Angular Velocity Vector Research Articles

Convex Optimization-Based Rotation Parameter Estimation Using Micro-Doppler

This paper analyze the relation between rotation of wing or rotor and micro Doppler frequency obtained from Doppler spectrogram and propose the rotation parameter estimation algorithm. At least three or more monostatic radars are used and maximum Doppler frequency and angular velocity are extracted from Doppler spectrogram for each radar. Additionally, to estimate angular velocity vector, convex optimization algorithm is applied. The performance of the proposed algorithm is demonstrated through the simulations.

Analytical solution of the optimal slew problem for an axisymmetric spacecraft in the class of conical motions

The traditional problem is discussed of an optimal spacecraft slew in terms of minimum energy costs. The spacecraft is considered as a rigid body with one symmetry axis under arbitrary boundary conditions for the angular position and angular velocity of the spacecraft in the quaternion formulation. Using substitutions of variables, the original problem is simplified (in terms of dynamic Euler equations) to the optimal slew problem for a rigid body with a spherical mass distribution. The simplified problem contains one additional scalar differential equation. A new analytical solution is presented for this problem in the class of conical motions, leading to constraints on the initial and final values of the angular velocity vector. In addition, the optimal slew problem is modified in the class of conical motions to derive an analytical solution under arbitrary boundary conditions for the angular position and angular velocity of the spacecraft. A numerical example is given for the conical motion of the spacecraft, as well as examples showing the closeness of the solutions of the traditional and modified optimal slew problems for an axisymmetric spacecraft.

Theory of physical libration of the Moon with the liquid core: Forced librations

For a two-layer model of the Moon that consists of a solid nonspherical mantle and an ellipsoidal homogeneous liquid core, a theory of forced librations under the effect of gravitational Earth’s moments has been developed. The motion of the Moon over its orbit has been described by the high-accuracy theory of DE/LE-4 orbital motion. Tables have been constructed that present forced librations of the Moon caused by the second harmonic of its force function, in the neighborhood of its motion according to the generalized Cassini laws. Disturbances of the first-order with respect to dynamic compressions of the Moon and its core are obtained in analytical form for Andoyer variables and Poincare variables and for the projection of the angular velocity vector of Moon’s mantle rotation and the Poincare coordinate system (relative to which core’s liquid accomplishes simple motion) on its major central axes of inertia, as well as for the classical variables in the Moon libration theory, etc. Constructed tables of the forced librations theory give the amplitudes and periods of librations and combinations of arguments of the orbital motion theory that correspond to libration parameters. The interpretation of basic variations has been given and a comparison with the previous theories has been carried out, in particular with the modern empirical theory constructed based on the laser observation data.

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics.

On the recovery of the reference trajectory of rotation

The boundary value problem of determining the time dependence of the spacecraft angular velocity vector from measurements performed by uniaxial transducers rigidly fixed in the body-fixed frame is stated and solved. The proposed algorithm ensures that the mean and variance of the variations in the estimates of the angular velocity vector are smaller than the corresponding accuracy characteristics of uniaxial transducers. The implementation of the proposed technique permits increasing the accuracy of inertial measurement devices.

Attitude Stabilization for Lunar and Planetary Lander with Variable Damper

This paper describes an attitude control method that has been designed to prevent the overturning of lunar and planetary landers, based on a variable-damping shock absorber for the landing gear. Conventionally, the landing gear of lunar and planetary landers has a fixed shock attenuation parameter that is not used proactively for attitude control of the lander during the touchdown sequence. The new method enables the suppression of any disturbance to the attitude of the lander by adjusting the damping coefficient of each landing leg independently, based on the angular velocity vector and displacement velocity of each leg of the lander. The results of a numerical simulation indicate that the control rule for a three-dimensional system is effective for preventing the overturning of the lander on inclined terrain. The results of the simulation and experiments show that the landing gear with the actively variable damping and the control rule play a major role in preventing the overturning of a lunar or planetary lander.

