Special Motions Research Articles

Periodic modes of group dominance in fully coupled neural networks

Nonlinear systems of differential equations with delay, which are mathematical models of fully connected networks of impulse neurons, are considered. Purpose of this work is to study the dynamic properties of one special class of solutions to these systems. Large parameter methods are used to study the existence and stability in сonsidered models of special periodic motions – the so-called group dominance or k-dominance modes, where k ∈ N. Results. It is shown that each such regime is a relaxation cycle, exactly k components of which perform synchronous impulse oscillations, and all other components are asymptotically small. The maximum number of stable coexisting group dominance cycles in the system with an appropriate choice of parameters is 2m − 1, where m is the number of network elements. Conclusion. Considered model with maximum possible number of couplings allows us to describe the most complex and diverse behavior that may be observed in biological neural associations. A feature of the k-dominance modes we have considered is that some of the network neurons are in a non-working (refractory) state. Each periodic k-dominance mode can be associated with a binary vector (α1, α2, . . . , αm), where αj = 1 if the j-th neuron is active and αj = 0 otherwise. Taking this into account, we come to the conclusion that these modes can be used to build devices with associative memory based on artificial neural networks.

Geometric kinematics of persistent rigid motions in three-dimensional Minkowski space

This paper investigates whether Lorentz geometry can be systematically implemented to study the geometric kinematics of persistent rigid motions in three-dimensional Minkowski space. The notion of persistence of a one-parameter rigid motion is identified by the property that the instantaneous twist of the motion has a constant pitch. The main difference between three-dimensional Euclidean and Minkowski spaces is that the pitch of twists will take three different values in Minkowski space depending on the causal character of the curve on which the motions are based. Furthermore, based on the fundamentals of screw theory, the paper establishes necessary and sufficient criteria for modeling the persistence of some significant frame motions, including Frenet–Serret, adapted frame, and Bishop motions. Then, the axode surfaces of these special motions and their geometric concepts are defined. Finally, for a thorough treatment of special frame motions in three-dimensional Minkowski space, this paper reveals some illustrative examples of persistent rigid motions and axode surfaces.

Effects of perforated crease line design on mechanical behaviors of origami structures

Recently, origami structures have been widely studied for various applications such as mechanical, electrical, bio, and nanosystems. Unlikely paper-like materials, engineering materials have higher stiffness and thickness so the hinge-like motion of the crease of paper origami is impossible. Therefore, origami, which is not made of paper-like materials, has different characteristics from paper origami. Several researchers reported that introducing slits or holes at or near the crease can make the hinge-like motion of the origami, but investigating the effects of the crease line design was not considered.In this paper, a perforated crease line was considered and parametric studies of the crease line design were investigated by finite element analysis and experiment. It was found that the length and distance of the perforated holes were significant factors to determine the stability and the barrier force and spring constant of Kresling origami could be optimized. Finally, it was shown that special motions could be realized with a combination of two origami with the same dimension but different crease line designs.

Erie Slapp Back

Dozens of states have enacted anti-Strategic Lawsuits Against Public Participation (SLAPP) laws to counter SLAPP suits, or lawsuits filed to silence a defendant who has spoken out against a plaintiff. The primary goal of a SLAPP suit is not to win on the merits, but rather to discourage the defendant’s right to free speech through the prospect of excessively expensive litigation. State anti-SLAPP laws provide for special motions to dismiss, discovery limitations, and fee shifting, all designed to allow a defendant to expeditiously dispose of the SLAPP suit before engaging in costly discovery. As most first year civil procedure students learn, the Supreme Court, in Erie Railroad Co. v. Tompkins and the cases that follow it, established that a federal court sitting in diversity is to apply state substantive law and federal procedural rules. However, following the Supreme Court’s decision in Shady Grove Orthopedic Associates, P.A. v. Allstate Insurance Co., it is unclear whether state statutes that create anti-SLAPP special motions to dismiss should apply in federal courts sitting in diversity. This Article discusses the development of state anti-SLAPP laws and the evolution of the Erie doctrine through the Shady Grove decision, ultimately examining how lower courts have struggled to make sense of Shady Grove in the context of state anti-SLAPP special motions to dismiss. This Article then discusses the various theoretical solutions that have been offered for this dilemma, concluding that the conflict between state anti-SLAPP laws and the Federal Rules of Civil Procedure is unavoidable and irreconcilable under the Rules Enabling Act and Erie and its progeny. Based on this analysis, this Article concludes that state anti-SLAPP laws cannot be applied by federal courts sitting in diversity. The only mechanism for accomplishing the specifically defined purpose of state anti-SLAPP laws in federal court is for the Congress to adopt a federal anti-SLAPP law that would supplement the operation of the Federal Rules of Civil Procedure.

