Translational Velocity Research Articles

Map building using helmet-mounted LiDAR for micro-mobility

This paper presents a point-cloud mapping method using a light detection and ranging (LiDAR) mounted on a helmet worn by a rider of micro-mobility. The distortion in LiDAR measurements, which is caused by motion and shaking of micro-mobility and rider, is corrected by estimating the pose (3D positions and attitude angles) of the helmet based on the information from normal distributions transform-based simultaneous localization and mapping (NDT SLAM) and an inertial measurement unit. A Kalman filter-based algorithm for the distortion correction is presented under the assumption that the helmet moves at nearly constant translational and angular velocities in any directions. The distortion-corrected LiDAR measurements are mapped onto an elevation map, and the measurements relating to stationary objects in the environments are extracted using the occupancy grid method. The stationary object measurements are utilized to build a point-cloud map. The experimental results in a campus road environment demonstrate the effectiveness of the proposed method.

Electrophoretic trajectories of non-uniformly charged particles in viscoelastic fluids: the weak surface charge limit

Electrophoretic motion of a particle carrying a weak but arbitrary non-uniform surface charge density in an Oldroyd-B fluid is analysed here in the thin electrical double layer limit. A semi-analytical generic framework, based on regular perturbation, the Lamb's general solutions and the generalized reciprocal theorem, assuming the viscoelastic effects to remain subdominant, is developed for tracing the particle's trajectory using its instantaneous translational velocity and accounting for the temporal evolution of its surface charge driven by rotation. Our results reveal that in a viscoelastic medium, non-uniformly charged particles may generally follow distinct trajectories depending on their sizes, which is in stark contrast to Newtonian fluids. By considering the multipole moments of the surface charge, we show that the particle may initially rotate until its dipole moment becomes collinear with the imposed electric field, and the nature of the surrounding medium does not alter this fundamental behaviour. However, during the course of rotation, the excess polymeric stresses within the electrical double layer and the bulk may cause the particle to migrate perpendicular to the applied field, by forcing the multipole moments of the surface charge to interact with each other. The final steady-state trajectory of the particle and its possible migration normal to the applied electric field are also largely governed by these interactions and more specifically, presence of non-zero quadrupole moments. The present framework may be helpful towards designing tools for particle separation and sorting, relevant in many biological applications.

Second-order inertial forces and torques on a sphere in a viscous steady linear flow

We compute the full set of second-order inertial corrections to the instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in a general steady linear flow. This is achieved by using matched asymptotic expansions and formulating the problem in a coordinate system co-moving with the background flow. Effects of unsteadiness and fluid-velocity gradients are assumed to be small, but to dominate in the far field over those of the velocity difference between the body and fluid, making the results essentially relevant to weakly positively or negatively buoyant particles. The outer solution (which at first order is responsible for the Basset–Boussinesq history force at short time and for shear-induced forces such as the Saffman lift force at long time) is expressed via a flow-dependent tensorial kernel. The second-order inner solution brings a number of different contributions to the force and torque. Some are proportional to the relative translational or angular acceleration between the particle and fluid, while others take the form of products of the rotation/strain rate of the background flow and the relative translational or angular velocity between the particle and fluid. Adding the outer and inner contributions, the known added-mass force or the spin-induced lift force are recovered, and new effects involving the velocity gradients of the background flow are revealed. The resulting force and torque equations provide a rational extension of the classical Basset–Boussinesq–Oseen equation incorporating all first- and second-order fluid inertia effects resulting from both unsteadiness and velocity gradients of the carrying flow.

Observer based Control for Paddle Juggling with Considering Ball Spin Effect

This paper deals with the 2-dimensional paddle juggling where a racket hit a ball vertically and iteratively. The racket rebound model is considered where both the translational and rotational velocities of the ball change at the rebound due to the effect of the racket rubber. The LQ servo controller is derived based on the complete ball transition with the racket rebound model. In addition, a whole observer system to estimate all the ball states is proposed which consists of a continuous one for the free flying ball and a discrete one for the ball rebound. Note that it is essential that the rotational velocity can be only estimated by the discrete observer at the rebound. A numerical simulation is performed in order to verify the effectiveness of the total discrete output feedback controller.

