Showing papers on "Angular velocity published in 2018"

Continuous Finite-Time Attitude Control for Rigid Spacecraft Based on Angular Velocity Observer

Abstract: This paper addresses the problem of designing an angular velocity observer and an output feedback attitude controller with finite-time convergence and disturbances for spacecraft. First, two new concepts of finite-time stability are proposed and defined as the local fast-finite-time stability and the fast-finite-time uniformly ultimately boundness, which can be seen as the extensions of the traditional fast-finite-time stability. Then, based on these two concepts of stability, a fast-finite-time observer is designed to estimate the unknown angular velocity. Next, based on the estimation of the angular velocity, a nonsingular and continuous attitude control algorithm is proposed to achieve the finite-time stability or finite-time boundness. With consideration of the observation errors and disturbances in the closed-loop system, a rigorous analysis of the proposed strategy is provided through Lyapunov approach. It shows that the observation errors and the spacecraft attitude will converge to a region of zero in finite time. Numerical simulation studies are presented to illustrate the effectiveness of the proposed observer-based attitude control scheme.

Memory-Induced Transition from a Persistent Random Walk to Circular Motion for Achiral Microswimmers.

Abstract: We experimentally study the motion of light-activated colloidal microswimmers in a viscoelastic fluid. We find that, in such a non-Newtonian environment, the active colloids undergo an unexpected transition from enhanced angular diffusion to persistent rotational motion above a critical propulsion speed, despite their spherical shape and stiffness. We observe that, in contrast to chiral asymmetric microswimmers, the resulting circular orbits can spontaneously reverse their sense of rotation and exhibit an angular velocity and a radius of curvature that nonlinearly depend on the propulsion speed. By means of a minimal non-Markovian Langevin model for active Brownian motion, we show that these nonequilibrium effects emerge from the delayed response of the fluid with respect to the self-propulsion of the particle without counterpart in Newtonian fluids.

Decentralized Adaptive Control for Collaborative Manipulation

Abstract: This paper presents a design for a decentralized adaptive controller that allows a team of agents to manipulate a common payload in $\mathbb{R}^{2}$ or $\mathbb{R}^{3}$ The controller requires no communication between agents and requires no a priori knowledge of agent positions or payload properties The agents can control the payload to track a reference trajectory in linear and angular velocity with center-of-mass measurements, in angular velocity using only local measurements and a common frame, and can stabilize its rotation with only local measurements The controller is designed via a Lyapunov-style analysis and has proven stability and convergence The controller is validated in simulation and experimentally with four robots manipulating an object in the plane

Detecting the Rotation Direction in Contactless Angular Velocity Sensors Implemented With Rotors Loaded With Multiple Chains of Resonators

Abstract: In this paper, a strategy to detect the rotation direction in angular displacement and velocity sensors based on rotors loaded with circular chains of split ring resonators (SRRs) is presented The rotor (made of a dielectric material) is loaded with two concentric SRR chains for measuring the angular velocity (angular velocity chains) and with one additional (also concentric) non-periodic resonator chain for detecting the direction of motion (rotation direction chain) The stator is a CPW transmission line placed below the rotor chains, in close proximity to them, with the line axis oriented in the radial direction of the rotor A novel relevant contribution of this paper concerns the detailed study of the rotation direction sensor, from which we have concluded that the design must be completely different than the one of the angular velocity sensor (single SRR on the rotor) By this means, the transmission coefficient of the CPW is modulated by rotor motion (through electromagnetic coupling), as the SRRs of the different chains cross the CPW axis By injecting a double-tuned signal to the line (with carrier frequencies tuned to the SRR resonance frequencies of both chains), two superposed amplitude modulated (AM) signals at the output port of the CPW arise From the envelope of both AM signals, discriminated by means of a designed diplexer, the angular velocity and the rotation direction can be determined

Integrating Rotations Using Nonunit Quaternions

Abstract: In this letter, we propose and demonstrate a method for integration of rotations using nonunit quaternions. Unit quaternions are commonly used to represent rotation, in which case the rotation operation involves the conjugate of the unit quaternion. However, a redundant mapping can be defined from all nonzero quaternions to the set of rotation matrices, ${\mathrm{SO}(3)}$ , based on the more general rotation operation involving the quaternion inverse. From this we show that the well-known formula that maps angular velocity to the derivative of a unit quaternion actually represents the minimum-norm solution within a set of solutions for the derivative of a nonunit quaternion. This fact enables efficient, singularity free, numerical integration of rotations over long intervals. The approach inherently preserves the structure of ${\mathrm{SO}(3)}$ during the integration with any standard routine or ordinary differential equation (ODE) solver package without employing specially designed geometric integration schemes, exponential updates, or the many quaternion length enforcement techniques found in the literature. We demonstrate the accuracy of this approach compared to other common methods applied to integrate a known angular velocity function and a classic Lagrange top.

