Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Anisotropic Force Ellipsoid Based Multi-axis Motion Optimization of Machine Tools

The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In motion optimization, the stiffness characteristics of the whole machining system, including machine tool and cutter, are not considered. The paper presents a new method to establish a general stiffness model of multi-axis machining system. An analytical stiffness model is established by Jacobi and point transformation matrix method. Based on the stiffness model, feed-direction stiffness index is calculated by the intersection of force ellipsoid and the cutting feed direction at the cutter tip. The stiffness index can help analyze the stiffness performance of the whole machining system in the available workspace. Based on the analysis of the stiffness performance, multi-axis motion optimization along tool paths is accomplished by mixed programming using Matlab and Visual C＋＋. The effectiveness of the motion optimization method is verified by the experimental research about the machining performance of a 7-axis 5-linkage machine tool. The proposed research showed that machining stability and production efficiency can be improved by multi-axis motion optimization based on the anisotropic force ellipsoid of the whole machining system.

AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE

In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequalities.

COORDINATION OF THE MOTION PARAMETERS WITHIN STEP-BY-STEP INTEGRATION FOR DYNAMIC EQUATION

A method is presented that coordinates the calculation of the displacement, velocity and acceleration of structures within the time-steps of different types of step-by-step integration. The dynamic equation is solved using an energy equation and the calculating data of the original method. The method presented is better than the original method in terms of calculating postulations and is in better conformity with the system's movement. Take the Wilson-θ method as an example. By using the coordination process, the calculation precision has been greatly im proved (reducing the errors by approximately 90% ), and the greater part of overshooting of the calculation result has been eliminated. The study suggests that the mal-coordination of the motion parameters within the time-step is the major factor that contributes to the result errors of step-by-step integration for the dynamic equation.

Research on Contour Error Based on CNC Multi-axis Motion Control System

The contour error was analyzed based on CNC multi-axis motion control, the contour error model was obtained focused on beeline and different radius of curvature and common contour of curve, for a CNC biaxial motion control system and the mechanism of producing contour error and the relationship between tracking error and contour error were presented. The theoretical and practical significance of modeling error and controlling error in motion control systems was carried out.

A Bio-Inspired Integration Model of Basal Ganglia and Cerebellum for Motion Learning of a Musculoskeletal Robot

It is a significant research direction for highly complex musculoskeletal robots that how to develop the ability of motion learning and generalization.The cooperations of multiple brain regions are crucial to improving motion performance.Inspired by the neural mechanisms of structures,functions,and interconnections of basal ganglia and cerebellum,a biologically inspired integration model for motor learning of musculoskeletal robots is proposed.Based on the neural characteristics of the basal ganglia,the basal ganglia actor network,which mainly simulates the dorsal striatum,outputs motion commands,and the basal ganglia critic network,which simulates the ventral striatum,estimates actionstate values.Their network parameters are updated using the soft actor-critic method.Based on the sensorimotor prediction mechanism of the cerebellum,the cerebellum network evaluates the state feature extraction quality of the basal ganglia actor network and then updates the weights of its feature layer.This learning method is proven to converge to the optimal policy.Furthermore,drawing on the mechanism of dopaminergic dynamic regulation in the basal ganglia,the adaptive adjustment of target entropy and the dopaminergic experience replay are proposed to further improve the integration model,which contributes to the exploration-exploitation trade-off of motor learning.The bio-inspired integration model is validated on a musculoskeletal system.Experimental results indicate that this model can effectively control the musculoskeletal robot to accomplish the motion task from random starting locations to random target positions with high precision and robustness.

Potential method of integration for solving the equations of mechanical systems

This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.

Comparison of capability of time integration methods in capturing dynamic loading

Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.

Integrating Factors and Conservation Theorems of Nonholonomic Dynamical System of Relative Motion

The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.