Robust Structure from Motion observer: Input to State Stability approach

The authors present a novel nonlinear Thau-Luenberger observer for estimating Structure from Motion using a calibrated camera. Accurate reconstruction of the 3D structure of a scene relies on precise estimation of the camera's translational and angular velocities, which can be challenging for cameras on mobile platforms. The proposed observer aims to estimate these velocities robustly in the presence of measurement noise, with stability characterized through Input to State Stability analysis and Lyapunov theory. The stability conditions are determined using optimization techniques based on Linear Matrix Inequalities. The performance of the proposed approach is validated through simulation and experimental data, demonstrating its effectiveness in recovering the depth of tracked features and its robustness against disturbances.

A Switched Adaptive Controller for Robotic Gripping of Novel Objects With Minimal Force

We present the design and implementation of an algorithm, equipped with a switched adaptive controller, for grasping unknown objects using a robot gripper. A Lyapunov-based analysis demonstrates that the switching controller is indeed asymptotically stable with both the translational and rotational slip velocities converging to the origin. Experimental results using a novel sensorized gripper prototype and objects of different sizes, shapes, and weights show that the proposed algorithm not only ensures the prevention of slippage of the grasped objects, but is also able to apply the minimal force needed to safely grasp these objects without causing excessive deformation.

Oxygen transport across tank-treading red blood cell: Individual and joint roles of flow convection and oxygen-hemoglobin reaction.

Gas, especially oxygen, transport in the microcirculation is a complex phenomenon, however, of critical importance for maintaining normal biological functions, and the cytoplasm fluid in red blood cells (RBCs) is the major vehicle for transporting oxygen from lungs to tissues via the circulatory system. Existing theoretical and numerical studies have neglected the cytoplasm convection effect by treating RBCs as rigid particles undergoing a constant translation velocity. As a consequence, the influence and mechanism of the cytoplasm flow on oxygen transport are still not clear in microcirculation research. In this study, we consider a tank-treading capsule in shear flow, which is generated with two parallel plates moving in opposite directions: the top plate of a higher oxygen pressure (PO2) representing the RBC core in the central region of a microvessel and the bottom plate of a lower PO2 representing the microvessel wall. Numerical simulations are conducted to investigate the individual and combined effects of cytoplasm convection and oxygen-hemoglobin (O2-Hb) reaction on the oxygen transport efficiency across the tank-treading capsule, and different PO2 situations and shear rates are also tested. Due to the lower oxygen diffusivity in cytoplasm, the presence of the capsule reduces the oxygen transfer flux across the gap by 7.34% in the pure diffusion system where the flow convection and O2-Hb reaction are both neglected. Including the flow convection or the O2-Hb reaction has little influence on the oxygen flux; however, when they act together as in real microcirculation situations, the enhancement in oxygen transport could be significant, especially in the low PO2 and high shear rate situations. In particular, with the respective PO2 at 60 and 30mmHg on the top and bottom plates and a 400 s-1 shear rate, the oxygen flux reduction is only 0.02%, suggesting that the cytoplasm convection can improve the oxygen transport across RBCs considerably. The simulation results are scrutinized to explore the underlying mechanism for the enhancement, and a new nondimensional parameter is introduced to characterize the importance of cytoplasm convection in oxygen transport. These simulation results, discussion and analysis could be helpful for a better understanding of the complex oxygen transport process and therefor valuable for relevant studies.

