Angular Rate Research Articles

A Robust Angular Rate Sensor Utilizing 2:1 Auto-Parametric Resonance Excitation.

This paper presents a single-axis angular rate sensor that is robust to variations in its operating voltage and frequencies. The sensor is developed to overcome the shortcomings of conventional mode-matched Micromachined Vibratory Gyroscopes in open loop operations, namely narrow frequency bandwidths and unstable scale factors. The developed sensor utilizes inherent forcing and inertial nonlinearities from electrostatic forces and fabrication imperfections to auto-parametrically excite the sense mode via 2:1 auto-parametric resonance, which yields a broader bandwidth frequency response for the sensor’s sense mode. The experimental results demonstrated frequency bandwidth of , a scale factor of , and a dynamic range of .

A Digital Control Structure for Lissajous Frequency-Modulated Mode MEMS Gyroscope

This article proposes a digital control structure for a doubly decoupled gyroscope working in the Lissajous frequency-modulated (LFM) mode based on digital phase-locked loops (PLLs), which demodulates the angular rate signal directly from the readable digital gyroscope resonance frequency, eliminating the need for specific frequency readout circuits. The resonance frequencies of the LFM gyroscope working modes contain a mode mismatch frequency modulated by input angular rate, respectively, which are tracked by two digital PLLs followed by subsequent digital demodulation and filtering. A linearized model of the digital PLL is built to analyze noise and control characteristics for different PI parameters. The impact of different amplitude–phase extraction architectures on the extracted phase signal is also addressed in this article. Contrast experiments are carried out using the same gyroscope with large internal thermal stress due to the silicon-glass bonding process and no stress relief structure around the sensing element, working in the traditional amplitude-modulated (AM) mode and the LFM mode. Overall, the LFM working mode maintains its low-temperature sensitivity and high stability in spite of the large internal thermal stress in the gyroscope compared to AM working modes. The maximum scale factor variation over the temperature range from 10 °C to 50 °C is 1000 ppm for the LFM mode compared to 51 900 ppm for the AM closed mode. The maximum zero rate output drift over the same temperature range is 0.1248 °/s for the LFM mode and 10.7139 °/s for the AM closed mode. The scale factor nonlinearity is 329 ppm with an angular rate input range of ±50 °/s for the LFM mode compared to 1902 ppm for the AM closed mode. The LFM mode zero-bias fluctuation for ten days is less than 0.12 °/s. The angle random walk (ARW) and the bias instability (BI) of the LFM gyroscope are 0.316 °/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd \text{h}$ </tex-math></inline-formula> and 2 °/h, respectively.

Resident Space Object Characterization Using Polarized Light Curves

Light curves, or the time-history of photometric brightness, have previously been demonstrated to allow for estimation of a space object’s attitude, shape, and surface parameters. However, these methods are subject to many limitations, including the need for accurate initial estimates to initialize filters, and the inability to regularly estimate attitude and surface parameters simultaneously due to information dilution, or the increase in uncertainty of each state when more states are simultaneously estimated. Monochromatic, unpolarized light curves can also only allow for surface reflectance parameter determination, and not determination of the materials themselves. This work develops a polarized bidirectional reflectance distribution function, and demonstrates that polarized measurements increase the uniqueness of light-curve attitude solutions to allow larger tolerance to initial error while also providing surface material estimation. Polarization of reflected light can also be measured more accurately than the intensity of reflected light through the atmosphere, thereby increasing the attitude observability from the light curves. Observability of attitude and surface materials is assessed. An unscented multiple-model adaptive estimation filter is implemented to estimate attitude, angular rate, surface material, surface roughness, and size of the space object.

Whitewater Helmet STAR: Evaluation of the Biomechanical Performance and Risk of Head Injury for Whitewater Helmets.