L2 Syntactic Alignment in the Reading-Writing Integrated Continuation Task: Evidence From Chinese EFL Learners’ Description of Motion Events

This study investigated how the mode in which the reading-writing integrated continuation task was conducted modulates the effects of second language(L2) syntactic alignment, through the English motion event construction with manner verbs. Ninety Chinese students were assigned to either of the two experimental groups or a control group, and they all experienced a pretest, an alignment phase and a posttest. In the alignment phase, the two experimental groups completed a reading-writing integrated continuation task but in different modes. For the multi-turn mode,participants reconstructed a picture story by continuing the episodes extracted from the story with one episode presented and continued at a time;for the single-turn mode, the first half of the same picture story was presented as a chunk, and then participants read and continued it. Results show that L2 learners aligned with the target structure in completing the story, and the alignment effect was retained in the posttest conducted after a delay of two weeks. Moreover, syntactic alignment was modulated by task mode with the multi-turn group exhibiting stronger immediate and longterm alignment effects. We conclude that the continuation task is a fruitful context for L2 structural alignment, and the magnitude of alignment effect hinges on interactive intensity.

Higher-Dimensional Integrable Systems Arising from Motions of Curves on S^2(R)and S^3(R)

We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).

Integrated modeling of spacecraft relative motion dynamics using dual quaternion

To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom(6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative(PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.

Consistency and Stability Issues in the Numerical Integration of the First and Second Order Initial Value Problem

In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.

ONE TYPE OF INTEGRALS FOR THE EQUATIONS OF MOTION OF HIGHER-ORDER NONHOLONOMIC SYSTEMS

This paper presents one type of integrals and its condition of existence for the equations of motion of higher-order nonholonomic systems, including l-order integral (generalized energy integral), 2-order integral and p-order integral (p>2)All of these integrals can be constructed by the Lagrangian function of the system. Two examples are given to illustrate the application of the suggested method.

Integrable System and Motion of Curves in Projective and Similarity Geometries

Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.

Multiple G-Stratonovich Integral Driven by G-Brownian Motion

In this paper, we propose the multiple Stratonovich integral driven by G-Brownian motion under the G-expectation framework. Then based on G-Itöformula, we obtain the relationship between Hermite polynomials and multiple G-Stratonovich integrals by using mathematical induction method.

循证训练理念下签派员技能全生命周期全动模拟机融合训练研究

为了培养高素质签派员队伍,借鉴飞行员技能全生命周期管理(PLM)体系建设相关理论,结合试点开展的“飞行员-签派员”融合训练,梳理其实施的可行性和必要性,探索签派员整个职业生涯岗位胜任力提升的实施路径。基于循证训练(EBT)理念总结“飞行员-签派员”融合训练的保障机制,为优化签派员训练模式提供参考。

CNN-LSTM车辆运动状态识别的AUKF组合导航方法

针对固定的噪声协方差难以适应车辆不同运动行为下噪声统计特性差异大的问题,提出了一种基于卷积神经网络与长短期记忆网络(CNN-LSTM)的车辆运动状态识别自适应无迹卡尔曼滤波(AUKF)组合导航方法。首先,应用CNN-LSTM网络模型进行车辆运动状态识别,解决车辆自我运动不确定性的问题;其次,将特定运动状态约束下的噪声协方差应用于UKF的时间更新与量测更新;最后,将所提方法在采集的数据集上进行验证。实验结果表明,与经典的UKF算法相比,所提方法的位置均方根误差与速度均方根误差分别下降了22.67%与2.63%,验证了所提方法的有效性。

基于计算机视觉和DNN的运动姿态检测算法

针对传统人体运动姿态检测算法存在鲁棒性较差及准确率偏低的问题,文中基于改进的深度图卷积网络提出了一种运动姿态检测算法。该算法将图卷积网络的时域和空间域模型相结合,提升了模型的感受野,并从时、空两个维度提取人体特征点的数据,再利用残差网络将时域和空间域卷积相连接,进而改善了模型拟合能力较差的不足。同时,对于模型因卷积核固定而导致无法适应多种类数据的缺陷,使用多头注意力机制来增强其自适应能力。在实验测试中,所提出的模型改进项相较原算法性能有一定提升,且与最优算法相比,该模型的误差指标降低了1.14 mm,准确率则提升了1.3%,证明了所提方法的有效性及优越性。