Higher estimates for the solution of a heavy rigid body moving under the action of a Newtonian force field

In this paper, we introduce a new solution of the Euler’s dynamic equations for the rotational motion of a rigid bodyabout a fixed point under the action of a Newtonian force field. The components of the angular velocity vector for this solution arediffering from the most famous cases. We assumed that the center of mass of the rigid body coincides with the fixed point and arestriction on an initial condition is applied. The obtained solution is represented graphically using most recent computer codes todescribe the motion at any time and is considered as a modification of Euler’s case.

Rigid body pose estimation based on the Lagrange–d’Alembert principle

Stable estimation of rigid body pose and velocities from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange–d’Alembert principle from variational mechanics. With body-fixed vision and inertial sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation error and the sum of two artificial potential functions; one obtained from a generalization of Wahba’s function for attitude estimation and another which is quadratic in the position estimate error. An additional dissipation term that is linear in the velocity estimation error is introduced, and the Lagrange–d’Alembert principle is applied to the Lagrangian with this dissipation. A Lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise, with an almost global domain of attraction. This estimation scheme is discretized for computer implementation using discrete variational mechanics, as a first order Lie group variational integrator. The discrete estimation scheme can also estimate velocities from such onboard sensor measurements. Moreover, all states can be estimated during time periods when measurements of only two inertial vectors, the angular velocity vector, and one feature point position vector are available in body frame. In the presence of bounded measurement noise in the vector measurements, numerical simulations show that the estimated states converge to a bounded neighborhood of the true states.

SWIRL FLOW ANALYSIS BASED ON ELECTRICAL CAPACITANCE TOMOGRAPHY

This paper describes an application of dual-plane Electrical Capacitance Tomography (ECT) system for gas-solid swirl flow measuremetns. The angular component of the velocity in the pipes cross section was calculated. The angular velocity was determined based on tomographic data sets obtained from the physical model and also simulated data sets of the swirl flow phenomena. Analysis of material concentration changes in time, with the aid of sequences of 2D reconstruction images, allowed to swirling flow, angular velocity vectors to be successfully evaluated.

Model of an Integrated Inertial-Satellite Navigation System Without Gyroscopes

A device for determining the angular velocity vector of a moving object as part of an inertial-satellite navigation system without gyroscopes and a system for receiving data from navigation satellites are proposed. A multimodel artificial neural network with a nucleus-free mechanism for adjusting the synaptic coefficients is used to integrate these systems. The results of a numerical simulation are presented.

Lie Algebra of Unit Tangent Bundle

In this paper, semi-quaternions are studied with their basic properties. Unit tangent bundle of \({{\mathbb {R}}^2}\) is also obtained by using unit semi-quaternions and it is shown that the set \({{T {\mathbb {R}}^2}}\) of all unit semi-quaternions based on the group operation of semi-quaternion multiplication is a Lie group. Furthermore, the vector space matrix of angular velocity vectors forming the Lie algebra \({{T_{1} {\mathbb {R}}^2}}\) of the group \({{T {\mathbb {R}}^2}}\) is obtained. Finally, it is shown that the rigid body displacements obtained by using semi-quaternions correspond to planar displacements in \({{\mathbb {R}^3}}\).

Об определении ориентации и стабилизации космического аппарата с помощью наблюдателя состояния

For spacecrafts with long operational life, the development of reserve ways for maintaining exact three-axis orientation, when there is no opportunity to use measurements of the full state vector, is a topical problem. In such cases, state observers are usually applied for asymptotic estimation (restoration) of unmeasured components of the state vector and subsequent use of the received estimations in the feedback path. In this article, we consider the problem of asymptotic estimation of the three angles of orientation, which are inaccessible to direct measurement, in the fine orientation mode in the orbital reference system by means of a state observer. Data from the gyroscopic angular velocity measuring device and from the sensor of a local vertical are used in the observer equations. Feedback coefficients for the observer, which provide attenuation of the estimation error, are obtained. Efficiency of the observer is validated by numerical simulation of the control system with the observer designed for a satellite with elastic elements. For the case of failure of the gyroscopic angular velocity measuring device, we also consider the problem of determination of angular velocity vector components on the basis of measurements of the angles of orientation obtained from high-precision star sensors. Here, the state observer is proposed to compute derivatives of the measured angles via polynomial approximation of measurements by using the method of least squares.