More than six million people participate in whitewater kayaking and rafting in the United States each year. Unfortunately, with these six million whitewater participants come 50 deaths annually, making it one of the highest fatality rates of all sports. As the popularity in whitewater activities grows, the number of injuries, including concussions, also increases. The objective of this study was to create a new rating system for whitewater helmets by evaluating the biomechanical performance and risk of head injury of whitewater helmets using the Summation of Tests for the Analysis of Risk (STAR) system. All watersport helmets that passed the EN: 1385: 2012 standard and that were clearly marketed for whitewater use were selected for this study. Two samples of each helmet model were tested on a custom pendulum impactor under conditions known to be associated with the highest risk of head injury and death. A 50th percentile male NOCSAE headform instrumented with three linear accelerometers and a triaxial angular rate sensor coupled with a Hybrid III 50th percentile neck were used for data collection. A total of 126 tests were performed using six different configurations. These included impacts to the front, side, and rear using two speeds of 3.1 and 4.9m/s that modeled whitewater river flow rates. Each helmet's STAR score was calculated using the combination of exposure and injury risk that was determined from the linear and rotational head accelerations. The resulting head impact accelerations predicted a very high risk of concussion for all impact locations at the 4.9m/s speed. The STAR score varied between helmets indicating that some helmets provide better protection than others. Overall, these results show a clear need for improvement in whitewater helmets, and the methodologies developed in this research project should provide manufacturers a design tool for improving these products.

Distributed Cooperative Surrounding Control for Mobile Robots With Uncertainties and Aperiodic Sampling

In this paper, we present a distributed cooperative surrounding control for mobile robots with uncertainties and aperiodic sampling. At the kinematic level, a cooperative circumnavigation guidance law with the capability of spatial-temporal decoupling, employing a line-of-sight (LOS) principle to accomplish closed orbit following and a path parameter synchronization to assign the desired speed, is devised to generate reference velocity and angular rate. At the kinetic level, to reduce the transmission burden in sensor-to-controller channel and compensate for the total uncertainties existing in velocity channels, aperiodic sampling based extended state observers (AS-ESOs), are developed to provide precise disturbance estimates with guaranteed convergence, while a nonnegative threshold-based event-triggering condition with a straightforward tuning procedure is designed to schedule the communication frequency without inducing Zeno behaviors. Then a robust anti-disturbance kinetic control protocol is synthesized that renders an equiangular distribution along the common circle. The salient merit is that a symmetric formation pattern over a closed curve defined by parameterized path, instead of time-related functions, can be obtained in a distributed manner with decreased sampling cost and disturbances. Moreover, all error variables in the closed-loop system are demonstrated to be bounded. Finally, the effectiveness of algorithm is verified by simulations.

From raw measurements to human pose - a dataset with low-cost and high-end inertial-magnetic sensor data

Wearable technology is expanding for motion monitoring. However, open challenges still limit its widespread use, especially in low-cost systems. Most solutions are either expensive commercial products or lower performance ad-hoc systems. Moreover, few datasets are available for the development of complete and general solutions. This work presents 2 datasets, with low-cost and high-end Magnetic, Angular Rate, and Gravity(MARG) sensor data. Provides data for the complete inertial pose pipeline analysis, starting from raw data, sensor-to-segment calibration, multi-sensor fusion, skeleton-kinematics, to complete Human pose. Contains data from 21 and 10 participants, respectively, performing 6 types of sequences, presenting high variability and complex dynamics with almost complete range-of-motion. Amounts to 3.5 M samples, synchronized with a ground-truth inertial motion capture system. Presents a method to evaluate data quality. This database may contribute to develop novel algorithms for each pipeline’s processing steps, with applications in inertial pose estimation algorithms, human movement forecasting, and motion assessment in industrial or rehabilitation settings. All data and code to process and analyze the complete pipeline is freely available.

