Rate Gyro Research Articles

Modeling and Implementation of Multi-Position Non-Continuous Rotation Gyroscope North Finder

Even when the Global Positioning System (GPS) signal is blocked, a rate gyroscope (gyro) north finder is capable of providing the required azimuth reference information to a certain extent. In order to measure the azimuth between the observer and the north direction very accurately, we propose a multi-position non-continuous rotation gyro north finding scheme. Our new generalized mathematical model analyzes the elements that affect the azimuth measurement precision and can thus provide high precision azimuth reference information. Based on the gyro’s principle of detecting a projection of the earth rotation rate on its sensitive axis and the proposed north finding scheme, we are able to deduct an accurate mathematical model of the gyro outputs against azimuth with the gyro and shaft misalignments. Combining the gyro outputs model and the theory of propagation of uncertainty, some approaches to optimize north finding are provided, including reducing the gyro bias error, constraining the gyro random error, increasing the number of rotation points, improving rotation angle measurement precision, decreasing the gyro and the shaft misalignment angles. According them, a north finder setup is built and the azimuth uncertainty of 18” is obtained. This paper provides systematic theory for analyzing the details of the gyro north finder scheme from simulation to implementation. The proposed theory can guide both applied researchers in academia and advanced practitioners in industry for designing high precision robust north finder based on different types of rate gyroscopes.

Extended Kalman filtering based parameter estimation and drift compensation for a MEMS rate integrating gyroscope

This paper presents an offline extended Kalman filtering based parameter identification and drift compensation for a MEMS ring vibratory gyroscope. Damping and stiffness imperfections are the major error sources in MEMS vibratory gyroscopes. In the rate integrating operation mode, where angle is output instead of angular velocity as in the case of the rate gyroscope, parameter identification is an essential prerequisite for any feedback control and compensation algorithm to minimize angle drift and other errors. The proposed EKF method provides five estimates for the resonator DC loop gain, and another four parameters related to the non-proportional damping and aniso-elasticities. The method is based on the slowly varying averaged dynamic model expressed in terms of orbital elements. The averaging methodology offers important advantages over similar attempts based directly on the dynamic model expressed in terms of fast time varying displacement and velocity of vibration. Firstly, the observed measurements are subjected to significantly lower levels of noise as a consequence of the narrowband demodulation process employed in the calculation of the orbital elements. Secondly, the EKF requires much lower update rate due to the slowly varying nature of the augmented states. These advantages result in a more accurate estimation, improved stability performance and the possibility for real time implementation of the EKF. Numerical simulation and offline implementation of the EKF using experimental gyroscope operation data are provided to validate the proposed method. Moreover, the identified damping imperfections have been used in the drift compensation control in a DSP based real time rate integrating gyroscope control system. Ultimately, the maximum angular drift has been reduced to 1° per second. Spectrum analysis shows the angle drift error is dominated by 4th harmonics caused by dynamics not included in the conventional gyroscope model.

Angular Velocity Nonlinear Observer From Single Vector Measurements

The paper proposes a technique to estimate the angular velocity of a rigid body from single vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector measurements are directly filtered through a nonlinear observer estimating the angular velocity. Convergence is established using a detailed analysis of a linear-time varying dynamics appearing in the estimation error equation. This equation stems from the classic Euler equations and measurement equations. As is proven, the case of free-rotation allows one to relax the persistence of excitation assumption. Simulation results are provided to illustrate the method.

Feasibility of Development of a Quasi-Imperturbable Pendulum Vertical Sensor

The authors consider feasibility of development of a quasi-imperturbable pendulum vertical sensor. The result is achieved due to compensation for the error caused by the acceleration of an object by means of the corrective actions on the pendulum formed by the signals of the inertial sensors. They also consider a possibility of reduction of the displacement of the pendulum from the vertical position under the influence of the horizontal acceleration of an object by formation of a reaction, which compensates for the inertial forces by the sensors of the same physical nature - an accelerometer and additional sources of information - rate gyro and additional feedback from the output signal. The article discusses versions of various combinations of the corrective devices, namely: 1) basic option - pendulum corrected by an accelerometer 2) basic option and additional feedback from the output signal 3) version of paragraph 2, with additional correction sensor - rate gyro. It was demonstrated that the basic option does not reduce the pendulum static displacement from the vertical, but significantly increases the time constant depending on the feedback factor, and significantly reduces the rate of the displacement increase from the vertical. It may be used in a number of technical applications. Version of paragraph 2 has the following features: in the presence of a horizontal acceleration and in the absence of the deviation angles of the housing of the pendulum it becomes quasi-imperturbable, and the steady-state value of the displacement angle in relative units at a single step unit of acceleration is defined as a x (1 - d)/g, where d - feedback factor 0 x (1 - d)/g. The carried out physical experiments of modeling and simulation confirm the findings and possibility of development of a number of technical applications on this basis.