Dynamic analysis of Coriolis flow meter using Timoshenko beam element

Coriolis mass flow meter (CFM) is used to measure the rate of mass flow through a pipe conveying fluid. In the present work, the Coriolis effect produced in the pipe due to a lateral excitation is modeled using the finite element (FE) method in MATLAB©. The coupled equation of motion for the fluid and pipe is converted to FE equations by applying Galerkin technique. The pipe conveying fluid is excited at its fundamental natural frequency. The time lag observed between symmetrically located measurement points which are equidistant from the point of excitation, is utilized to predict the mass flow rate. The results predicted by the present code is validated using the experimental, and numerical results published in the literature. The main contribution is the development of a FE model, using three node Timoshenko beam element to analyse the dynamics of fluid conveying pipes subjected to external excitation. The direction of the Coriolis force is perpendicular to the plane containing the velocity of flow vector and angular velocity vector of the pipe. Hence a three dimensional FE model is essential. This model can include curved geometry, damping, velocity and gyroscopic effects for three dimensional flexible tubes. The reduced integration used for overcoming shear locking in two node elements, will result in the formation of spurious modes leading to an incorrect prediction of natural frequencies and velocity. These modes will not occur while using three node elements. Influence of spatial as well as temporal discretisation on the time lag and frequency are also discussed. The sensitivity analysis shows that the time lag varies linearly with the mass flow rate.

Radiation and dynamics of a nanoparticle in equilibrium background radiation upon translational–rotational motion

We have obtained general expressions for the intensity of radiation and tangential force of a small polarizable particle in the process of translational-rotational motion in equilibrium radiation background (thermalized photon gas) of certain temperature at an arbitrary relative orientation of the linear and angular velocity vectors. It is shown that in cold vacuum background the translational velocity of particle is independent of time and the intensity of its spontaneous emission is determined by the angular velocity and imaginary part of the polarizability.

2個のホイール駆動による球体の運動制御

A ball-driven mechanism is used for RoboCup middle size soccer robots for the control of the soccer ball. The ball-driven mechanism has two actuated wheels. The arrangement of the two actuated wheels has been dicusssed for a certain extent. However detailed and quantitative analysis has not been done yet. The paper discusses general motion of sphere by the ball driven mechanism. Several mechanisms such as in CAMBADA (Portugal), Tech United (Holland team robot), Hibikino-Musashi (Japanese, KIT robot) and Water (Chinese team robot) are discussed based on the analysis. The analysis maily focuses on geometrical consideration for the set of end-points for the angular velocity vector.

Main Contributors to the Baseball Bat Head Speed Considering the Generating Factor of Motion-dependent Term

Motion-dependent term (MDT), which consists of centrifugal force, Coriolis force and gyro moment expressed in the equation of motion for a multi-link system, plays significant roles in the generation of tip speed in a high speed swing motion. A phenomenon caused by the MDT is usually called as “whip-like effect” and “kinetic chain”. Since the baseball batting is one of high speed swing motion manipulating a bat by both hands, it is important to make clear the generating factor of MDT and main contributors to the generation of bat head speed. The purpose of this study was to quantify main contributors to the bat head speed considering the generating factor of MDT. The whole-body segments with bat were modelled as a system of sixteen-rigid linked segments. The equation of motion for the system was obtained by considering anatomical constraint axes at joints and modelling errors. A recurrence formula with respect to the generalized velocity vector consisting of linear and angular velocity vectors of all segments was derived. Five collegiate baseball players, participated as subjects, hit a teed ball as strong as possible. The kinematic and kinetic data were measured with the motion capture system with 3 force platforms and an instrumented bat. The results indicates that the abduction and extension torques at the knob-side shoulder joint and the forward rotation torque at the torso joint are the main positive contributors to the generation of bat head speed among the participants.