Inadequacies in the Current Definition of the Meter and Ramifications Affecting Einstein’s Second Postulate of Relativity

The current definition of the meter as based on the time of light transmission and the postulated universal constant light speed is ill-defined and inadequate. The definition fails to identify which second is required, whether to use coordinate or proper time, or which method to construct an exact meter, besides ignoring gravity’s effect. In Einstein’s 1905 paper that defined special relativity, Einstein stipulated correctly that light traversing the ends of a resting rod takes equal time transmissions in either direction. If that rod is oriented parallel to a constant velocity, a photon from one end of the moving rod takes a longer time span with a universal constant light speed to overtake the receding end and takes a shorter time span to intercept the approaching end of the rod when transmitted in the opposite direction, resulting in a longer roundtrip distance of photons traversing the moving rod versus the resting rod. Length contraction undercompensates this difference. Einstein did not address this issue. However, Einstein claimed the unequal time intervals over the moving rod versus equal intervals over the resting rod are because simultaneous states for the resting observer and resting rod are nonsimultaneous for the constant moving observer. This contradicts his first postulate of relativity: any state of a physical system (e.g., equal timed traverses of photons moving over a rod) is unaffected by a constant translational velocity between inertial reference frames. An in-depth analysis examines Einstein’s thought experiment for an adequate redefinition. The analysis reveals one-way photon velocities obey vector velocity addition involving moving photon sources, but it proves by induction that roundtrip photon traverses have an average speed that is identical to the standard light speed c. Thus, Einstein’s second postulate of relativity is not general, but is valid for roundtrip traverses of photon transmissions. This may change many physical concepts, since one-way velocities for photons and particles are not limited by the second postulate. A suggested redefinition of the meter is submitted.

角柱近傍を移動する渦対による音波発生について

The sound generated by a vortex pair moving close to a rectangular cylinder is studied by high-resolution simulations of the two-dimensional unsteady compressible Navier-Stokes equations at Mach numbers ranging from 0.05 to 0.3. In this study, the Mach number Ma is defined by Ma=Vt /c0, where Vt is the translation velocity of the co-moving vortex pair and c0 denotes the speed of sound. The directly computed far-field sound is compared to the prediction of the acoustic analogy proposed by Lighthill (1952) and Curle (1955). The prediction is in excellent agreement with the simulation, where the two-dimensional form of Curle’s modified solution is adopted for an accurate calculation of the sound waves with a phase difference between various vortices around the cylinder. It could be confirmed that the scaling law in two dimensions holds in this simulation. In this study, the sound generation due to the dipole and quadrupole fields is investigated by calculating the two terms in Curle’s analogy. Examining the surface distribution of dipoles on the cylinder indicates that the force exerted on the fluid by the solid boundaries of the side/upper wall of the rectangular cylinder generates the sound when the co-translating vortices approach /pass the rectangular cylinder, which is the sound due to dipoles corresponding to the directivity of the sound in the polar diagrams. The area distribution of quadrupoles which is the second time derivative of the area integral of Lighthill’s stress tensor indicates that the sound is emitted from a vortex generated at the corner of the rectangular cylinder when the vortex pair approaches the cylinder and where the interaction between many vortices around the cylinder and the co-translating vortices generates the sound when the co-translating vortices pass the cylinder.

A Comparative Study on Longitudinal Dynamics Stability Between Two Aircraft Models

The present work presents a comparative study on the longitudinal dynamic’s stability behavior for two aircraft models, namely the Learjet 24 and the Cessna 182. The longitudinal flight dynamics behaviors are evaluated by introducing a disturbance to the elevator. This device uses a single doublet impulse as well as multiple doublet impulses. The governing equation of longitudinal flight motion, which was derived based on a small perturbation theory and a linearized process by dropping the second order and above to the disturbance quantities, allowed one to formulate the governing equation of flight motion in the form of an equation known as the longitudinal equation of flight motion. This equation describes the flight behavior of an aircraft and can be expressed in the disturbance quantity as translational velocity in the x-direction u, angle of attack 𝛼, and pitch angle 𝜃. The implementation in the case of the Cessna 182 and the Learjet 24, where the Cessna 182 uses a single doublet impulse or a multiple doublet impulse, demonstrates that the aircraft response in these three variable states is better than that of the Learjet 24.