Ray-Space Epipolar Geometry for Light Field Cameras.

Light field essentially represents rays in space. The epipolar geometry between two light fields is an important relationship that captures ray-ray correspondences and relative configuration of two views. Unfortunately, so far little work has been done in deriving a formal epipolar geometry model that is specifically tailored for light field cameras. This is primarily due to the high-dimensional nature of the ray sampling process with a light field camera. This paper fills in this gap by developing a novel ray-space epipolar geometry which intrinsically encapsulates the complete projective relationship between two light fields, while the generalized epipolar geometry which describes relationship of normalized light fields is the specialization of the proposed model to calibrated cameras. With Plücker parameterization, we propose the ray-space projection model involving a 6×6 ray-space intrinsic matrix for ray sampling of light field camera. Ray-space fundamental matrix and its properties are then derived to constrain ray-ray correspondences for general and special motions. Finally, based on ray-space epipolar geometry, we present two novel algorithms, one for fundamental matrix estimation, and the other for calibration. Experiments on synthetic and real data have validated the effectiveness of ray-space epipolar geometry in solving 3D computer vision tasks with light field cameras.

ACK-MSCKF: Tightly-Coupled Ackermann Multi-State Constraint Kalman Filter for Autonomous Vehicle Localization.

Visual-Inertial Odometry (VIO) is subjected to additional unobservable directions under the special motions of ground vehicles, resulting in larger pose estimation errors. To address this problem, a tightly-coupled Ackermann visual-inertial odometry (ACK-MSCKF) is proposed to fuse Ackermann error state measurements and the Stereo Multi-State Constraint Kalman Filter (S-MSCKF) with a tightly-coupled filter-based mechanism. In contrast with S-MSCKF, in which the inertial measurement unit (IMU) propagates the vehicle motion and then the propagation is corrected by stereo visual measurements, we successively update the propagation with Ackermann error state measurements and visual measurements after the process model and state augmentation. This way, additional constraints from the Ackermann measurements are exploited to improve the pose estimation accuracy. Both qualitative and quantitative experimental results evaluated under real-world datasets from an Ackermann steering vehicle lead to the following demonstration: ACK-MSCKF can significantly improve the pose estimation accuracy of S-MSCKF under the special motions of autonomous vehicles, and keep accurate and robust pose estimation available under different vehicle driving cycles and environmental conditions. This paper accompanies the source code for the robotics community.

Robocentric visual–inertial odometry

In this paper, we propose a novel robocentric formulation of the visual–inertial navigation system (VINS) within a sliding-window filtering framework and design an efficient, lightweight, robocentric visual–inertial odometry (R-VIO) algorithm for consistent motion tracking even in challenging environments using only a monocular camera and a six-axis inertial measurement unit (IMU). The key idea is to deliberately reformulate the VINS with respect to a moving local frame, rather than a fixed global frame of reference as in the standard world-centric VINS, in order to obtain relative motion estimates of higher accuracy for updating global pose. As an immediate advantage of this robocentric formulation, the proposed R-VIO can start from an arbitrary pose, without the need to align the initial orientation with the global gravitational direction. More importantly, we analytically show that the linearized robocentric VINS does not undergo the observability mismatch issue as in the standard world-centric counterparts that has been identified in the literature as the main cause of estimation inconsistency. Furthermore, we investigate in depth the special motions that degrade the performance in the world-centric formulation and show that such degenerate cases can be easily compensated for by the proposed robocentric formulation, without resorting to additional sensors as in the world-centric formulation, thus leading to better robustness. The proposed R-VIO algorithm has been extensively validated through both Monte Carlo simulation and real-world experiments with different sensing platforms navigating in different environments, and shown to achieve better (or competitive at least) performance than the state-of-the-art VINS, in terms of consistency, accuracy, and efficiency.

Two- and three-dimensional motions of a body controlled by an internal movable mass

The prescribed movement of a rigid body can be achieved by means of auxiliary internal masses performing special motions relative to the body. This principle of movement is used in mobile robots (capsule robots, vibro-robots) and is also applicable to the attitude control of spacecraft. Whereas one-dimensional motions of bodies controlled by internal movable masses are well-studied, two- and three-dimensional motions of such systems are not investigated thoroughly. In the paper, these motions are considered in the absence of external forces. Two-dimensional time-optimal motions of a body controlled by an internal mass are obtained for the case where the internal mass is small compared to the mass of the body. Based on this solution, suboptimal controls are presented for the general case. An approach to three-dimensional motions of such systems is presented which is based on three two-dimensional optimal rotations.

