Problem Of Motion Research Articles

A Computationally Efficient Dynamic Grid Motion Approach for Arbitrary Lagrange–Euler Simulations

The present article addresses the topic of grid motion computation in Arbitrary Lagrange–Euler (ALE) simulations, where a fluid mesh must be updated to follow the displacements of Lagrangian boundaries. A widespread practice is to deduce the motion for the internal mesh nodes from a parabolic equation, such as the harmonic equation, introducing an extra computational cost to the fluid solver. An alternative strategy is proposed to minimize that cost by changing from the parabolic equation to a hyperbolic equation, implementing an additional time derivative term allowing an explicit solution of the grid motion problem. A fictitious dynamic problem is thus obtained for the grid, with dedicated material parameters to be carefully chosen to enhance the computational efficiency and preserve the mesh quality and the accuracy of the physical problem solution. After reminding the basics of the ALE expression of the Navier–Stokes equations and describing the proposed hyperbolic equation for the grid motion problem, the paper provides the necessary characterization of the influence of the fictitious grid parameters and the analysis of the robustness of the new approach compared to the harmonic reference equation on a significant 2D test case. A 3D test case is finally extensively studied in terms of computational performance to highlight and discuss the benefits of the hyperbolic equation for ALE grid motion.

Online Avatar Motion Adaptation to Morphologically‐similar Spaces

AbstractIn avatar‐mediated telepresence systems, a similar environment is assumed for involved spaces, so that the avatar in a remote space can imitate the user's motion with proper semantic intention performed in a local space. For example, touching on the desk by the user should be reproduced by the avatar in the remote space to correctly convey the intended meaning. It is unlikely, however, that the two involved physical spaces are exactly the same in terms of the size of the room or the locations of the placed objects. Therefore, a naive mapping of the user's joint motion to the avatar will not create the semantically correct motion of the avatar in relation to the remote environment. Existing studies have addressed the problem of retargeting human motions to an avatar for telepresence applications. Few studies, however, have focused on retargeting continuous full‐body motions such as locomotion and object interaction motions in a unified manner. In this paper, we propose a novel motion adaptation method that allows to generate the full‐body motions of a human‐like avatar on‐the‐fly in the remote space. The proposed method handles locomotion and object interaction motions as well as smooth transitions between them according to given user actions under the condition of a bijective environment mapping between morphologically‐similar spaces. Our experiments show the effectiveness of the proposed method in generating plausible and semantically correct full‐body motions of an avatar in room‐scale space.

Improving the procedure for modeling low-frequency oscillations of the free surface liquid in a tractor tank

This paper considers the influence of hydrodynamic processes in the movement of the free surface of liquid in partially filled tractor tanks. Splashing liquid in partially filled containers is a significant problem in the study of functional stability of movement in the marine, aerospace, rail, and automotive industries. After all, it affects productivity and traffic safety. The same effect was observed when performing transportation work while delivering liquid cargoes in the agricultural sector. That was due to increasing the transportation speeds of wheeled tractors. In the procedure, using the Rayleigh theory of surface waves, a linearized problem of motion of the free surface of a liquid is obtained. Based on Helmholtz's theorem, the components of scalar and Laplace field vector potentials of fluid velocity vector are separated. The potential problem for translational motion of fluid, in which vortex component of the field is absent, is considered. Instead of the fluid velocity potential, a scalar fluid displacement potential in Rayleigh surface waves was introduced. Comparing the results of calculating fluid splashing with the work of other scientists, a high convergence of natural frequencies of partial oscillators in 3D space was found. This is noticeable in the last quarter of the filling of the tank, in which significant displacements of the deep liquid occur. A feature of the results is the introduction, instead of the real shape of the container, an equivalent form of a parallelepiped, the final shape of which depends on the level of fullness. The frequency properties of movement of the free surface of liquid based on the standard size of tanks used in agriculture are separated. The proposed improved methodology could be used to increase stability, controllability, and smoothness when operating tanks with a wheeled tractor.

