Calibration Method of Accelerometer Based on Rotation Principle Using Double Turntable Centrifuge

For linear accelerometers, calibration with a precision centrifuge is a key technology, and the input acceleration imposed on the accelerometer should be accurately obtained in the calibration. However, there are often errors in the installation of sample that make the calibration inaccurate. To solve installation errors and obtain the input acceleration in the calibration of the accelerometer, a calibration method based on the rotation principle using a double turntable centrifuge is proposed in this work. The key operation is that the sub-turntable is rotated to make the input axis of the accelerometer perpendicular to the direction of the centripetal acceleration vector. Models of installation errors of angle and radius were built. Based on these models, the static radius and input acceleration can be obtained accurately, and the calibration of the scale factor, nonlinearity and asymmetry can be implemented. Using this method, measurements of the MEMS accelerometer with a range of ±30 g were carried out. The results show that the discrepancy of performance obtained from different installation positions was smaller than 100 ppm after calibrating the input acceleration. Moreover, the results using this method were consistent with those using the back-calculation method. These results demonstrate that the effectiveness of our proposed method was confirmed. This method can measure the static radius directly eliminating the installation errors of angle and radius, and it simplifies the accelerometer calibration procedure.

Quaternion Algorithm for Initial Alignment of Strapdown INS Using the A. N. Tikhonov Regularization Method

For the functioning of algorithms of inertial orientation and navigation of strapdown inertial navigation system (SINS), it is necessary to conduct a mathematical initial alignment of SINS immediately before the operation of these algorithms. An efficient method of initial alignment (not calibration!) of SINS is the method of vector matching. Its essence is to determine the relative orientation of the instrument trihedron Y (related to the unit of SINS sensors) and the reference trihedron X according to the results of measuring the projections of at least two non-collinear vectors of the axes on both trihedrons. We address the estimation of the initial orientation of the object using the method of gyrocompassing, which is a form of vector matching method. This initial alignment method is based upon using the projections of the apparent acceleration vector a and the absolute angular velocity vector ω of the object in the coordinate systems X and Y. It is assumed that the three single-axis accelerometers and the three gyroscopes (generally speaking, the three absolute angular velocity sensors of any type), which measure the projections of the vectors a and ω, are installed along the axes of the instrument coordinate system Y. If the projections of the same vectors on the axes of the base coordinate system X are known, then it is possible to estimate the mutual orientation of X and Y trihedrons. We are solving the problem of the initial alignment of SINS for the case of a fixed base, when the accelerometers measure the projection gi (i = 1, 2, 3) of the gravity acceleration vector g, and the gyroscopes measure the projections u i of the vector u of angular velocity of Earth’s rotation on the body-fixed axes. The projections of the same vectors on the axes of the normal geographic coordinate system X are also estimated using the known formulas. The correlation between the projections of the vectors u and g in X and Y coordinate system is given by known quaternion relations. In these relations the unknown variable is the orientation quaternion of the object in the X coordinate system. By separating the scalar and vector parts in the equations, we obtain an overdetermined system of linear algebraic equations (SLAE), where the unknown variable is the finite rotation vector θ, which aligns the X and Y coordinate systems (it is assumed that there is no half-turn of the X coordinate system with respect to the Y coordinate system). Thus, the mathematical formulation of the problem of SINS initial alignment by means of gyrocompassing is to find the unknown vector θ from the derived overdetermined SLAE. When finding the vector θ directly from the SLAE (algorithm 1) and data containing measurement errors, the components of the vector q are also determined with errors (especially the component of the vector θ, which is responsible for the course ψ of an object). Depending on the pre-defined in the course of numerical experiments values of heading ψ, roll ϑ, pitch γ angles of an object and errors of the input data (measurements of gyroscopes and accelerometers), the errors of estimating the heading angle Δψ of an object may in many cases differ from the errors of estimating the roll Δϑ and pitch Δγ angles by two-three (typically) or more orders. Therefore, in order to smooth out these effects, we have used the A. N. Tikhonov regularization method (algorithm 2), which consists of multiplying the left and right sides of the SLAE by the transposed matrix of coefficients for that SLAE, and adding the system regularization parameter to the elements of the main diagonal of the coefficient matrix for the newly derived SLAE (if necessary, depending on the value of the determinant of this matrix). Analysis of the results of the numerical experiments on the initial alignment shows that the errors of estimating the object’s orientation angles Δψ, Δϑ, Δγ using algorithm 2 are more comparable (more consistent) regarding their order.