Three-dimensional coverage-based cooperative guidance law with overload constraints to intercept a hypersonic vehicle

This paper proposes a coverage-based cooperative guidance (CBCG) law to enable low-velocity and constrained-manoeuvrability interceptors to intercept a hypersonic vehicle, considering overload constraints. First, the reachable, feasible, and escape areas are considered to establish the guidance law under a nonlinear interception model. Second, the problem of intercepting the hypersonic vehicle is transformed into a coverage problem by using the coverage strategy. A guidance command including basis and bias terms is generated considering the standard trajectory. The basis term generates the guidance command for nonstandard trajectories to nullify the line-of-sight angular rate at the time of interception to ensure successful interception, and the bias term generates the guidance command for the standard trajectory to enhance the coverage ability of the interceptors. The optimal number and location constraints of the interceptors are theoretically analysed. The effectiveness, applicability, superiority, sensitivity, and robustness of the CBCG law are evaluated through a series of numerical simulations, and its performance is compared with that of the proportional navigation guidance law. The results demonstrate that the CBCG law can ensure that at least one interceptor successfully intercepts the hypersonic vehicle, with high robustness to errors and noise.

Appointed-time guaranteed adaptive fault-tolerant attitude tracking for quadrotors with aperiodic data updating

In this paper, an appointed-time guaranteed adaptive fault-tolerant attitude tracking for quadrotors with aperiodic data updating is concerned, where inertial moment variation, extraneous disturbance and unknown actuator faults are simultaneously involved. An adaptive parameter estimation law is updated to identify the partial effectiveness loss of actuation and alleviate the estimation burden of suggested observer. Then through filtering manipulations upon aperiodic system states, a novel event-triggered unknown system dynamics estimator (ETUSDE) is developed to learn the remaining uncertainties with exponential error decaying and decreased updating cost, where an event-triggering criterion is incorporated to schedule the transmission instants for control behavior and angular rate, and the explicit formulation between estimation error upper boundary and design coefficients is derived. An appointed-time prescribed performance control (APPC) is introduced to allow for pregiven attitude behaviors. By fusion of adaptive law, ETUSDE and APPC, an adaptive event-triggered attitude control policy is synthesized that delivers appointed-time convergence, accurate steady response and decreased sampling burden. Meanwhile, Lyapunov analysis shows that all the error variables contained in the closed-loop system are ultimately uniformly bounded. Eventually, experiments on a quadrotor attitude test rig are conducted to confirm the superiorities of suggested control strategy.

Enhanced estimation method and approximation method of the PDF of roll angular acceleration and jerk in beam seas

So far, the authors have established the theoretical estimation method of the Probability Density Function (PDF) of roll angular acceleration and jerk with the use of PLIM (PDF Line Integral Method), and estimations of the PDF of these properties were successfully achieved. PLIM, on the other hand, necessitates numerical integration along the complex shaped integral path. The integral path, in particular, becomes challenging in the calculation of the jerk property. However, if the restoring term is only represented by a linear component, then explicit expressions of PDF of roll angular acceleration can be obtained using the nonlinearization technique. It is noteworthy that the form of the nonlinear damping component does not constrain the applicability. This paper aims to show the derivation of the theoretical result and comparison with Monte Carlo Simulation (MCS) results. Furthermore, using the current form of the acceleration PDF, the PDF of roll angular jerk was obtained. The variance of roll angular rate determines the PDF form of the acceleration, which is the method's main advantage.

An Investigation of the Bifurcation Behavior of an F-18 Aircraft Model

Bifurcations of equilibria and limit cycles of an F-18 aircraft model have been investigated in this paper based on one or two continuation parameters. First, it is shown that the aircraft can be in a stable straight-and-level flight state by coordinating the elevator deflection and the engine thrust and fixing the other parameters. Second, the aircraft may be disturbed by perturbations out of the longitudinal plane and get into the lateral-directional motion mode by a branch point bifurcation. Third, when the straight flight state loses its stability, body axis angular rates will present periodic or quasi-periodic motion pattern by the Hopf or Neimark–Sacker bifurcation. Finally, bifurcation structure of limit cycles has been exhibited, including the generalized Hopf bifurcation, the Neimark–Sacker bifurcation, the Hopf-Hopf bifurcation and the fold-Neimark–Sacker bifurcation. Meanwhile corresponding bifurcation curves in two-parameter plane have been depicted with the help of numerical continuation techniques.