МОДЕЛЬ РУХУ БЕЗПІЛОТНИХ ЛІТАЛЬНИХ АПАРАТІВ НА ОСНОВІ АЛГЕБРИ ДУАЛЬНИХ КВАТЕРНІОНІВ

The widespread use of unmanned aerial vehicles during warfare has intensified the problem of their management, especially when they are used in large groups. One of the main tasks is to ensure coordinated movement of the group's aircraft in space. Optimizing the movement of each device of the group in three-dimensional space is expedient to use mathematical models. The movement of any unmanned aerial vehicle can be presented as a combination of translational and rotational movements, and its speed as a combination of translational and rotational velocities. Previously, these movements were modeled separately using a system of differential equations or quaternions. In this article, a mathematical model of rotational and translational movements of an aircraft based on the algebra of dual quaternions is developed. Dual quaternions consisting of eight scalars are a compact representation of rigid transformations in space. Therefore, their properties determine the advantage in the course of motion simulation, as they reduce the amount of calculations. Thus, with the help of one dual quaternion, it is possible to provide both translational and rotational motions at once, and the operation of non-commutative multiplication of dual quaternions is used to simulate the movement. The model assumes that the real part of the dual quaternion determines the orientation of the UAV in space, and the dual part determines its position in three-dimensional space. In order to connect aircraft coordinate systems with the model, expressions for the transition from aircraft orientation angles (roll, yaw, and pitch) to dual quaternion parameters and vice versa are obtained. The functionality of the proposed model was confirmed using the developed software for modeling the coordinated movement of aircraft. The software is adapted for graphical display of a large number of aircraft in web browsers with WebGl support. Keywords: motion modeling; rotational and translational movement; unmanned aerial vehicles; quaternions; dual quaternions; algebra of quaternions.

Material Removal Capability and Profile Quality Assessment on Silicon Carbide Micropillar Fabrication with a Femtosecond Laser.

Silicon carbide (SiC) has a variety of applications because of its favorable chemical stability and outstanding physical characteristics, such as high hardness and high rigidity. In this study, a femtosecond laser with a spiral scanning radial offset of 5 μm and a spot radius of 6 μm is utilized to process micropillars on a SiC plate. The influence of pulsed laser beam energies and laser translation velocities on the micropillar profiles, dimensions, surface roughness Ra, and material removal capability (MRC) of micropillars was investigated. The processing results indicate that the micropillar has the best perpendicularity, with a micropillar bottom angle of 75.59° under a pulsed beam energy of 50 μJ in the range of 10-70 μJ, with a pulsed repetition rate of 600 kHz and a translation velocity of 0.1 m/s. As the laser translation velocity increases between 0.2 m/s and 1.0 m/s under a fixed pulsed beam energy of 50 μJ and a constant pulsed repetition rate of 600 kHz, the micropillar height decreases from 119.88 μm to 81.79 μm, with the MRC value increasing from 1.998 μm3/μJ to 6.816 μm3/μJ, while the micropillar bottom angle increases from 68.87° to 75.59°, and the Ra value diminishes from 0.836 μm to 0.341 μm. It is suggested that a combination of a higher pulsed laser beam energy with a faster laser translation speed is recommended to achieve micropillars with the same height, as well as an improved processing efficiency and surface finish.

Flows in parallelepiped cells of nematic liquid crystals.

We identified three types of flow in a nematic liquid crystal parallelepiped cell subjected to an ac electric field at low frequency. Our observations show the existence of translational flow, backflow, and convection flow in parallelepiped cells. We measured the backflow velocity by introducing microparticles into the sample. The backflow velocity at the normalized voltage ɛ=0.05 is approximately 0.1μm/s. It has the same order as the translational flow velocity at ɛ=0.05. Furthermore, convection flow occurs earlier than translational flow.