Torque exerted on the side of crustal blocks controls the kinematics of Ethiopian Rift

Plate tectonic stress at active plate boundary can arises from 1) a torque applied on the side of lithospheric blocks and 2) a torque at the base of the lithosphere due to the flow of the underlying mantle. In this paper we use a simple force balance analysis to compare side and basal shear stresses and their contribution in driving kinematics and deformation in the Ethiopian Rift (ER), in the northern part of the East African Rift System (EARS). Assuming the constraints of the ER given by the dimension of the lithospheric blocks, the strain rate, the viscosity of the low velocity zone (LVZ) and the depth of the brittle–ductile transition zone, the lateral torque is several orders of magnitude higher than the basal torque. The minor contribution of basal torque might be due to low viscosity in the LVZ. Both Africa and Somalia plates are moving to the ”west” relative to the mantle and there are not slabs that can justify this pull and consequent motion. Therefore, we invoke that westerly oriented tidal torque on Africa and Somalia plates in providing the necessary side torque in the region. This plate motion predicts significant sinistral transtension along the ER and rift parallel strike-slip faulting similar to the estimated angular velocity vector for tectonic blocks and GPS observations. Vertical axis block rotations are observed in areas where the lithospheric mantle is removed and strain is widely distributed.

Comparative assessment of the effects of different error sources on the estimate of 3D orientation using magnetic-inertial measurement units

Main topics: Technical developments in movement science; Mathematical simulation in human mov. science Introduction and aim: The determination of the accurate 3D orientation of a body segment is a crucial aspect in clinical movement analysis [1]. Among motion capture technologies, wearable sensors, suchasmagnetic-inertialmeasurementunits (MIMUs), are gaining popularity. Several methods were developed to estimate 3D orientation from MIMU data, in order to effectively exploit the complementary properties of inertial (gyroscopes and accelerometers) and magnetic sensors embedded in the MIMUs [2]. It is well known that these sensors are affected by several error sources, including measurement noise, bias instability, calibration errors, ferromagneticdisturbances, external accelerations [3]. Thepurpose of the present study is to assess the contribution of the sources of error associated to each sensor to the uncertainty affecting the 3D orientation estimation, during a consolidated clinical test. Patients/materials andmethods:ATimedUpandGo test (TUG) was performed by ten healthy subjects (5M, 5 F, 28 5 y). OneMIMU (Opal, APDM Inc.) was secured to the lower back of each subject and angular velocity, acceleration and local magnetic field vector data were collected. The trajectories of four markers attached to theMIMUwere trackedby a stereophotogrammetric system (Vicon MX3), and the orientation of a marker-based frame was obtained andconsideredas reference. Thesemarker trajectorieswereused to calculate the same variablesmeasured by theMIMU.Measured and simulated MIMU data were then combined, as detailed in Table 1, obtaining five different scenarios. Each signal combination was fed as an input of an Extended Kalman Filter (EKF) [2] to estimate the 3D MIMU orientation. The rationale was to assess, both individually and jointly, the effect of the errors associated to the EKFmodel, as well as to each MIMU sensor. The accuracy of the obtained orientations was then evaluated in terms of orientation error [2]. A Kruskal–Wallis testwithpost-hocDunncomparisons ( =0.05)was performed to investigate whether significance differences existed among the obtained orientation errors. Results: Results (mean one standard deviation) about the error contribution associated to the EKF model and to the MIMU sensors

Алгоритм вычисления программных значений компонент вектора угловой скорости при терминальном пространственном развороте космического аппарата в инерциальной системе координат

Алгоритм вычисления программных значений компонент вектора угловой скорости при терминальном пространственном развороте космического аппарата в инерциальной системе координат

The equations of relative motion in the orbital reference frame

The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill–Clohessy–Wiltshire equations. Circular motion is not, however, a solution when the Earth’s flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the \(J_2\) effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the \(J_2\) perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a \(J_2\)-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill–Clohessy–Wiltshire equations for circular reference motion, or the de Vries/Tschauner–Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the \(J_2\) perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession of the node and the argument of perigee, i.e., of the entire orbital plane. Here we provide a derivation of the exact equations of relative motion by expressing the angular velocity of the RTN frame in terms of the state vector of the reference spacecraft. As such, these equations are completely general, in the sense that the orbit of the reference spacecraft need only be known through its ephemeris, and therefore subject to any force field whatever. It is also shown that these equations reduce to either the Hill–Clohessy–Wiltshire, or the Tschauner–Hempel equations, depending on the level of approximation. The explicit form of the equations of relative motion with respect to a \(J_2\)-perturbed reference orbit is also introduced.