Rotation Control and Characterization of High-Speed Variable-Capacitance Micromotor Supported on Electrostatic Bearing

This paper presents the rotation control design and experimental performance of a microelectromechanical systems (MEMS) variable-capacitance motor where a free-spinning rotor is suspended and centered in an evacuated vacuum cavity by a contactless electrostatic bearing. The micromachined device is based on a glass/silicon/glass bonding structure, fabricated by bulk micromachining, driven by a three-phase electrostatic motor, and used as an angular rate gyroscope by spinning-up the rotor rate over 104 r/min. A closed-loop phase commutation scheme is proposed in our rotation design where three-phase drives are switched depending on one channel of the rotor's angular position. The design of the micromotor spin-up and constant-speed operation is described based on the proposed electronic commutation. Experimental results of the motor spin-up process under different vacuum settings, static, and dynamic characteristics of the constant-speed control loop together with scale factor of the spinning-rotor gyroscope are described for the device operated in vacuum. It is indicated that the rotor can be spun up to 2.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> r/min within 400 s, and up to 2.96 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> r/min in steady state under a drive voltage of 11.8 V. Measurement data in constant-speed control mode show that the standard deviation of the spin rate error is 0.07 r/min at a rated speed of 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> r/min.

Slip-based terrain estimation with a skid-steer vehicle

ABSTRACTIn this paper, a novel approach for online terrain characterisation is presented using a skid-steer vehicle. In the context of this research, terrain characterisation refers to the estimation of physical parameters that affects the terrain ability to support vehicular motion. These parameters are inferred from the modelling of the kinematic and dynamic behaviour of a skid-steer vehicle that reveals the underlying relationships governing the vehicle-terrain interaction. The concept of slip track is introduced as a measure of the slippage experienced by the vehicle during turning motion. The proposed terrain estimation system includes common onboard sensors, that is, wheel encoders, electrical current sensors and yaw rate gyroscope. Using these components, the system can characterise terrain online during normal vehicle operations. Experimental results obtained from different surfaces are presented to validate the system in the field showing its effectiveness and potential benefits to implement adaptive driving assistance systems or to automatically update the parameters of onboard control and planning algorithms.

Linear Accelerometers and Rate Gyros for Rotary Joint Angle Estimation of Heavy-Duty Mobile Manipulators Using Forward Kinematic Modeling

A gravity-referenced joint angle estimation approach is proposed for multiple-degree-of-freedom hydraulic manipulators. The approach is built solely upon easy-to-install linear accelerometers and angular rate gyroscopes to avoid physical contact to rotary joint mechanisms and the use of in-axis sensors. As a significant novelty, a comprehensive kinematics model for linear accelerations acting on the accelerometers during motion is associated with the well-known principles of complementary sensor fusion for the first time, which provides a practical solution for using the force of gravity as an angular reference while in fast motion. In experiments with a serial-link manipulator of a multiton off-road forestry vehicle, gyro-aided sensor fusion employing the kinematics model achieved a joint angle sensing error of less than $\pm$ 1 $^\circ$ , which translated to a centimeter end-effector positioning accuracy. This can be considered a significant result in view of the vibrations oscillating through the manipulator structure, coupled linear accelerations of linkage motion, and nonstatic interaction between the vehicle base and the terrain.

Design and Verification of a Digital Controller for a 2-Piece Hemispherical Resonator Gyroscope.