RodFIter: Attitude Reconstruction From Inertial Measurement by Functional Iteration

Abstract: Rigid motion computation or estimation is a cornerstone in numerous fields. Attitude computation can be achieved by integrating the angular velocity measured by gyroscopes, the accuracy of which is crucially important for the dead-reckoning inertial navigation. The state-of-the-art attitude algorithms have unexceptionally relied on the simplified differential equation of the rotation vector to obtain the attitude. This paper proposes a functional iteration technique with the Rodrigues vector (named the RodFIter method) to analytically reconstruct the attitude from gyroscope measurements. The RodFIter method is provably exact in reconstructing the incremental attitude as long as the angular velocity is exact. Notably, the Rodrigues vector is analytically obtained and can be used to update the attitude over the considered time interval. The proposed method gives birth to an ultimate attitude algorithm scheme that can be naturally extended to the general rigid motion computation. It is extensively evaluated under the attitude coning motion and compares favorably in accuracy with the mainstream attitude algorithms. This paper is believed having eliminated the long-standing theoretical barrier in exact motion integration from inertial measurements.

Couple stress fluid flow in a rotating channel with peristalsis

Abstract: This article describes a new model for obtaining closed-form semi-analytical solutions of peristaltic flow induced by sinusoidal wave trains propagating with constant speed on the walls of a two-dimensional rotating infinite channel. The channel rotates with a constant angular speed about the z - axis and is filled with couple stress fluid. The governing equations of the channel deformation and the flow rate inside the channel are derived using the lubrication theory approach. The resulting equations are solved, using the homotopy perturbation method (HPM), for exact solutions to the longitudinal velocity distribution, pressure gradient, flow rate due to secondary velocity, and pressure rise per wavelength. The effect of various values of physical parameters, such as, Taylor’s number and couple stress parameter, together with some interesting features of peristaltic flow are discussed through graphs. The trapping phenomenon is investigated for different values of parameters under consideration. It is shown that Taylor’s number and the couple stress parameter have an increasing effect on the longitudinal velocity distribution till half of the channel, on the flow rate due to secondary velocity, and on the number of closed streamlines circulating the bolus.

Rigid-Body Attitude Tracking Control Under Actuator Faults and Angular Velocity Constraints

Abstract: The problem of rigid-body attitude tracking is examined for the case that there exist actuator faults and angular velocity constraints during the attitude maneuver. With a hyperbolic tangent function as input signal, a first-order command filter is proposed to generate a virtual velocity error command for the angular velocity tracking error to follow. Then, an adaptive fault-tolerant controller based on the command filter is designed without requiring information of actuator fault, moment of inertia, and external disturbances. Through Lyapunov stability analysis, it is shown that the control law guarantees that the desired attitude is tracked even in the presence of actuator faults and external disturbances. Finally, simulations are conducted on a rigid spacecraft and results demonstrate the effectiveness of the proposed strategy.

Chiral vortical effect with finite rotation, temperature, and curvature

Abstract: We perform an explicit calculation of the axial current at finite rotation and temperature in curved space. We find that finite curvature and mass corrections to the chiral vortical effect satisfy a relation of the chiral gap effect, that is, a fermion mass shift by a scalar curvature. We also point out that a product term of the angular velocity and the scalar curvature shares the same coefficient as the mixed gravitational chiral anomaly. We discuss possible applications of the curvature-induced chiral vortical effect to rotating astrophysical compact objects described by the Kerr metric. Instead of direct calculation, we assume that the Chern-Simons current can approximate the physical axial current. We make a proposal that the chiral vortical current from rotating compact objects could provide a novel microscopic mechanism behind the generation of collimated jets.

A genetic algorithm–based nonlinear scaling method for optimal motion cueing algorithm in driving simulator

Abstract: A motion cueing algorithm plays an important role in generating motion cues in driving simulators. The motion cueing algorithm is used to transform the linear acceleration and angular velocity of a...