Overcoming 1 part in 10^9 of earth angular rotation rate measurement with the G Wettzell data

The absolute measurement of the Earth angular rotation rate with ground-based instruments becomes challenging if the 1 part in 10^9 of precision has to be obtained. This threshold is important for fundamental physics and for geodesy, to investigate effects of General Relativity and Lorentz violation in the gravity sector and to provide the fast variation of the Earth rotation rate. High sensitivity Ring Laser Gyroscopes (RLG) are currently the only promising technique to achieve this task in the near future, but their precision has been so far limited by systematics related to the laser operation. In this paper we analyze two different sets of observations, each of them three days long. They were obtained from the G ring laser at the Geodetic Observatory Wettzell. The applied method has been developed for the GINGERINO ring laser in order to identify and extract the laser systematics. For the available data sets the residuals show mostly white noise behavior and the Allan deviation drops below 1 part in 10^9 after an integration time of about 10^4 s.

Upper limb orientation assessment as an articulated body chain.

Upper limb orientation estimation based on Magnetic, Angular Rate, and Gravity sensors considering multiple body segments is presented in this work. The proposal allowed assessing the activity of two or more body segments individually and jointly, regardless of their spatial relationship. A custom-made system was developed incorporating a complementary filter and a proportional-integral control for data sensor merging and, noise and instrumentation error reduction. Two controlled tests were carried out to assess the performance of the system. The former evaluated the response of the method in motionless conditions, while the latter assessed the feasibility to follow trajectories in 3D space. Ten volunteers were recruited to evaluate the system performance in three semi-controlled and daily life task tests. The system was evaluated using the common parameters in motion tracking methods and relied on a digital motion processor. The system's outcome presented a root mean square error in the range of 2.65°-3.98° for the semi-controlled tests and 0.48°-1.389° for the daily life task test. The system tests analysis proved that the proposal permitted obtaining the articulated body chain information of multiple segments when three or more MARG sensors are used.

Tidal excitation of auto-resonant oscillations in stars with close-by planets

Context. Close-by planets can excite various kinds of oscillations in their host stars through their time-varying tidal potential. Aims. Magnetostrophic oscillations with a frequency much smaller than the stellar rotation frequency have recently been proposed to account for the spin-orbit commensurability observed in several planet-hosting stars. In principle, they can be resonantly excited in an isolated slender magnetic flux tube by a Fourier component of the time-varying tidal potential with a very low frequency in the reference frame rotating with the host. However, due to the weakness of such high-order tidal components, a mechanism is required to lock the oscillations in phase with the forcing for long time intervals (103–107 yr) in order to allow the oscillation amplitude to grow. Methods. We propose that the locking mechanism is an auto-resonance produced by the nonlinear dependence of the oscillation frequency on its amplitude. We suggest that the angular momentum loss rate is remarkably reduced in hosts entering auto-resonance and this contributes to maintaining those systems in that regime for a long time. Results. We apply our model to a sample of ten systems that show spin-orbit commensurability and estimate the maximum drifts of the relevant tidal potential frequencies that allow them to enter the auto-resonant regime. Such drifts are compared with the drifts expected from the tidal evolution of the planetary orbits and the stellar angular momentum loss in the magnetized winds, and we find that auto-resonance is a viable mechanism in eight systems, at least in our idealized model. Conclusions. The duration of the auto-resonant regime and the associated spin-orbit commensurability may be comparable with the main-sequence lifetimes of the host stars, indicating that gyrochronology may not be applicable to those hosts.