Controlling the Orientation of a Solid Using the Internal Mass

A problem of changing of the orientation of a solid in a space by means of motion of the internal mass is under consideration. It is shown that it is possible for a solid to be arbitrarily reoriented due to special motions of the internal mass. Approaches to controlling the internal motions ensuring this reorientation are proposed.

A robot motion design scheme for watching the elderly based on human gesture sensing

Watching the elderly is one of promising IoT applications in the field of nursing care. Humanoid robots are considered to be useful agents for not only relaxing the elderly but also watching and alerting them in a daily life. Detecting and preventing the risk of indoor heat stroke is an important issue especially for the elderly who live alone. A method for reliably conveying the possible danger of the indoor heat stroke to the elderly is a crucial factor to implement a practical system. In this paper, we describe the system for detecting possible risk of suffering from the indoor heat stroke and informing the detected state to the elderly by using a communication robot. While the robot normally gives users healing, the proposed system implements a method for certainly notifying the abnormal conditions to the elderly by using robot motions. Because designing natural robot motions is a difficult task even for skilled engineers, we also devise a method to easily creating new robot motions by imitating human body gestures. We design a set of normal and special motions for a desktop humanoid robot and evaluated whether the robot motions can effectively make users aware of abnormal situations.

High-speed autonomous quadrotor navigation through visual and inertial paths

This paper addresses the problem of autonomous quadrotor navigation within indoor spaces. In particular, we focus on the case where a visual map of the area, represented as a graph of linked images, is constructed offline (from visual and potentially inertial data collected beforehand) and used to determine visual paths for the quadrotor to follow. In addition, during the actual navigation, the quadrotor employs both wide- and short-baseline random sample consensuses (RANSACs) to efficiently determine its desired motion toward the next reference image and handle special motions, such as rotations in place. In particular, when the quadrotor relies only on visual observations, it uses the 5pt and 2pt algorithms in the wide- and short-baseline RANSACs, respectively. On the other hand, when information about the gravity direction is available, significant gains in speed are realized by using the 3pt+1 and 1pt+1 algorithms instead. Lastly, we introduce an adaptive optical-flow algorithm that can accurately estimate the quadrotor’s horizontal velocity under adverse conditions (e.g., when flying over dark, textureless floors) by progressively using information from more parts of the images. The speed and robustness of our algorithms are evaluated experimentally using a commercial-off-the-shelf quadrotor navigating in the presence of dynamic obstacles (i.e., people walking) along lengthy corridors and through tight corners, as well as across building floors via poorly lit staircases.

On the Workspace of a Free-Floating Space Robot

The planar problem of controlling the motion of a free-floating space robot is investigated. The robot consists of a body and a telescopic manipulator arm. The motion of the manipulator arm changes the body’s center of mass and causes the body to rotate. It is assumed that the length of the manipulator arm and the angle of its turn relative to the body are restricted. It is shown that the workspace of such a robot is significantly larger than the workspace of a robot with a fixed body. Due to the special motions of the manipulator arm, the robot’s body can be turned and the gripper can be moved from an arbitrary position to another arbitrary position if they are within the workspace, which is a ring centered at the robot’s center of mass. In addition, the prescribed angle between the manipulator arm and the body in the terminal position can be ensured.

Optimal Motions of Bodies Controlled by Internal Moving Masses

Abstract Locomotion of robots in a resistive medium can be based on special motions of auxiliary internal masses inside the main body of the robot. This locomotion principle is used in micro-robots and vibro-robots moving in tubes. In the paper, optimal motions of systems controlled by internal moving masses are considered. One-dimensional optimal motions are examined for systems moving in the presence of dry friction forces. Two-dimensional motions are considered for bodies subject to dry friction and containing internal moving masses. Optimal motions of a two-body system are obtained for the case where external forces are negligible. This situation is a model for the re-orientation of a spacecraft containing a moving internal mass.

Spin angular momentum of proton spin puzzle in complex octonion spaces

The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially the proton spin, decomposition, quarks and gluons, and polarization and so forth. Maxwell was the first to use the quaternions to study the electromagnetic fields. Subsequently the complex octonions are utilized to depict the electromagnetic field, gravitational field, and quantum mechanics and so forth. In the complex octonion space, the precessional equilibrium equation infers the angular velocity of precession. The external electromagnetic strength may induce a new precessional motion, generating a new term of angular momentum, even if the orbital angular momentum is zero. This new term of angular momentum can be regarded as the spin angular momentum, and its angular velocity of precession is different from the angular velocity of revolution. The study reveals that the angular momentum of the proton must be separated into more components than ever before. In the proton spin puzzle, the orbital angular momentum and magnetic dipole moment are independent of each other, and they should be measured and calculated respectively.