A Hemispherical Resonator Gyro (HRG) is the Coriolis Vibratory Gyro (CVG) that measures rotation angle or angular velocity using Coriolis force acting the vibrating mass. A HRG can be used as a rate gyro or integrating gyro without structural modification by simply changing the control scheme. In this paper, differential control algorithms are designed for a 2-piece HRG. To design a precision controller, the electromechanical modelling and signal processing must be pre-performed accurately. Therefore, the equations of motion for the HRG resonator with switched harmonic excitations are derived with the Duhamel Integral method. Electromechanical modeling of the resonator, electric module and charge amplifier is performed by considering the mode shape of a thin hemispherical shell. Further, signal processing and control algorithms are designed. The multi-flexing scheme of sensing, driving cycles and x, y-axis switching cycles is appropriate for high precision and low maneuverability systems. The differential control scheme is easily capable of rejecting the common mode errors of x, y-axis signals and changing the rate integrating mode on basis of these studies. In the rate gyro mode the controller is composed of Phase-Locked Loop (PLL), amplitude, quadrature and rate control loop. All controllers are designed on basis of a digital PI controller. The signal processing and control algorithms are verified through Matlab/Simulink simulations. Finally, a FPGA and DSP board with these algorithms is verified through experiments.

Design of predictive control and evaluate the effects of flight dynamics on performance of one axis gimbal system, considering disturbance torques

In this paper, we aim to present control of one axis gimbal system. Indeed, the purpose of using the model of predictive control is twofold. Firstly, it runs the stabilization loop. Stabilization loop is constructed with DC motor, Rate Gyro and inertia utilizing MPC type controller. The gimbal torque relationships are obtained from using Newton's second law equation on the assumption that gimbal is rigid body. The second purpose is to analyze the effects of flight dynamics on performance of one axis gimbal system. A set of scenarios' tests is performed to evaluate the act of the proposed system in various conditions, considering the gimbal friction, mass imbalance and disturbance torques. SIMULINK/MATLAB is administered to assess the entire control system. The simulation results are discussed to show the validity of the proposed system during the flight and show that the gimbal system stabilizes the line of sight even when the disturbance torques affect the system performance.

Investigating the effects of quadrature error in parametrically and harmonically excited MEMS rate gyroscopes

Some factors like environmental conditions and manufacturing errors affect performance of a MEMS rate gyroscope. Because they may result to parameter mismatch between the designed gyroscope and the fabricated one. The Parametrically excited gyros are more robust to these changes than the harmonically excited gyros. However, these types of gyros also experience reduction in their accuracy in angular velocity determination due to these changes. One of parameters that affect the accuracy of the gyroscope is quadrature error that here, its effect in the accuracy of angular velocity determination is investigated in two typically designed harmonically and parametrically excited MEMS gyroscopes. The studies are done solving the gyroscopes’ equations analytically and numerically after addition of quadrature error. Finally, it’s found that the quadrature error reduces the accuracy of the gyroscope. Accuracy reduction (equivalent to output error increasing) decreases with increasing angular velocity or decreasing quadrature error almost the same for two types of gyroscope.

Low-cost land vehicle attitude determination using single-epoch GPS data, MEMS-based inclinometer measurements

GPS compasses equipped with short baselines can provide precise heading and elevation information for land vehicles. Most recent research in this area has focused on developing single-frequency, single-epoch ambiguity resolution, as the ambiguity resolution in a single epoch can guarantee total independence from carrier phase slips and lock losses. The reliability of single-frequency, single-epoch ambiguity resolution, however, are often insufficient for actual applications due to the weak baseline model. For land vehicle applications, baseline elevation can also be measured by inclinometer, which provides an important constraint that can be exploited to directly assist the ambiguity resolution process. In this study, we developed an innovative method that fully integrates MEMS-based inclinometer measurements into single-difference GPS observation equations and obtains the fixed baseline solution via weighted constrained integer least squares. We then explored the performance and effectiveness of the proposed method by building an integrated GPS/inclinometer compass system (IGICS) with low-cost GPS receivers (U-Blox LEA-6T) and a MEMS-based inclinometer (SCA-100T). Both actual static and dynamic experiments demonstrated that our method is capable of successfully fixing the set of integer ambiguities to the correct value for land vehicles equipped with very short baselines. The proposed method is also more easily implemented than the traditional augmenting scheme with rate gyros and IMU, as evidenced by a comparative experiment conducted using three approaches: (1) the new method; (2) horizontal constraint without inclinometer measurements; and (3) exploiting inclinometer measurements without imposing horizontal constraints.