Extension of Galilean invariance to uniform motions for a relativistic equation of fluid flows

Galilean invariance and the Lorentz transformation are the two pillars of mechanics that an equation of motion must respect. The objective is to extend the Galilean invariance to uniform rotational motion and to expansion motion of which motion at constant translational velocity is only a special case. The second goal is to show that the discrete equation of motion is naturally relativistic without using the Lorentz transformation. The realization of these two aims leads to different concepts of special relativity: (i) space is homogeneous and isotropic and (ii) time, which flows regularly, is invariant by translation. These invariances, symmetric for translation and rotation, observed by the discrete equation of motion give it fundamental conservation properties to extend the scope of the equations of fluid mechanics to other fields of physics.

Dynamic analysis of a translating five-bar linkage mechanism

In this paper, the dynamic analysis of a translating five-bar linkage mechanism is presented. The dynamic model of the mechanism is developed with the applied force to the crank arm resolved into the two principal planes, that is, x- and y- directions and the resulting reaction forces and moments at the pin joints determined at various translating acceleration of 0, 10, 20, 30 and 40 m/s2 in the direction as well as in the opposite direction of the crank rotation. It was observed that the horizontal reaction forces at the pin joints were decreasing as the translating acceleration increases in the direction of crank rotation while it increases when the acceleration increases in the opposite direction to the crank rotation. It was also observed that the pin joint moments at point A decreases as the translation velocities increases in the crank arm rotation direction while it increases as the acceleration increases in the opposite direction. The converse is the case for pin joint B, while there were no significant differences for pin joint moments at pin joints C and D in all the considered acceleration in both directions. Also, the vertical reaction forces at the pin joints did not change in magnitude as the magnitude and directions of the acceleration were altered. The analysis brings to the fore the importance of the consideration of translating acceleration in the design, development and utilization of five – bar linkage to avoid failure at any of the joints.

Numerical simulation of flow and mass transfer during growth of the long seed KDP crystals under 2D translation method

A novel motion method, namely, the two-dimensional translation method (2D TM) had been proposed by our team to effectively utilize convection to enhance morphological stability and mass transfer. To evaluate this new method and apply it to the long seed KDP crystals growth, numerical simulations on the hydrodynamics and mass transfer involved in the growth of the long seed KDP crystals through this new method have been performed. Comparisons with the rotating crystal method (RCM) indicates that 2D TM improves the value and distribution homogeneity of the surface supersaturation. As the translational velocity increases, the value of the surface supersaturation on the prismatic faces increases. However, as the translational distance becomes long, there is a decrease in the value of the prismatic surface supersaturation, but the homogeneity of the surface supersaturation is improved. Moreover, the increase of the crystal size not only reduces the value of the surface supersaturation on the prismatic faces, but also degrades the homogeneity of the surface supersaturation. A further improvement in the magnitude and distribution homogeneity of the prismatic face supersaturation can be observed through modifying the crystal mounting method.

Multi-modal framework to model wet milling through numerical simulations and artificial intelligence (part 1)

Stirred media mills are used in many industries from mechanochemistry, to ore crushing, battery production and pharmaceutics. Investigation and modelling can be a costly, difficult and time consuming endeavour, limiting the investigable parameter space with some aspects only being accessible via numerical methods such as simulations or artificial intelligence (AI). Simulations allow investigations of inner mechanisms and generate large quantities of data while being computationally demanding. AI requires large data quantities yet is applicable with limited computing power for large parameter spaces. For this reason, the intelligent integration of different methods holds great promise to achieve maximum benefits at minimum cost by synergistically combining respective advantages. Here, a multi-modal framework is demonstrated, combining experiments, simulations and AI. In this first paper direct magnetic measurements via a tracer particle are compared with simulations of wet mills. With two way coupled CFD-DEM simulations inner mechanisms like the impact of disc geometry, tip speed and grinding bead size are investigated. Differences in translational and relative velocity distributions are investigated, showing a consistent displacement of a factor three toward higher energies throughout the complete distribution for the hole disc in comparison to the full disc, and less consistent deviations for translational velocity, specifically for the higher energy collisions, being larger by a factor of 8. Also comparisons with the existing mechanistic model of Kwade are performed. An additional indirect influence of diameter on tip speed could be detected. In a second publication AI modelling will be performed on the basis of the simulations.