Feasibility of tracking involuntary head movement for MRI using a coil as a magnetic dipole in a time-varying gradient

Accurate tracking involuntary head movements is fairly a challenging problem in MR imaging of the brain. Though there are few techniques available to monitor the head movement of the subject for a prospective motion correction, it is still an unsolved problem in MRI. In this theoretical study, we aim to describe an analytical investigation to track head movement inside an MR scanner by calculating the change in induced voltage in the head-mounted coils during the execution of time-varying gradients. We derive an expression to calculate the change in induced voltage in a coil placed in a time-varying gradient. We also derive a general equation to investigate the changes in the induced voltage in a set of coils mounted onto the head for the planar position and orientation of the coils. Each coil is considered as a magnetic dipole with location and sensitivity vectors. The changes of the vectors can track the head movement in the MR scanner by measuring the changes in the induced voltage in the coils. The dipole concept is valid for a wide range of coils. The changes in induced voltage in the coils are linear due to small changes in pose of the head. Movement parameters are estimated from the induced voltage changes. If the random noise voltage is less than 100 μV, it does not significantly affect movement parameters because the change in induced voltage in the coils dominates over the small noise voltage. This method and array of the coils may provide a real-life solution to the long-standing problem of head motion during MRI.

Laser 3D tightly coupled mapping method based on visual information

PurposeSimultaneous localization and map building (SLAM), as a state estimation problem, is a prerequisite for solving the problem of autonomous vehicle motion in unknown environments. Existing algorithms are based on laser or visual odometry; however, the lidar sensing range is small, the amount of data features is small, the camera is vulnerable to external conditions and the localization and map building cannot be performed stably and accurately using a single sensor. This paper aims to propose a laser three dimensions tightly coupled map building method that incorporates visual information, and uses laser point cloud information and image information to complement each other to improve the overall performance of the algorithm.Design/methodology/approachThe visual feature points are first matched at the front end of the method, and the mismatched point pairs are removed using the bidirectional random sample consensus (RANSAC) algorithm. The laser point cloud is then used to obtain its depth information, while the two types of feature points are fed into the pose estimation module for a tightly coupled local bundle adjustment solution using a heuristic simulated annealing algorithm. Finally, the visual bag-of-words model is fused in the laser point cloud information to establish a threshold to construct a loopback framework to further reduce the cumulative drift error of the system over time.FindingsExperiments on publicly available data sets show that the proposed method in this paper can match its real trajectory well. For various scenes, the map can be constructed by using the complementary laser and vision sensors, with high accuracy and robustness. At the same time, the method is verified in a real environment using an autonomous walking acquisition platform, and the system loaded with the method can run well for a long time and take into account the environmental adaptability of multiple scenes.Originality/valueA multi-sensor data tight coupling method is proposed to fuse laser and vision information for optimal solution of the positional attitude. A bidirectional RANSAC algorithm is used for the removal of visual mismatched point pairs. Further, oriented fast and rotated brief feature points are used to build a bag-of-words model and construct a real-time loopback framework to reduce error accumulation. According to the experimental validation results, the accuracy and robustness of the single-sensor SLAM algorithm can be improved.

Motion Trajectory Error of Robotic Arm Based on Neural Network Algorithm

In order to solve the problems of unstable motion and large trajectory tracking error of the manipulator when it is disturbed by the outside world, the author proposes an adaptive neural network manipulator motion trajectory error method. The author gives the dynamic equation of the manipulator and uses the positive feedback neural network to study the dynamic characteristics of the manipulator. An adaptive neural network control system is designed, and the stability and convergence of the closed-loop system are proved by the Lyapunov function. A schematic diagram of the manipulator model is established, and MATLAB/Simulink software is used to simulate the dynamic parameters of the manipulator. At the same time, it is compared and analyzed with the simulation results of the PID control system. Simulation results show that in robot arm 3, the expected motion trajectory is θ3 = 0.4cos(2πt), the initial condition θ(0) = [000]τ, the control parameter K = diag(40,40),40), the disturbance parameter τ’ = 20cos(πt), robot arm link parameters l1 = 0.62 m, l2 = 0.41 m, l3 = 0.34 m, m1 = 3.5, m2 = 2.5 kg, m3 = 2 kg, g = 9.82 m/s2, under t = 2s, the motion trajectory of the robotic arm is disturbed by the outside world, and the adaptive neural network is used to control the motion trajectory with a small tracking error, input torque ripple is small. Conclusion. The manipulator adopts the adaptive neural network control method, which can improve the control accuracy of the motion trajectory and weaken the jitter phenomenon of the manipulator motion.

