the first time. The analysis and experiment results show that the systematic calibration method provided by this work can meet the requirement of FOG IMU calibration.

A Novel Design of High Resolution MEMS Gyroscope Using Mode-Localization in Weakly Coupled Resonators

This paper presents a novel design for a high resolution microelectromechanical systems (MEMS) technology based resonant gyroscope using the mode-localization effect in weekly coupled resonators (WCRs) as a mechanism for sensing the input angular rate. The design consists of a single proof mass with two three degree-of-freedom (3-DoF) WCRs systems attached on either side. The MEMS gyroscope is designed according to the microfabrication constraints of the foundry process, silicon-on-insulator multi-user MEMS process (SOIMUMPs). The shift in the resonance frequency values, amplitude ratios of the WCRs, and amplitude ratios difference of two sets due to electrostatic stiffness perturbation, corresponding to the input angular rotation, are discussed as an output metric for the measurement of angular rate. The results show that the amplitude ratio difference as an output metric allows to achieve a linear output response and large dynamic range in comparison to the shift in the amplitude ratio and resonance frequency in 3-DoF WCRs in a single set. The dynamic range and resolution of the MEMS gyroscope in terms of maximum allowed resonators amplitude and noise floor is discussed. The proposed MEMS gyroscope design has a sensitivity of 62830 ppm/°/s based on a difference in the amplitude ratios of resonators in two 3-DoF WCRs systems and a dynamic range of ±100 °/s. The resolution of the MEMS gyroscope is 31.09 × 10-6 °/s which is significantly higher than existing MEMS gyroscopes and is comparable to traditional bulky ring laser gyroscopes. This high resolution makes the proposed MEMS gyroscope design suitable for use in applications such as earth rotation rate measurement for gyrocompassing and high precision robotics.

Roll Angular Rate Measurement for High Spinning Projectiles Based on Redundant Gyroscope System.

Precision-guided projectiles, which can significantly improve the accuracy and efficiency of fire strikes, are on the rise in current military engagements. The accurate measurement of roll angular rate is critical to guide a gun-launched projectile. However, Micro-Electro-Mechanical System (MEMS) gyroscope with low cost and large range cannot meet the requirement of high precision roll angular rate measurement due to the limitation by the current technology level. Aiming at the problem, the optimization-based angular rate estimation (OBARS) method specific for projectiles is proposed in this study. First, the output angular rate model of redundant gyroscope system based on the autoregressive integrated moving average (ARIMA) model is established, and then the conventional random error model is improved with the ARIMA model. After that, a Sage-Husa Adaptive Kalman Filter (SHAKF) algorithm that can suppress the time-varying process and measurement noise under the flight condition of the high dynamic of the projectile is designed for the fusion of dynamic data. Finally, simulations and experiments have been carried out to validate the performance of the method. The results demonstrate the proposed method can effectively improve the angular rate accuracy more than the related traditional methods for high spinning projectiles.

Extraterritorial motor function in carpal tunnel syndrome: A study with angular rate measurement system based on gyrosensor

Extraterritorial motor function in carpal tunnel syndrome: A study with angular rate measurement system based on gyrosensor

Performance Enhancement Method for Angular Rate Measurement Based on Redundant MEMS IMUs

Aiming at the low-cost, wide-range, and accurate measurement requirement for Microelectromechanical System (MEMS) Inertial Measurement Unit (IMU) on a multi-rotor Unmanned Aerial Vehicle (UAV), the paper designs a heterogeneous parallel redundancy configuration scheme. In redundant MEMS IMUs, a high-cost and small-range MEMS gyroscope is combined with low-cost and large-range MEMS gyroscopes. Then, an adaptive data fusion method of redundant MEMS gyroscopes is proposed. By the designed experiments based on the simulation data and the sensor measurement data, the proposed method has been proved that it can effectively improve the angular rate measurement performance of the multi-rotor UAV and broaden the angular rate measurement range on the basis of saving the configuration cost and volume of the micro IMU.

Nonlinear electrostatic effects in MEMS ring-based rate sensors under shock excitation

The vibration response of a capacitive ring-based Coriolis Vibrating Gyroscope (CVG) subjected to in-plane shock is modelled and analysed to quantify the effect of shock on angular velocity measurement. The model developed considers a ring resonator with 8 uniformly spaced support legs and describes the in-plane ring response as the sum of the first 3 modes of a perfect ring and the nonlinear electrostatic force as a Taylor series. When a severe in-plane shock is applied, the rigid body response of the ring reduces the electrode gap significantly and a high order expansion is needed to represent the electrostatic force. These nonlinear forces are shown to cause direct and mixed mode coupling to occur, which can significantly modify the response characteristics. Numerical results are presented and interpreted for a range of shock cases to demonstrate the importance of mode coupling, and estimates are made to quantify the angular rate measurement error caused by shock for devices based on 2θ- and 3θ-modes of operation. To aid the design of devices that are more resilient to shock, a parameter study is performed to identify the modal frequency ratios that minimise this coupling.