Real-time relative orbit estimation of noncooperative space target based on nonlinear filtering

The problem of real-time relative orbit estimation of long range and high speed between a noncooperative target and a chaser is addressed. A high precision relative orbit model, in which the Earth J2 perturbation has been taken into consideration, is established for state estimation. As the attitude of the chaser is required for relative orbit estimation, it has also been estimated. The range, elevation, and azimuth between the target and the chaser, which can be measured by a laser rangefinder and a CCD device, are chosen as measuring vector, while a rate gyroscope and one star sensor is installed on the chaser to measure its rate and attitude parameters. On the basis of nonlinear filtering technology, two kinds of filtering systems are designed, namely the separated filtering system and the united filtering system, and the relationship between the two filtering systems are analyzed. Simulation results indicate the united filtering system is more robust than the separated filtering system against realistic initial attitude errors and attitude measurement noises.

Statistical Modeling of Random Walk Errors for Triaxial Rate Gyros

Microelectromechanical systems (MEMS) gyroscope is a new type of inertial sensor with small size, light weight, low cost, and low power consumption. Thus, it has been widely used for guidance and stabilization of many platforms. Although these MEMS devices have such crucial advantages, the stochastic errors, mainly including random walk, bias instability, and quantization noise, may suddenly degrade the system performance in a short period of time. Therefore, a suitable modeling of these errors is vital to guarantee the system performance. In the previous work, Allan variance (AV) (time domain analysis) and power spectral density (frequency domain analysis) techniques are used to identify the random process and get the precise parameter estimation. However, they mainly deal with univariate situations and only give a suitable modeling of uniaxial gyro signal and not a precise estimation for an array of gyros. Aiming at an application in practical engineering and dealing with triaxial rate gyros’ stochastic errors, a new algorithm for estimating the statistical parameters of the triaxial rate gyros is proposed. The algorithm in this paper first extends the definition of AV from univariate to multivariable and gives the corresponding statistical properties, i.e., the theoretical mean, variance of the new AV, and covariance between different AV points, and then gives the algorithm based on the best linear unbiased estimator from statistical estimation theory. The performance of the algorithm is demonstrated using both simulated data and experimental data.

Quaternion-based pseudo kalman filter for wearable inertial/magnetic sensor applications

This paper deals with orientation estimation using miniature inertial/magnetic sensor comprised of a tri-axial rate gyro, a tri-axial accelerometer, and a tri-axial magnetometer. Particularly, a novel quaternion-based pseudo Kalman filter (KF) is proposed by modifying an indirect KF, in order to maximize the computational efficiency and implementation simplicity. In the proposed pseudo KF, time-update process for prediction is based on the quaternion itself, while measurement-update process for correction is performed through the quaternion error. Experimental tests were conducted to verify performance of the proposed algorithm in various dynamic conditions. By designing the pseudo KF structure, matrix operations required in a typical KF are simplified. For instance, the proposed KF does not require the evaluation of the a priori and a posteriori error covariance matrices. Thus, the proposed algorithm achieves higher computational efficiency even than a typical indirect KF, without sacrificing estimation accuracy. Due to its high efficiency, the proposed algorithm can be suitable for battery-powered and low cost processor-based wearable inertial/magnetic sensor applications.

A Sensor-based Method for Diagnostics of Geometric Performance of Machine Tool Linear Axes

A linear axis is a vital subsystem of machine tools, and when installed and operating within a manufacturing facility, a machine tool needs to stay in good condition for parts production. All machine tools degrade during operations, yet knowledge of that degradation is elusive; accurate detection of linear axis degradation is a manual and time-consuming process. Thus, manufacturers need automated and efficient methods to diagnose the condition of their machine tool linear axes without disruptions to production. Towards this end, a sensor-based method was developed to quickly estimate the performance degradation of linear axes. The multi-sensor-based method uses data from inclinometers, accelerometers, and rate gyroscopes to identify changes in linear and angular errors due to axis degradation. A linear axis testbed, developed for verification and validation of the sensor-based method, contains a linear axis and a reference laser-based system for measurement of the axis geometric performance. Comparison of the sensor-based results and the laser-based results shows that the sensor-based method is capable of detecting micrometer-level and microradian-level degradation of linear axes. Consequently, if a sensor box resides on a machine tool, then the degradation of the linear axes can be periodically measured and used to help optimize maintenance.