Multiple states in turbulent plane Couette flow with spanwise rotation

Abstract: Turbulence is ubiquitous in nature and engineering applications. Although Kolmogorov’s (C. R. Acad. Sci. URSS, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk URSS, vol. 30, 1941b, pp. 538–540) theory suggested a unique turbulent state for high Reynolds numbers, multiple states were reported for several flow problems, such as Rayleigh–Benard convection and Taylor–Couette flows. In this paper, we report that multiple states also exist for turbulent plane Couette flow with spanwise rotation through direct numerical simulations at rotation number and Reynolds number based on the angular velocity in the spanwise direction and half of the wall velocity difference. With two different initial flow fields, our results show that the flow statistics, including the mean streamwise velocity and Reynolds stresses, show different profiles. These different flow statistics are closely related to the flow structures in the domain, where one state corresponds to two pairs of roll cells, and the other shows three pairs. The present result enriches the studies on multiple states in turbulence.

Gradient-Based Observer for Simultaneous Localization and Mapping

Abstract: An observer for simultaneous localization and mapping is considered in this paper. The proposed observer is based on recent theoretical foundations in a gradient-based observer design on Lie groups. As such, the form of the observer is similar to recently developed nonlinear attitude and pose observers. Translational and angular velocity measurements, as well as relative position measurements of nearby landmarks, are used directly within the observer structure. The case of biased translational and angular velocity measurements is also considered. Stability results are presented that demonstrate an asymptotic convergence of the pose and map estimates. The proposed algorithm is implemented successfully in experiment.

Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate

Abstract: In this paper, the free vibration of a rotating variable thickness two-directional FG circular microplate is studied. The governing equations of motion for the microplate are extracted utilizing the Hamiltonian’s principle in conjunction with the first shear deformation theory as well as the modified couple stress theory. The solution of equations is presented utilizing the differential quadrature method. In special cases, the natural frequency results obtained by the reduced form of the proposed formulation are compared with those available in the literature, indicating a very good accuracy. The results reveal that there is a non-proportional relation between the natural frequencies of the microplate and the thickness-variations of the section. In contrast, the critical angular velocity of that is not much sensitive with respect to the thickness variation. Moreover, the analyses indicate the significant impact of the two-directionality-variation of the graded material on the natural frequencies as well as the critical angular velocities. A map on the effects of the two-directionality-variation of the material property on the free vibration of the microplate is presented. The results show that the increase of the size dependency would lead to the reduction of the non-dimensional natural frequency as well as the critical angular velocity.

Unsteady flow over a decelerating rotating sphere

Abstract: Unsteady flow analysis induced by a decelerating rotating sphere is the main concern of this paper. A revolving sphere in a still fluid is supposed to slow down at an angular velocity rate that is inversely proportional to time. The governing partial differential equations of motion are scaled in accordance with the literature, reducing to the well-documented von Karman equations in the special circumstance near the pole. Both numerical and perturbation approaches are pursued to identify the velocity fields, shear stresses, and suction velocity far above the sphere. It is detected that an induced flow surrounding the sphere acts accordingly to adapt to the motion of the sphere up to some critical unsteadiness parameters at certain latitudes. Afterward, the decay rate of rotation ceases such that the flow at the remaining azimuths starts revolving freely. At a critical unsteadiness parameter corresponding to s = −0.681, the decelerating sphere rotates freely and requires no more torque. At a value of s exa...

A Novel Method for Estimating Knee Angle Using Two Leg-Mounted Gyroscopes for Continuous Monitoring with Mobile Health Devices

Abstract: Tele-rehabilitation of patients with gait abnormalities could benefit from continuous monitoring of knee joint angle in the home and community. Continuous monitoring with mobile devices can be restricted by the number of body-worn sensors, signal bandwidth, and the complexity of operating algorithms. Therefore, this paper proposes a novel algorithm for estimating knee joint angle using lower limb angular velocity, obtained with only two leg-mounted gyroscopes. This gyroscope only (GO) algorithm calculates knee angle by integrating gyroscope-derived knee angular velocity signal, and thus avoids reliance on noisy accelerometer data. To eliminate drift in gyroscope data, a zero-angle update derived from a characteristic point in the knee angular velocity is applied to every stride. The concurrent validity and construct convergent validity of the GO algorithm was determined with two existing IMU-based algorithms, complementary and Kalman filters, and an optical motion capture system, respectively. Bland–Altman analysis indicated a high-level of agreement between the GO algorithm and other measures of knee angle.

A study on avoiding joint limits for inverse kinematics of redundant manipulators using improved clamping weighted least-norm method

Abstract: A general method is presented for the inverse kinematics resolution of redundant manipulators with joint limits. The success of avoiding joint angular position limits of the original clamping weighted least-norm method is ascribable to the strength of the repulsive potential field function. However, the repulsive potential field function may lead to excessive joint angular velocities that can exceed the corresponding limits. We propose an improved clamping weighted least-norm method that adds an elastic field function into the original method for the sake of sustaining the constraints of joint angular velocity limits. Moreover, for hierarchical task-level construction, the priority of avoiding joint angular velocity limits is lower than that of avoiding joint angular position limits. To adequately illustrate the effectiveness of the proposed method, case studies were performed in comparison with other methods in singular configurations of a redundant manipulator.