Extraction and Filter Algorithm of Roll Angular Rate for High Spinning Projectiles

The accurate measurement of roll angular rate for high spinning projectile has long been a challenging problem. Aiming to obtain the accurate roll angular rate of high spinning projectile, a novel extraction and filter algorithm, BSCZT-KF, is proposed in this paper. Firstly, a compound angular motion model of high spinning projectile is established. According to the model, we translate the roll angular rate measurement problem into a frequency estimation problem. Then the improved CZT algorithm, BSCZT, was employed to realize an accurate estimation of the narrowband signal frequency. Combined with the peak detection method, the BSCZT-KF algorithm is presented to further enhance the frequency estimation accuracy and the real-time performance. Finally, two sets of actual flight tests were conducted to verify the effectiveness and accuracy of the algorithm. The test results show that the average error of estimated roll angular rate is about 0.095% of the maximum of roll angular rate. Compared with the existing methods, the BSCZT-KF has the highest frequency estimation accuracy for narrowband signal.

Research of a novel stereoscopic symmetrical quadruple hair gyroscope

This paper presents a novel stereoscopic symmetrical quadruple hair gyroscope (SSQHG) which is distinguished from the conventional flat structures to achieve better angular rate measurement performance. A symmetrical device architecture is designed to realize the differential detection of Coriolis force, thereby effectively eliminate the common mode interference. Four stereoscopic hair posts are adopted to increase the quality of the lumped inertia masses, so as to enhance the measurement sensitivity. A simplified mass-spring-damper model of idealized SSQHG is established and verified by a modal simulation to synthetic analysis the motion modal. A set of finite element method simulations including modal distribution simulation and harmonic response simulation are implemented to acquire accurate vibration information and to identify the structure parameters quantitatively. A micromachining procedure based on the standard deep dry silicon on glass is adopted to fabricate the proposed micro-gyroscope. The frequency response experiments indicate that the vacuum packaged prototype has a drive mode frequency of 536.2 Hz with a quality factor of 1319.7 and a sense mode frequency of 535.7 Hz with a quality factor of 1334.5. An analog closed-loop driving circuit is designed to realize the self-excited oscillation of SSQHG and an open-loop sensing circuit is designed to extract the Coriolis force signal. The preliminary experimental results demonstrate that the fabricated SSQHG prototype exhibits an angular rate sensitivity of 16.03 mV/°/s and a bias instability of 16.26°/h at room temperature.

Three-Dimensional Dynamic-Model-Aided Navigation of Multirotor Unmanned Aerial Vehicles

This paper presents a dynamic-model-aided navigation (DMAN) method for a small multirotor unmanned aerial vehicle. The method can be used for temporary navigation in cases where location and velocity measurements from external sources, e.g., global navigation satellite system, are missing or unreliable. The method combines proprioceptive measurements with a Kalman filter through a dynamic model to obtain the velocity and location of the vehicle. Acceleration and angular rate measurements from an inertial measurement unit, altitude measurements from a barometric altimeter, and proprioceptive measurements of the revolution speed of propellers are considered in the method. The dynamic model of the aerial vehicle relates the linear and angular velocities of the vehicle with the revolution speed of the propeller. The revolution speed is first converted into a thrust force and torque and then included in the model. The model avoids the singularity problem and describes processes and measurements in a three-dimensional space by representing attitude using quaternions instead of Euler angles. This study details two implementations of the DMAN method: extended Kalman filter (EKF) and unscented Kalman filter (UKF). The dynamic model is incorporated into the process model and measurement model of the implementations. A model that converts the revolution speed of propellers to thrust force and torque has been derived from unmanned aerial vehicle flight experiments. Experiments that implement the proposed method for quadrotor navigation verify the performance and state the limitations of the DMAN method. Compared with previous methods, the proposed method extends the application of DMAN to the three-dimensional space and obtains location and velocity measurements in a world coordinate system.

Roll angle estimator based on angular rate measurements for bicycles

ABSTRACTMeasuring the roll angle of single-track vehicles has always been a challenging task; however, accurate and reliable measurements of this magnitude are paramount for controlling the stability of these vehicles, both for autonomous riding and for safety reasons. A roll angle estimation is also useful in other situations, such as tests to perform the identification of the parameters of the rider control. In this work, a new algorithm is presented for estimating the roll angle of bicycles. This estimator, based on the well-known Kalman filter, employs a wheel speed sensor to approximate the speed of the vehicle, and three angular rate sensors, which are currently small and affordable sensors. The proposed method was implemented in a microcontroller and tested in a bicycle and the results were compared with measurements obtained with optical sensors, showing a good correlation. Although it has not been tested in motorcycles, comparable results are expected.