Predictive Force-Centric Emergency Collision Avoidance

A controller for critical vehicle maneuvering is proposed that avoids obstacles and keeps the vehicle on the road while achieving heavy braking. It operates at the limit of friction and is structured in two main steps: a motion-planning step based on receding-horizon planning to obtain acceleration-vector references, and a low-level controller for following these acceleration references and transforming them into actuator commands. The controller is evaluated in a number of challenging scenarios and results in a well behaved vehicle with respect to, e.g., the steering angle, the body slip, and the path. It is also demonstrated that the controller successfully balances braking and avoidance, such that it really takes advantage of the braking possibilities. Specifically, for a moving obstacle it makes use of a widening gap to perform more braking, which is a clear advantage of the online replanning capability if the obstacle should be a moving human or animal. Finally, real-time capabilities are demonstrated. In conclusion, the controller performs well, both from a functional perspective and from a real-time perspective.

The inverse problem of stabilization of a spherical pendulum in a given position under oblique vibration

The inverse problem is posed of stabilizing a spherical pendulum (a mass point at the end of a weightless solid rod of length l ) in a given position using high-frequency vibration of the suspension point. The position of the pendulum is determined by the angle between the pendulum rod and the gravity acceleration vector. For any given position of the pendulum, a series of oblique vibration parameters (amplitude of the vibration velocity and the angle between the vibration velocity vector and the vertical) were found that stabilize the pendulum in this position. From the obtained series of solutions, the parameters of optimal vibration (vibration with a minimum amplitude of velocity) are selected depending on the position of the pendulum. The region of initial conditions is studied, of which the optimal vibration leads the pendulum to a predetermined stable position after a sufficiently long time. This area, following N. F.Morozov et al., called the area of attraction.

Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements

In the presented work, a model of a microelectromechanical accelerometer with two movable beam elements located between two fixed electrodes is proposed. The action of the transfer forces of inertia in the longitudinal direction leads to a change in the spectral properties of the system, which is a useful output signal of the sensor. The dynamics of the system in the presence of a weak electrostatic coupling between the sensitive elements is characterized by the phenomenon of modal localization - a significant change in the amplitude ratios for the forms of inphase and antiphase oscillations with small changes in the measured component of the acceleration vector of the moving object. Diagrams of equilibrium positions are plotted for varying the potential difference between a fixed electrode and a movable element and between two movable elements. The dependences of the frequencies and the ratio of the components of the eigenvectors on the magnitude of the inertial action are investigated. It is shown that the sensitivity of a sensor based on modal localization can be orders of magnitude higher than the sensitivity of known systems based on measuring the shift of natural frequencies. A nonlinear dynamic model of an accelerometer with external harmonic electrostatic excitation of oscillations is constructed. Resonance characteristics are obtained, a comparison is made between the model describing the modal characteristics of the system and the model describing the real dynamic mode of operation taking into account nonlinear factors.

Clinorotation as a promising and environmentally friendly biotechnology in agriculture and some industries