A Fault-Tolerant Multiple Sensor Fusion Approach Applied to UAV Attitude Estimation

A novel sensor fusion design framework is presented with the objective of improving the overall multisensor measurement system performance and achieving graceful degradation following individual sensor failures. The Unscented Information Filter (UIF) is used to provide a useful tool for combining information from multiple sources. A two-step off-line and on-line calibration procedure refines sensor error models and improves the measurement performance. A Fault Detection and Identification (FDI) scheme crosschecks sensor measurements and simultaneously monitors sensor biases. Low-quality or faulty sensor readings are then rejected from the final sensor fusion process. The attitude estimation problem is used as a case study for the multiple sensor fusion algorithm design, with information provided by a set of low-cost rate gyroscopes, accelerometers, magnetometers, and a single-frequency GPS receiver’s position and velocity solution. Flight data collected with an Unmanned Aerial Vehicle (UAV) research test bed verifies the sensor fusion, adaptation, and fault-tolerance capabilities of the designed sensor fusion algorithm.

Static Behavior of Closed-Loop Micromachined Levitated Two-Axis Rate Gyroscope

In this paper, a model of Micromachined Levitated Gyroscope (MLG) with a closed-loop control is developed. The model provides a fundamental theoretical description of the operating principle of the MLG. Employing the obtained model, different operating modes of the MLG, which are depended on relationships between the speed of the rotor rotation, value of the stiffness provided by a contactless suspension and the rotor shape are considered. In particular, it is showed that decreasing the stiffness of the contactless suspension leads to two operating modes of the gyroscope, which are defined by the rotor shape. Moreover, an error model of the MLG for a closed loop is obtained, which allows us to give an explanation of the error-producing mechanics of the inherent errors of the MLG.

Design and optimization of a resonant output frequency gyroscope for robust sensitivity and bandwidth performance

This paper presents the architecture and optimization verification of a designed mode-mismatching gyroscope prototype made with fused silica in atmospheric pressure. The gyroscope prototype uses the decoupling frame and double-ended tuning fork (DETF) to achieve high sensitivity and quality factor. This structure can suppress residual quadrature error due to fabrication errors and imperfections. The angle rate-sensitive elements of the proposed gyroscope prototype with quasi-digital FM output are two DETF resonators resulting in differential implementation. We describe the principle of operation characterization of our micromechanical vibratory rate gyroscope based on resonant sensing of the Coriolis force and establish mathematical model called multi-parameters excitation system dynamics of Mathieu equation based on our previous work. We specify and quantify the impact functions of mechanical parameters on the properties of gyroscopes and identify sensitivity and limitation of sensitivity and bandwidth each other. A sample-based stochastic model is established to investigate the influence of different uncertain structure size on gyroscope performance. According to the uncertainty analysis, we modify the previous gyroscope structure, and then the parameters and structure of the improved third version gyroscope are obtained. This research can provide a reference for design and optimization of the structure size to improve robustness and performance of resonant angle rate sensor.

Attitude and gyro bias estimation by the rotation of an inertial measurement unit

In navigation applications, the presence of an unknown bias in the measurement of rate gyros is a key performance-limiting factor. In order to estimate the gyro bias and improve the accuracy of attitude measurement, we proposed a new method which uses the rotation of an inertial measurement unit, which is independent from rigid body motion. By actively changing the orientation of the inertial measurement unit (IMU), the proposed method generates sufficient relations between the gyro bias and tilt angle (roll and pitch) error via ridge body dynamics, and the gyro bias, including the bias that causes the heading error, can be estimated and compensated. The rotation inertial measurement unit method makes the gravity vector measured from the IMU continuously change in a body-fixed frame. By theoretically analyzing the mathematic model, the convergence of the attitude and gyro bias to the true values is proven. The proposed method provides a good attitude estimation using only measurements from an IMU, when other sensors such as magnetometers and GPS are unreliable. The performance of the proposed method is illustrated under realistic robotic motions and the results demonstrate an improvement in the accuracy of the attitude estimation.

A Deterministic Attitude Estimation Using a Single Vector Information and Rate Gyros

This paper proposes a deterministic estimator for the estimation of the attitude of a rigid body. A deterministic estimator uses a minimal set of information and does not try to minimize a cost function or fit the measurements into a stochastic process. The proposed estimator obtains the attitude estimation utilizing only the properties of the rotational group $SO(3)$ . The information set required by the proposed estimator is a single vector information and rate gyro readings. For systems in which one of the rotational freedom is constrained, the proposed estimator provides an accurate estimate of the reduced attitude. The performance of the algorithm is verified on different experimental testbeds.