Higher-order Rotation Vector Attitude Updating Algorithm

Rotation vector-based attitude updating algorithms have been used as the mainstream attitude computation algorithms for many years. The most popular methodology for designing the rotation vector algorithm is by leveraging multiple samples of gyro integrated angular rate measurements. However, it has been pointed out by many researchers that the attitude updating accuracy is limited when using the multiple samples rotation vector algorithms, especially when the platforms work under high rate manoeuvres. The third-, fourth-, fifth- and sixth-order Picard component solutions of the rotation vector differential equation are given in this paper. A new design methodology for rotation vector-based attitude updating algorithms is proposed. Different vibratory dynamics and high rate manoeuvre roller coaster experiments were conducted to validate the effectiveness of the new algorithm. The results demonstrate the high accuracy of the new algorithm compared with conventional coning correction methods. The proposed algorithm can also be used in high accuracy attitude computation of a post-processing system, especially when the output frequency of the gyro is limited.

EXPERIMENTAL AND ANALYTICAL STUDIES OF VERTICAL AXIS WIND TURBINES

The article carries out the experimental and analytical studies of three-blade wind power installation and gives the technique for measurements of angular rate of wind turbine rotation depending on the wind speeds, the rotating moment and its power. We have made the comparison of the calculation results according to the formulas offered with the indicators of the wind turbine tests executed in natural conditions. The tests were carried out at wind speeds from 0.709 m/s to 6.427 m/s. The wind power efficiency (WPE) for ideal traditional installation is known to be 0.45. According to the analytical calculations, wind power efficiency of the wind turbine with 3-bladed and 6 wind guide screens at wind speedsfrom 0.709 to 6.427 is equal to 0.317, and in the range of speed from 0.709 to 4.5 m/s – 0.351, but the experimental coefficient is much higher. The analysis of WPE variations shows that the work with the wind guide screens at insignificant average air flow velocity during the set period of time appears to be more effective, than the work without them. If the air flow velocity increases, the wind power efficiency gradually decreases. Such a good fit between experimental data and analytical calculations is confirmed by comparison of F-test design criterion with its tabular values. In the design of wind turbines, it allows determining the wind turbine power, setting the geometrical parameters and mass of all details for their efficient performance.

Quaternion-based Robust Trajectory Tracking Control of a Quadrotor Hover System

This paper presents a robust nonlinear output feedback control method that achieves three degree of freedom (3-DOF) attitude trajectory tracking of a hover system test bed. The proposed control method formally incorporates dynamic model uncertainty in addition to test bed voltage constraints. To reduce the computational requirement in the closed-loop system, constant feedforward estimates of the input-multiplicative parametric uncertainty are utilized in lieu of adaptive parameter estimates. To eliminate the need for angular rate measurements, the control design employs a bank of dynamic filters, which operates as a velocity estimator in the closed-loop system. A rigorous error system development and Lyapunov-based stability analysis are presented to prove asymptotic 3-DOF attitude trajectory tracking control. Computer simulation and experimental results are also included to illustrate the performance of the attitude control method using the Quanser 3-DOF hover system test bed.

Design, fabrication and on-the-die characterization of a MEMS tuning-fork gyroscope

In this paper, we report design, fabrication and characterization of a MEMS tuning-fork gyroscope. The main novelty of the reported work is in devising and using an experimental set-up for angular rate measurements using an open die MEMS gyroscope structure. A detailed methodology of characterization of the gyroscope is discussed. The complete experimental setup for angular rate measurement is presented. Using in-house fabrication facilities, the gyroscopes are fabricated and tested for rate measurements at different applied rotation rates from 1 $$^{\circ }/\hbox {s}$$ to $$35^{\circ }/\hbox {s}$$ . The rate sensitivity is recorded as $$60\,\upmu \hbox {V}/^{\circ }/\hbox {s}$$ with a noise floor of $$20\,\upmu \hbox {V}$$ .