Particle and guiding-center orbits in crossed electric and magnetic fields

The problem of the charged-particle motion in crossed electric and magnetic fields is investigated, and the validity of the guiding-center representation is assessed in comparison with the exact particle dynamics. While the magnetic field is considered to be straight and uniform, the (perpendicular) radial electric field is nonuniform. The Hamiltonian guiding-center theory of charged-particle motion is presented for arbitrary radial electric fields, and explicit examples are provided for the case of a linear radial electric field.

Faithful guiding-center orbits in an axisymmetric magnetic field

The problem of the charged-particle motion in an axisymmetric magnetic geometry is used to assess the validity of higher-order Hamiltonian guiding-center theory, which includes higher-order corrections associated with gyrogauge invariance as well as guiding-center polarization induced by magnetic-field non-uniformity. Two axisymmetric magnetic geometries are considered: a magnetic mirror geometry and a simple tokamak geometry. When a magnetically confined charged-particle orbit is regular (i.e., its guiding-center magnetic moment is adiabatically invariant), the guiding-center approximation, which conserves both energy and azimuthal canonical angular momentum, is shown to be faithful to the particle orbit when higher-order corrections are taken into account.

Dirichlet Sub-Laplacians on Homogeneous Carnot Groups: Spectral Properties, Asymptotics, and Heat Content

Abstract We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and study their spectral properties. We prove that these operators have a pure point spectrum and prove the existence of the spectral gap. In addition, we give applications to the small ball problem for a hypoelliptic Brownian motion and the large time behavior of the heat content in a regular domain.

The blindfolded traveler’s problem: A search framework for motion planning with contact estimates

We address the problem of robot motion planning under uncertainty where the only observations are through contact with the environment. Such problems are typically solved by planning optimistically assuming unknown space is free, moving along the planned path and re-planning if the robot collides. However this approach can be very inefficient, leading to many unnecessary collisions and unproductive motion. We propose a new formulation, the Blindfolded Traveler’s Problem (BTP), for planning on a graph containing edges with unknown validity, with true validity observed only through attempted traversal by the robot. The solution to a BTP is a policy indicating the next edge to attempt given previous observations and an initial belief. We prove that BTP is NP-complete and show that exact modeling of the belief is intractable, therefore we present several approximation-based policies and beliefs. For the policy we propose graph search with edge weights augmented by the probability of collision. For the belief representation we propose a weighted Mixture of Experts of Collision Hypothesis Sets and a Manifold Particle Filter. Empirical evaluation in simulation and on a real robot arm shows that our proposed approach vastly outperforms several baselines as well as a previous approach that does not employ the BTP framework.

Necessary Existence Conditions for an Additional Integral in the Problem of Motion of a Rigid Body with a Fixed Point Bounded by the Surface of an Ellipsoid of Revolution in a Particle Flow

Necessary Existence Conditions for an Additional Integral in the Problem of Motion of a Rigid Body with a Fixed Point Bounded by the Surface of an Ellipsoid of Revolution in a Particle Flow

Promoting Transfer of Robot Neuro-Motion-Controllers by Many-Objective Topology and Weight Evolution

The ability of robot motion controllers to quickly adapt to new environments is expected to extend the applications of mobile robots. Using the concept of transfer optimization, this study investigates the capabilities of neuro-motion-controllers, which were obtained by simultaneously solving several source problems, to adapt to target problems. In particular, the adaptation comparison is carried out between specialized controllers, which are optimal for a single source motion problem, and nonspecialized controllers that can solve several source motion problems. The compared types of controllers were simultaneously obtained by a many-objective evolution search that is tailored for the optimization of the topology and weights of neural networks. Based on the examined problems, it appears that nonspecialized solutions, which are “good enough” in all the source motion problems, show significantly better transfer capabilities as compared with solutions that were optimized for a single source motion problem. The proposed approach opens up new opportunities to develop controllers that have good enough performances in various environments while also exhibiting efficient adaptation capabilities to changes in the environments.