HMM Based Adaptive Kalman Filter for Orientation Estimation

An adaptive orientation estimation method based on hidden Markov model (HMM) using multiple Magnetic Angular Rate Gravity (MARG) sensor is proposed to address the problem of linear acceleration and ferromagnetic disturbance. Two parallel Kalman filters containing first-order Gauss-Markov disturbance models are implemented to estimate the disturbances before estimating the orientation. It is important that the noise covariance of the disturbance model should match the magnitude of the disturbance to ensure the estimation performance; otherwise, the disturbance estimation accuracy will reduce significantly. Therefore, an adaptive Kalman filter based on HMM is designed to adjust the disturbance noise covariance. After the disturbances are separated, the estimated gravity acceleration and geomagnetic field as well as the gyroscope measurement are taken as the inputs, and the orientation estimation procedure is established by using the multiplicative extended Kalman filter (MEKF). Experiments show that the proposed method achieves a higher level of accuracy in comparison with other orientation estimation methods under various conditions.

Acquisition and cognition information of human body swing

Man plays an important role as the moving sensor platform in information systems, including 6G communication and intelligent applications. In particular, personal self-position and attitude are critical for firefighters performing rescues, athletes competing in sports, and the shooter with a shoulder launcher aiming at a target. Due to the swinging of the human body and respiratory fluctuations, the real-time miniature inertial measurement unit (MIMU) data combines body motion noise and degrades navigation precision. Two scenarios are discussed in this paper, including aiming at a stationary and moving target. The angular rate and acceleration of MIMU data for a stationary target are obtained from the turntable and shooter's shoulder, respectively. Data are collected via a stimulated launcher mounted on the shooter's shoulder and the theoretical solution for a moving target. A technology known as error cumulative amplitude spectrum (CAS) is adapted to extract the specific frequency caused by the shooter's body swing, which exhibits low-frequency characteristics. Thus, a mixed filter frame composed of an adaptive notch filter (ANF) and a cubature Kalman filter (CKF) is described in detail to reduce both high- and low-frequency measurement errors. The results of series tests indicate that the acceleration and angular rate errors caused by shooter swing are reduced by more than 98% and more than 81%, respectively, in the stationary and moving cases. As a result, the presented method effectively suppresses body swing and enhances navigation performance.

Biomechanical effects of a halo orthotic on a pediatric anthropomorphic test device in a simulated frontal motor vehicle collision

Objective: Cervical spine injuries in children under 10 frequently involve the craniocervical junction. In patients too small for conventional spinal instrumentation, treatment may involve placement of a halo orthotic, and these patients will frequently be discharged home in a halo orthotic. To date, little research has been done on the biomechanics of motor vehicle collisions involving young children in halo orthotics. To better understand possible safety concerns, we applied a halo orthotic to an appropriately sized anthropomorphic test device (ATD, or crash test dummy) on an acceleration sled to simulate a frontal motor vehicle collision. Methods: For the tests, a Hybrid III 3-year-old ATD was instrumented with head and chest accelerometers, head angular rate sensors, a six-axis upper neck load cell, and a chest linear potentiometer. Four tests were conducted on an acceleration sled, and kinematics were recorded with high speed video. Testing variables included 1) with or without a halo orthotic and 2) with a standard booster seat or a commercially available harness vest. Results: The halo orthotic reduced flexion and extension but was associated with increased rotation, especially in the condition of a halo orthotic with a standard booster seat. Increased cervical distraction was noted with the halo orthotic, and this was especially increased in the condition of a halo orthotic with the harness vest. Conclusions: The biomechanics of a child involved in a motor vehicular collision may be dramatically altered with a halo orthotic, as modeled by an acceleration sled test. While cervical spine flexion and extension are reduced with the halo orthotic, rotation appears to increase. Immobilization from a halo orthotic also appears to increase cervical distraction, especially when used in conjunction with a harness vest. Further testing is needed to determine the safest restraints for this small, but at-risk, population.