3-D impact angle constrained distributed cooperative guidance for maneuvering targets without angular-rate measurements

In this paper, a three-dimensional (3-D) distributed cooperative guidance scheme is presented for multiple missiles to attack a single maneuvering target at pre-specified impact angles. A finite time observer is firstly proposed to provide accurate estimates of full states and disturbances; this is particularly crucial since some system states are not available as they are dependent on the unknown acceleration of the target. Then the guidance law is designed, which consists of two parts: the individual part and cooperative part. In the individual part, each missile is designed separately such that it will fly along the desired line of sight (LOS) after a given time which ensures hit-to-kill attack for the maneuvering target at the desired impact angles. In the cooperative part, the guidance law is designed for each missile using only information from adjacent missiles, to make all missiles hit the target at the same time. Hence it is ensured that all missiles can hit the target simultaneously, as well as at the desired directions (impact angles), then successfully achieving salvo attack. Finally, simulations are performed to verify the effectiveness of the proposed scheme.

Attitude estimation by multiplicative exogenous Kalman filter

This paper presents a novel attitude estimator called the multiplicative exogenous Kalman filter. The estimator inherits the stability properties of a nonlinear observer and the near-optimal steady-state performance of the linearized Kalman filter for estimation in nonlinear systems. The multiplicative exogenous Kalman filter is derived in detail, and its error dynamics is shown to be globally exponentially stable, which provides guarantees on robustness and transient performance. It is shown in simulations and experiments to yield similar steady-state performance as the multiplicative extended Kalman filter, which is the workhorse for attitude estimation today. The filter assumes biased angular rate measurements and two or more time-varying vector measurements, and it estimates the attitude represented by the quaternion and the angular rate sensor bias.

A new MEMS three-axial frequency-modulated (FM) gyroscope: a mechanical perspective

Abstract Micro-Electro-Mechanical Systems (MEMS) gyroscopes are inertial sensors for the measurement of angular rates. They have a variety of applications from consumer electronics to drones and the need of stability against environmental fluctuations, such as temperature, is a key factor in order to avoid expensive calibration procedures. Frequency Modulation (FM) has been recently proposed as an innovative working principle for MEMS gyroscopes and as the desired solution in terms of stability against environmental fluctuations. In this paper, the FM working principle is formalized for the three-axial case for the first time and the governing equations are derived both in the idealized case of a point-mass gyroscope and in the real case of a distributed-mass gyroscope. Moreover, the mechanical structure of the first three-axial MEMS FM gyroscope is proposed and studied. Preliminary experimental measurements prove the validity of both the model and the simulations results employed during the design process. The proposed structure overcomes lots of the constraints of the surface micromachining fabrication processes and represents an important step towards the development of a new class of MEMS gyroscopes.

Sculling Compensation Algorithm for SINS Based on Two-Time Scale Perturbation Model of Inertial Measurements

In order to decrease the velocity sculling error under vibration environments, a new sculling error compensation algorithm for strapdown inertial navigation system (SINS) using angular rate and specific force measurements as inputs is proposed in this paper. First, the sculling error formula in incremental velocity update is analytically derived in terms of the angular rate and specific force. Next, two-time scale perturbation models of the angular rate and specific force are constructed. The new sculling correction term is derived and a gravitational search optimization method is used to determine the parameters in the two-time scale perturbation models. Finally, the performance of the proposed algorithm is evaluated in a stochastic real sculling environment, which is different from the conventional algorithms simulated in a pure sculling circumstance. A series of test results demonstrate that the new sculling compensation algorithm can achieve balanced real/pseudo sculling correction performance during velocity update with the advantage of less computation load compared with conventional algorithms.

Modelling of aerodynamic interference of three-DOF GyroWheel rotor

GyroWheel is an integrated mechanism which provides both attitude control torques and measurements of attitude angular rates for tiny spacecrafts. However, aerodynamic interference is inevitable in the process of ground test which hinders the improvement of the system performance. In this paper, the modelling issue of aerodynamic interference with respect to the three-DOF GyroWheel rotor is investigated. Based on the analysis of force distributions associated with each degree of freedom, the dynamical model of the GyroWheel rotor is established with Euler's method. According to the analysis of medium flow field, the mathematical model of the aerodynamic interference is formulated by utilising the boundary layer theory and Navier-Stokes (N-S) equations, which is illustrated by some numerical simulations in the environment of FLUENT.

Modelling of aerodynamic interference of three-DOF GyroWheel rotor

GyroWheel is an integrated mechanism which provides both attitude control torques and measurements of attitude angular rates for tiny spacecrafts. However, aerodynamic interference is inevitable in the process of ground test which hinders the improvement of the system performance. In this paper, the modelling issue of aerodynamic interference with respect to the three-DOF GyroWheel rotor is investigated. Based on the analysis of force distributions associated with each degree of freedom, the dynamical model of the GyroWheel rotor is established with Euler's method. According to the analysis of medium flow field, the mathematical model of the aerodynamic interference is formulated by utilising the boundary layer theory and Navier-Stokes (N-S) equations, which is illustrated by some numerical simulations in the environment of FLUENT.