End Motion Path Analysis of Notched Variable Cross-section Flexible Manipulator Based on 3R Pseudo-Rigid Body Model

A wire-driven planar curved notched flexible manipulator with variable cross-section is designed. Based on the Bernoulli Euler beam equation, the end track and rotation angle of the notched flexible manipulator with variable cross-section after applying force is deduced theoretically. In addition, the 3R pseudo rigid body model is used to calculate the end track and rotation angle, and ABAQUS finite element analysis software is used for motion simulation. Then, MATLAB is used for post-processing to obtain the end track of the flexible manipulator. By comparing the track of the 3R pseudo rigid body model with the ABAQUS simulation track, the relative error is obtained. The conclusion proves that the 3R pseudo rigid body model can effectively simulate the end track of a notched flexible manipulator with variable cross-section after bending, which expands a new method for solving the complex end motion problem of a flexible manipulator with variable cross-section, and also broadens the applicable structure of the 3R pseudo rigid body model.

Brownian Motion in an N-Scale Periodic Potential

We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+1 scales (i.e. N small scales and one macroscale) and to depend periodically on all the small scales. We show that for nonseparable potentials, i.e. potentials in which the microscales and the macroscale are fully coupled, the homogenized equation is an overdamped Langevin equation with multiplicative noise driven by the free energy, for which the detailed balance condition still holds. This means, in particular, that homogenized dynamics is reversible and that the coarse-grained Fokker–Planck equation is still a Wasserstein gradient flow with respect to the coarse-grained free energy. The calculation of the effective diffusion tensor requires the solution of a system of N coupled Poisson equations.

Mobility of the arytenoid cartilage in glottic carcinoma: a CT image study

Background Laryngeal carcinomas cause vocal cord (VC) mobility problems. Other than evaluation through flexible laryngoscopy, rare reports concerning CT findings for the motion of the VC or arytenoid cartilage (AC) are found. Aims/objectives To explore a novel evaluation of the mobility of the AC in glottic carcinoma. Material and Methods In 39 patients with glottic carcinoma grouped upon lesion locations and AC mobilities, laryngeal CT scans were collected during inspiration and phonation. AC static position and motion data were compared between paired lesion and control sides. Results No significant difference showed in the group with glottic carcinoma invading the anterior 2/3 of VC. In the abnormal mobility group, significant AC position changes and weaker motion of most measurements were proved on the lesion side. Lesion invading the posterior 1/3 of VC also resulted in an adducted, medially rotated and forward-tilted AC, rotation of axial angle (RAA) was the only motion item that decreased significantly. Conclusions and Significance In most glottic cancer cases, CT and laryngoscope had similar judgments for AC mobility. For lesions extending to the cartilaginous VC with laryngoscopically confirmed normal mobility, CT measurement of RAA showed the feasibility of being an indicator for the earliest motion problem.

A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions

This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference frame. The problem of the 6-DOF relative motion of two spacecraft in the specific case of Keplerian confocal orbits is proposed. The result is an analytical method without secular terms and singularities. Tensors dual algebra and dual quaternions play a fundamental role, with the solution representation being the relative problem. Furthermore, the representation theorems for the rotation and translation parts of the 6-DOF relative orbital motion problems are obtained.