High-energy velocity tails in uniformly heated granular materials.

We experimentally investigate the velocity distributions of quasi-two-dimensional granular materials uniformly heated by an electromagnetic vibrator, where the translational velocity and the rotation of a single particle are Gaussian and independent. We observe the non-Gaussian distributions of particle velocity, with the density-independent high-energy tails characterized by an exponent of β=1.50±0.03 for volume fractions of 0.111≤ϕ≤0.832, covering a wide range of structures and dynamics. Surprisingly, our results are not only in excellent agreement with the prediction of the kinetic theories of granular gas but also hold for an extremely high-volume fraction of ϕ=0.832 where the granular material forms a crystalline solid and the kinetic theory of granular gas fails fantastically. Our experiment suggests that the density-independent high-energy velocity tails of β=1.50 are a characteristic of uniformly heated granular matter.

Real-Time Stereo Visual Odometry Based on an Improved KLT Method

Real-time stereo visual odometry (SVO) localization is a challenging problem, especially for a mobile platform without parallel computing capability. A possible solution is to reduce the computational complexity of SVO using a Kanade–Lucas–Tomasi (KLT) feature tracker. However, the standard KLT is susceptible to scale distortion and affine transformation. Therefore, this work presents a novel SVO algorithm yielding robust and real-time localization based on an improved KLT method. First, in order to improve real-time performance, feature inheritance is applied to avoid time-consuming feature detection and matching processes as much as possible. Furthermore, a joint adaptive function with respect to the average disparity, translation velocity, and yaw angle is proposed to determine a suitable window size for the adaptive KLT tracker. Then, combining the standard KLT method with an epipolar constraint, a simplified KLT matcher is introduced to substitute feature-based stereo matching. Additionally, an effective veer chain matching scheme is employed to reduce the drift error. Comparative experiments on the KITTI odometry benchmark show that the proposed method achieves significant improvement in terms of time performance than the state-of-the-art single-thread approaches and strikes a better trade-off between efficiency and accuracy than the parallel SVO or multi-threaded SLAM.

Slender body theories for rotating filaments

Slender fibres are ubiquitous in biology, physics and engineering, with prominent examples including bacterial flagella and cytoskeletal fibres. In this setting, slender body theories (SBTs), which give the resistance on the fibre asymptotically in its slenderness $\epsilon$ , are useful tools for both analysis and computations. However, a difficulty arises when accounting for twist and cross-sectional rotation: because the angular velocity of a filament can vary depending on the order of magnitude of the applied torque, asymptotic theories must give accurate results for rotational dynamics over a range of angular velocities. In this paper, we first survey the challenges in applying existing SBTs, which are based on either singularity or full boundary integral representations, to rotating filaments, showing in particular that they fail to consistently treat rotation–translation coupling in curved filaments. We then provide an alternative approach which approximates the three-dimensional dynamics via a one-dimensional line integral of Rotne–Prager–Yamakawa regularized singularities. While unable to accurately resolve the flow field near the filament, this approach gives a grand mobility with symmetric rotation–translation and translation–rotation coupling, making it applicable to a broad range of angular velocities. To restore fidelity to the three-dimensional filament geometry, we use our regularized singularity model to inform a simple empirical equation which relates the mean force and torque along the filament centreline to the translational and rotational velocity of the cross-section. The single unknown coefficient in the model is estimated numerically from three-dimensional boundary integral calculations on a rotating, curved filament.