Almost global asymptotic stability of a grid-connected synchronous generator

Abstract: We study the global asymptotic behavior of a grid-connected constant field current synchronous generator (SG). The grid is regarded as an “infinite bus,” i.e., a three-phase AC voltage source. The generator does not include any controller other than the frequency droop loop. This means that the mechanical torque applied to this generator is an affine function of its angular velocity. The negative slope of this function is the frequency droop constant. We derive sufficient conditions on the SG parameters under which there exist exactly two periodic state trajectories for the SG, one stable and another unstable, and for almost all initial states, the state trajectory of the SG converges to the stable periodic trajectory (all the angles are measured modulo $$2\pi $$ ). Along both periodic state trajectories, the angular velocity of the SG is equal to the grid frequency. Our sufficient conditions are easy to check computationally. An important tool in our analysis is an integro-differential equation called the exact swing equation, which resembles a forced pendulum equation and is equivalent to our fourth-order model of the grid-connected SG. Apart from our objective of providing an analytical proof for a global asymptotic behavior observed in a classical dynamical system, a key motivation for this work is the development of synchronverters which are inverters that mimic the behavior of SGs. Understanding the global dynamics of SGs can guide the choice of synchronverter parameters and operation. As an application we find a set of stable nominal parameters for a 500-kW synchronverter.

Contribution of angular measurements to intelligent gear faults diagnosis

Abstract: Currently, work on the automation of vibration diagnosis is mainly based on indicators extracted from Time sampled Acceleration signals. There are other attractive alternatives such as those based on Angle synchronized measurements, which can provide a considerable number of more relevant and diverse indicators and, thus, lead to better performance in gear fault classification. The diversity of angular measurements (Instantaneous Angular Speed, Transmission Error and Angular sampled Acceleration) represents potential sources of relevant information in fault detection and diagnosis systems. These complementary measurements of existing signals or new relevant signals allow the construction of Feature Vector (FV) offering robust and effective classification methods even for different or non-stationary running speed conditions. In this paper, we propose to build several FVs based on indicators derived from the angular techniques to compare them to the ones calculated from the time signals, proving their superior performance in detection and identification of gear faults. It will be a question to demonstrate the effectiveness of angular indicators in increasing classification performances, using a supervised classifier based on Artificial Neural Networks and thus determining the most suitable signals.

Design Rules of a Microscale PT-Symmetric Optical Gyroscope Using Group IV Platform

Abstract: We proposed a new readout scheme for an ultrasensitive gyroscope, which uses the physics of the exceptional points of a PT-symmetric system to enhance the device sensitivity. In particular, we demonstrated that the full-width at half-maximum linewidth (Δ ω FWHM ) of the light exiting the ring resonator system is proportional to the square root of the rotation rate (Ω). Moreover, we designed a PT-symmetric gyroscope, kept at the exceptional point (at rest) with two 100-μm-radius rings, obtaining a theoretical Δ ω FWHM of 3.37×104 rad/s for an angular velocity of 100 °/h. One algorithm capable to keep the system at the exceptional point and another one to identify the direction of rotation are also proposed.

Rotations and accumulation of ellipsoidal microswimmers in isotropic turbulence

Abstract: Aquatic micro-organisms and artificial microswimmers locomoting in turbulent flow encounter velocity gradients that rotate them, thereby changing their swimming direction and possibly providing cues about the local flow environment. Using numerical simulations of ellipsoidal particles in isotropic turbulence, we investigate the effects of body shape and swimming velocity on particle motion. Four particle shapes (sphere, rod, disc and triaxial ellipsoid) are investigated at five different swimming velocities in the range , where is the swimming velocity and is the Kolmogorov velocity scale. We find that anisotropic, swimming particles preferentially sample regions of lower fluid vorticity than passive particles do, and hence they accumulate in these regions. While this effect is monotonic with swimming velocity, the particle enstrophy (variance of particle angular velocity) varies non-monotonically with swimming velocity. In contrast to passive particles, the particle enstrophy is a function of shape for swimming particles. The particle enstrophy is largest for triaxial ellipsoids swimming at a velocity smaller than . We also observe that the average alignment of particles with the directions of the velocity gradient tensor are altered by swimming leading to a more equal distribution of rotation about different particle axes.