Uncertainty-Driven Dense Two-View Structure From Motion

This work introducesan effective and practical solution to the dense two-view structure from motion (S <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> M) problem. One vital question addressed is how to mindfully use per-pixel optical flow correspondence betweentwo frames for accurate pose estimation—as perfect per-pixel correspondence between two images is difficult, if not impossible, to establish. With the carefully estimated camera pose and predicted per-pixel optical flow correspondences, a dense depth of the scene is computed. Later, an iterative refinement procedure is introduced to further improve optical flow matching confidence, camera pose, and depth, exploiting their inherent dependency in rigid S <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> M. The fundamental idea presented is to benefit from per-pixel uncertainty in the optical flow estimation and provide robustness to the dense S <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> M system via an online refinement. Concretely, we introduce a pipeline consisting of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> an uncertainty-aware dense optical flow estimation approach that provides per-pixel correspondence with their confidence score of matching; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> a weighted dense bundle adjustment formulation that depends on optical flow uncertainty and bidirectional optical flow consistency to refine both pose and depth; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(iii)</i> A depth estimation network that considers its consistency with the estimated poses and optical flow respecting epipolar constraint. Extensive experiments show that the proposed approach achieves remarkable depth accuracy and state-of-the-art camera pose results superseding SuperPoint and SuperGlue accuracy when tested on benchmark datasets such as DeMoN, YFCC100 M, and ScanNet.

Equations of Motion for Spinning Fluids and their Deviation Equations in Finslerian Geometry

Finsler geometry is a natural extension of the Riemannian geometry and agood a platform used to interpret the infrastructure of physical phenomena,especially for relativistic applications. Accordingly it is worthy to study spinningfluids in the context of this geometry that would share their benefits incosmological applications. Equations of motion of spinning fluids and theircorresponding deviation equations are obtained. The problem of motion forstudying a fluid with a variable mass is also obtained. The set of Equations ofspinning fluids and spinning deviation fluids equations for some classes of theFinslerian geometry have been derived, using a modified type of the BazanskiLagrangian. Due to the richness of the Finslerian geometry, a new perspective forrevisiting the problem of stability is based on solving the deviation equations ofspinning fluids in strong fields of gravity is performed. Such a problem has adirect application on examining the stability of accretion disk orbiting Sgr A*.

Point to point time optimal handling of unmounted rigid objects and liquid-filled containers

Time optimal handling of parts loosely placed at the end-effector (EE) of a robot, known as waiter motion problem, has high practical relevance, which becomes more challenging if the object is a liquid-filled container. The waiter motion problem was often restricted to a time-optimal path following problem, which limits the flexibility and task efficiency. To overcome this restriction, in this paper, the general point to point (PtP) time-optimal motion planning problem is formulated and solved with a multiple shooting method. The formulation includes all relevant dynamic effects (joint friction, contact, motor limits, etc.) assuming rigid behavior of the robot as well as of the object placed at the EE. The trajectory is C2-continuous, avoiding bang–bang behavior of motor torques. The CasADi framework and the Ipopt solver are used for numerical computations. The reported experimental results confirm applicability of the trajectory to real robotic setup in case of rigid objects. Further, handling of containers filled with liquid is addressed. Experiments are compared with numerical results obtained with SPH particle simulation. Experiment and simulation indicate that sloshing effects must be taken into account in the control formulation.

Research on planing motion and stability of amphibious aircraft in waves based on cartesian grid finite difference method

The wave resistance of amphibious aircraft planing in waves is an important consideration in the design of seaplanes. Based on the Cartesian Grid Finite Difference Method (CGFDM), this paper investigates the effect of different wave elements and planing speeds on the motion response and vertical overload of amphibious aircraft, and analyzes the conditions for the occurrence of jump motion and stability of the aircraft. The finite difference method (FDM) based on a fixed regular cartesian grid system is used to solve the flow field, and the Tangent of Hyperbola for Interface Capturing with Slope Weighting (THINC/SW) method is used to capture the violent free surface flow, while the immersed boundary method (IBM) is used to effectively solve the problem of large motion of the object. The numerical simulation results are compared with the experimental values and show good agreement. The calculation results demonstrate that the heave and pitch motion responses of amphibious aircraft show a certain regularity with changing wave conditions. As the speed increases, the vertical overload rises sharply as the aircraft enters the complete planing state, and the slamming effect on the bottom of the aircraft's forward fuselage is most significant. When the wavelength reaches 1.38 to 2.76 times the length of the fuselage, high speeds and large wave steepness are more likely to induce jumping motions and reduce the stability of the aircraft's movement. This study can provide a reference basis for amphibious aircraft to effectively avoid unsafe sea state areas.