Three-dimensional cooperative guidance law for intercepting hypersonic targets

This paper proposes a three-dimensional adaptive sliding mode cooperative guidance law using multiple low-speed interceptors with time-varying speeds for effectively intercepting hypersonic targets. The guidance commands are divided into commands along and normal to the line-of-sight (LOS). First, based on the algebraic graph and consensus theories, the guidance command along the LOS is designed to ensure that multiple interceptors achieve finite-time convergence to simultaneously intercept a hypersonic target. Second, to address the external disturbance caused by the manoeuvring of the hypersonic target in the direction normal to the LOS, finite-time disturbance observers are designed to accurately estimate the acceleration information of the hypersonic target with rapid convergence. Next, the guidance command normal to the LOS is formulated based on the sliding mode control method, which can nullify the LOS angular rate, ensuring progressive convergence to zero at interception. Moreover, thrust and drag models are incorporated to ensure that the guidance model is reasonably realistic. Numerical simulations are performed for different manoeuvring modes of the hypersonic target, and comparative simulations are conducted using the proportional navigation and sliding mode cooperative guidance laws. The simulation results demonstrate the superiority and effectiveness of the proposed guidance law.

Use of low-cost accelerometers for landslides monitoring: results from a flume experiment

Early Warning Systems (EWS) are non-structural measures for landslides disaster prevention. They are based on the detection of impending failure signals. The results of a landslide simulation experiment where accelerometers were used to identify pre-failure signals are presented in this paper. Landslide was simulated in a tilting flume filled with sandy soil. During the experiment, the flume was fixed at 30° inclination and water percolated through the soil until it slid. Accelerometers were embedded into the soil and recorded acceleration data from the beginning of the experiment until failure. Acceleration data were analyzed in time domain aiming at estimating translational velocity of the movement. Angular variation was also estimated from acceleration data. The experiment was recorded with a camera and pictures were used for Particle Image Velocimetry (PIV) analysis, in order to validate the estimated translational velocity. Results showed that accelerometers can identify prefailure signals before any macroscopic movement could indicate impending failure in fast to very fast landslides, showing their potential to be used in EWS. Validation of estimated velocities was not always possible due to PIV setup constraints and the velocity of the mass movement simulated. In fact, the estimated translational velocities seem to be unreliable. On the other hand, the results suggest that acceleration data and angular position variation trend and rate can be incorporated into EWS.

Research on Gradient-Descent Extended Kalman Attitude Estimation Method for Low-Cost MARG.

Aiming at the problem of the weak dynamic performance of the gradient descent method in the attitude and heading reference system, the susceptibility to the interference of accelerometers and magnetometers, and the complex calculation of the nonlinear Kalman Filter method, an extended Kalman filter suitable for a low-cost magnetic, angular rate, and gravity (MARG) sensor system is proposed. The method proposed in this paper is a combination of a two-stage gradient descent algorithm and the extended Kalman filter (GDEKF). First, the accelerometer and magnetometer are used to correct the attitude angle according to the two-stage gradient descent algorithm. The obtained attitude quaternion is combined with the gyroscope measurement value as the observation vector of EKF and the calculated attitude of the gyroscope and the bias of the gyroscope are corrected. The elimination of the bias of the gyroscope can further improve the stability of the attitude observation results. Finally, the MARG sensor system was designed for mathematical model simulation and hardware-in-the-loop simulation to verify the performance of the filter. The results show that compared with the gradient descent method, it has better anti-interference performance and dynamic performance, and better measurement accuracy than the extended Kalman filter.

Vibrating Flexoelectric Micro-Beams as Angular Rate Sensors.

We studied flexoelectrically excited/detected bending vibrations in perpendicular directions of a micro-beam spinning about its axis. A set of one-dimensional equations was derived and used in a theoretical analysis. It is shown that the Coriolis effect associated with the spin produces an electrical output proportional to the angular rate of the spin when it is small. Thus, the beam can be used as a gyroscope for angular rate sensing. Compared to conventional piezoelectric beam gyroscopes, the flexoelectric beam proposed and analyzed has a simpler structure.