Aim. To investigate the direct and indirect impact of clinorotation on vital activity of gilled mushrooms (Agaricales) using the mycelium of the model organism Agaricus bisporus, clinorotated by the ground-based facility Ekoloh, as the example. Methods. The mycelium of Agaricus bisporus was cultivated on the medium with agar and compost extract. The microgravitational environment was simulated using the method of uniaxial clinorotation at the ground-based facility Ekoloh. The mycelia of Agaricus bisporus from the experimental group were clinorotated for 4 h a day for 12 days. The samples from the control group were cultivated in normal (1 g) conditions. The simulated gravitational acceleration value was 3.5 × 10–4 g at the rotational velocity of 2.5 rpm and the rotation radius of 0.05 m. The centrifugal acceleration, affecting the mycelium of Agaricus bisporus under clinorotation, was 0.00343 m/s2. The two-way ANOVA analysis demonstrated that the effects of g-level, the duration of the impact and their interaction were all statistically signifi cant. At the same time, 73.1 % of the variance in mycelium growth coeffi cient was triggered by the simulated value of the g, i.e. the duration of the impact was a minor factor. Results. Clinorotation stimulated growth and development of gilled mushroom (Agaricales) mycelium. In particular, in this study the clinorotated mycelium of Agaricus bisporus had approximately 3.4, 2.5, 1.6 times higher coeffi cients of mycelium growth compared against the mycelium, cultivated in stationary conditions (1 g) on day 5, 10, and 15 of the cultivation respectively. Contrary to the control mycelial colonies, the growth of clinorotated mycelial colonies of Agaricus bisporus was asymmetric. The direction of the gravitational acceleration vector regarding mycelium colonies was constantly changing in the microgravitational environment, simulated by the ground-based facility Ekoloh. At the same time, different organs of Agaricus bisporus are characterized by gravitropism of different orientation. Therefore, constant changes in the direction of gravitational acceleration vector regarding mycelium could have caused constant re-orientation of mycelium cells in terms of the gravitational acceleration vector, and thus, multidirectional asymmetric growth. In addition, the centrifugal acceleration, generated during clinorotation, is a mechanostimulator, capable of triggering stress responses in different living systems. The accelerated growth is one of the stress responses. At the same time, mycelium could expand in the environment mechanically due to the impact of centrifugal acceleration. However, the centrifugal acceleration was insignifi cant, thus, we believe that the main effect was caused by microgravity. Conclusions. Since clinorotation stimulates the growth and development of gilled mushrooms and is an effi cient way of forming virus-free planting material of different plants, this technology may have a wide scope of application. It may be used in agriculture, forestry and different industries, using raw plants or mushrooms, for instance, in food, pharmaceutical and textile industries, etc.

Physical activity, BMI and COVID-19: an observational and Mendelian randomisation study

Physical activity (PA) is known to be a protective lifestyle factor against several non-communicable diseases while its impact on infectious diseases, including Coronavirus Disease 2019 (COVID-19) is not as clear. We performed univariate and multivariate logistic regression to identify associations between body mass index (BMI) and both objectively and subjectively measured PA collected prospectively and COVID-19 related outcomes (Overall COVID-19, inpatient COVID-19, outpatient COVID-19, and COVID-19 death) in the UK Biobank (UKBB) cohort. Subsequently, we tested causality by using two-sample Mendelian randomisation (MR) analysis. In the multivariable model, the increased acceleration vector magnitude PA (AMPA) was associated with a decreased probability of overall and outpatient COVID-19. No association was found between self-reported moderate-to-vigorous PA (MVPA) or BMI and COVID-19 related outcomes. Although no causal association was found by MR analyses, this may be due to limited power and we conclude policies to encourage and facilitate exercise at a population level during the pandemic should be considered.

A Note on the Acceleration and Jerk in Motion Along a Space Curve

The resolution of the acceleration vector of a particle moving along a space curve is well known thanks to Siacci [1]. This resolution comprises two special oblique components which lie in the osculating plane of the curve. The jerk is the time derivative of acceleration vector. For the jerk vector of the aforementioned particle, a similar resolution is presented as a new contribution to field [2]. It comprises three special oblique components which lie in the osculating and rectifying planes. In this paper, we have studied the Siacci’s resolution of the acceleration vector and aforementioned resolution of the jerk vector for the space curves which are equipped with the modified orthogonal frame. Moreover, we have given some illustrative examples to show how the our theorems work.

On the added mass in a viscous incompressible fluid

It is proved that at the same instantaneous distribution of the flow velocity of a viscous incompressible fluid, the forces acting on a body moving with acceleration differ from forces acting on the body moving with constant velocity by a vector, which is equal to the added masses tensor multiplied by the acceleration vector. The tensor of the added masses coincides with the tensor calculated for potential flows with the same geometry of the body and surrounding surfaces, and does not depend either on viscosity or on the distribution of vorticity in the flow space. While the force corresponding to the motion with constant velocity depends on the history of movement.