Infinitesimally affine deformations of a hypersurface

Affine deformations serve as basic examples in the continuum mechanics of deformable three-dimensional bodies (usually referred to as homogeneous deformations). They preserve parallelism of straight lines, and are often used as an approximation to general deformations. However, when the deformable body is a membrane, a shell or an interface modeled by a surface, parallelism is defined by the affine connection of this surface. In this work we study the infinitesimally affine time-dependent deformations (motions) of such a continuum, but in a more general context, by considering that it is modeled by a Riemannian hypersurface. First we prove certain equivalent formulas for the variation of the connection of the hypersurface. Some of these formulas are expressed in terms of geometrical quantities, and others in terms of kinematical quantities of the deforming continuum. The latter is achieved by using an adapted version of the polar decomposition theorem, frequently used in continuum mechanics to analyze motion. We also apply our results to special motions like tangential and normal motions. Further, we find necessary and sufficient conditions for this variation to be zero (infinitesimal affine motions), providing insight on the form of these motions and the kind of hypersurfaces that allow such motions. Finally, we give some specific examples of mechanical interest which demonstrate motions that are infinitesimally affine but not infinitesimally isometric.

Persistent rigid-body motions and study\u2019s \u201cRibaucour\u201d problem

In this work we show that the concept of a one-parameter persistent rigid-body motion is a slight generalisation of a class of motions called Ribaucour motions by Study. This allows a simple description of these motions in terms of their axode surfaces. We then investigate other special rigid-body motions, and ask if these can be persistent. The special motions studied are line-symmetric motions and motions generated by the moving frame adapted to a smooth curve. We are able to find geometric conditions for the special motions to be persistent and, in most cases, we can describe the axode surfaces in some detail. In particular, this work reveals some subtle connections between persistent rigid-body motions and the classical differential geometry of curves and ruled surfaces.

Об устойчивости частных решений приближенных уравнений движения тяжелого твердого тела с вибрирующей точкой подвеса

Об устойчивости частных решений приближенных уравнений движения тяжелого твердого тела с вибрирующей точкой подвеса

Approximate equations of rotational motion of a rigid body carrying a movable point mass

The dynamics of a compound system, consisting of a rigid body and a point mass, which moves in a specified way along a curve, rigidly attached to the body is investigated. The system performs free motion in a uniform gravity field. Differential equations are derived which describe the rotation of the body about its centre of mass. In two special cases, which allow of the introduction of a small parameter, an approximate system of equations of motion is obtained using asymptotic methods. The accuracy with which the solutions of the approximate system approach the solutions of the exact equations of motion is indicated. In one case, it is assumed that the point mass has a mass that is small compared with the mass of the body, and performs rapid motion with respect to the rigid body. It is shown that in this case the approximate system is integrable. A number of special motions of the body, described by the approximate system, are indicated, and their stability is investigated. In the second case, no limitations are imposed on the mass of the point mass, but it is assumed that the relative motion of the point is rapid and occurs near a specified point of the body. It is shown that, in the approximate system, the motion of the rigid body about its centre of mass is Euler–Poinsot motion.

Alkylation Effects on the Energy Transfer of Highly Vibrationally Excited Naphthalene

The energy transfer of highly vibrationally excited isomers of dimethylnaphthalene and 2-ethylnaphthalene in collisions with krypton were investigated using crossed molecular beam/time-of-flight mass spectrometer/time-sliced velocity map ion imaging techniques at a collision energy of approximately 300 cm(-1). Angular-resolved energy-transfer distribution functions were obtained directly from the images of inelastic scattering. The results show that alkyl-substituted naphthalenes transfer more vibrational energy to translational energy than unsubstituted naphthalene. Alkylation enhances the V→T energy transfer in the range -ΔE(d)=-100~-1500 cm(-1) by approximately a factor of 2. However, the maximum values of V→T energy transfer for alkyl-substituted naphthalenes are about 1500~2000 cm(-1), which is similar to that of naphthalene. The lack of rotation-like wide-angle motion of the aromatic ring and no enhancement in very large V→T energy transfer, like supercollisions, indicates that very large V→T energy transfer requires special vibrational motions. This transfer cannot be achieved by the low-frequency vibrational motions of alkyl groups.

Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the Korteweg–de Vries (KdV) hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, we show that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlevé equation.