空间多刚体系统姿态的协同控制

将一种针对多个一般非线性系统的基于输出反馈的协同控制方法应用在采用四元数法描述的空间多个刚体姿态的协同控制系统中去，给出了空间多刚体系统姿态协同控制问题有解的充分条件，并设计了多刚体系统姿态的协同控制律．算例仿真结果表明，此法设计的协同控制器能够稳定控制描述各个刚体系统的姿态四元数，使其渐近稳定．     

一种新的多刚体系统的存储方法

指出了目前多刚体系统数据存储的不足,运用图论的概念和建模理论,分析了多刚体系统的结构图和有向图之间的关系,提出了一种新的基于十字链表的链式存储模型.该存储模型不仅解决了复杂多刚体系统的存储结构问题,而且避免了非树形多刚体向树形多刚体的切除转换,使非树形多刚体系统与树形多刚体系统从数学建模到数据存储达到高度一致.     

多刚体系统的一致性控制研究

基于非自治级联系统理论,以非完整移动机器人为研究对象,研究多刚体系统的一致性问题,提出了一种新的分布式控制器。通过引入持续激励扰动项,验证了无论参考信号是否为持续激励信号,所提出的控制器都能实现系统一致性的目的,且能一致到期望的参考值。利用李雅普诺夫方法对系统进行了稳定性分析。最后,对所提控制器进行数值仿真,结果验证了所提出的控制器的有效性。     

含摩擦滑移铰及驱动约束多刚体系统数值算法

研究了具有驱动约束及非光滑滑移铰多体系统动力学方程的建模与数值计算方法．将驱动约束视为非定常约束，非光滑滑移铰视为双边定常约束，滑移铰的摩擦模型采用库仑摩擦模型；应用第一类Lagrange方程建立系统的动力学方程，应用距离函数建立滑移铰的约束方程；将线性互补方法和Baumgarte约束稳定化方法引入，以解决滑移铰法向约束力的计算以及约束方程违约问题．最后应用曲柄摇杆机构作为算例，说明该方法的有效性．     

基于十字链表的多刚体系统的数据存储

针对多刚体系统数据存储的不足,对多刚体系统的结构图与图论的有向图之间的关系进行了研究,提出了一种新的基于十字链表的链式存储模型.该存储模型不但较好地解决了复杂多刚体系统的存储问题,而且充分满足了在存储物理多刚体系统时的结构正确性和数据完备性要求,避免了非树形多刚体向树形多刚体的回路切除转换,使多刚体系统在数学建模与数据存储方面达到高度一致.     

含干摩擦多体系统Lagrange方程的数值算法

利用第一类Lagrange方程建立了固定约束面含干摩擦的多体系统动力学方程,将摩擦力的广义力用矩阵形式描述．利用增广法。将微分-代数方程转换成常微分方程,并用矩阵形式给出,提高了计算效率．最后用算例说明该方法的有效性．     

一类空间机械臂系统的自适应控制与鲁棒控制

讨论载体位置与姿态均不受控制的自由浮动空间机械臂系统的控制问题。基于增广列反馈控制模型,提出当载荷参参数不确定时空间机械臂追踪惯性空间期望轨迹的自适应和鲁棒控制方法,通过仿真运算,证实了方法物有效性。     

基于碰撞响应的三维空间多刚体实时运动仿真

该文将计算机科学与理论力学相结合,以刚性球体为例介绍了多刚体物理运动仿真的步骤和方法。首先论述了单个及多个刚体的运动仿真步骤以及应用叠加原理计算合力及合力矩的方法。然后,针对刚体运动中的不同碰撞响应类型：碰撞接触与临时接触,提出分别建立不同的碰撞响应力学模型,前者采用动量及动量矩定理建立响应模型,后者通过分析刚体的受力和运动状态建立相应的动力学模型。最后,详细讨论了刚性球体的碰撞仿真,包括它的碰撞测定、碰撞响应模型的建立及求解等,实现了三维空间中刚性球体实时、精确、快速的运动仿真,为以后多刚体大规模仿真奠定基础。     

多刚体动力学仿真的李群变分积分算法

刚体的构形可用其质心位置和姿态矩阵描述.刚体的位置可以在欧几里得空间中表示，但是其姿态矩阵是在李群上演化的.由于李群独特的非线性性质，基于欧氏空间的多体动力学建模与数值算法难以完全真实地描述系统的动力学特性，特别是长时间历程的动力学特性.本文基于几何力学理论，首先根据离散Hamilton变分原理与离散Legendre变换，建立了多刚体系统的Hamilton体系李群变分积分公式.其次，给出李群变分积分公式的两种离散格式：一般离散格式和RATTLie离散格式.最后，采用这两种不同离散格式构建的算法计算了重力作用下空间刚体双摆的动力学问题，对比研究了算法在保持系统群结构、系统能量等方面的性质.计算结果表明，RATTLie离散格式较一般格式精度更高，且能更好地保持系统群结构与能量.     

履带车多刚体建模与仿真分析

首先以车辆地面力学理论为基础,分析了典型的履带与地面相互作用关系及其在RecurDyn/Track(LM)程序中的处理,分别定义了两种典型地面土力学参数,从而建立了基于Bekker理论与Janosi & Hanamoto理论的循环动载荷作用下履带与地面相互作用力学模型;同时分析了履带系统各部件之间的接触力学模型,定义各接触参数及约束关系,从而准确合理地建立了履带车多刚体模型,通过施加运动函数,实现模型在典型地面参数下的行走特性仿真分析,仿真结果与理论分析及实际情况相符合,互为验证,从而为进一步深入研究提供了理论依据与有效分析手段.     

Kinematic simulation of human gait with a multi-rigid-body foot model

The paper builds a multi-rigid-body model of human with a 4-rigid-body foot in the 3D CAD software Solidworks,based on human anatomy.By controlling the rotation of the ankle and major joints of human body while walking,the Kinematic simulation was performed in the dynamics simulation software ADAMS.The paper analyzes the simulate results and points out deficiencies in the current work and the direction of research efforts in future.     

Analysis and control of spatial limit sets and spatial chaos appearance in mimo cascade connected nonlinear systems

The oscillatory and chaotic dynamics of MIMO cascade connected nonlinear systems are analyzed in this paper. For that purpose the known theorems of limit sets existence in appropriate nonlinear discrete systems are used. Control of spatial limit sets and spatial chaos appearance in MIMO cascade connected nonlinear systems using modified Pyragas method is also analyzed. The results are illustrated by examples and confirmed with simulations.     

Impulsive observers with variable update intervals for Lipschitz nonlinear time-delay systems

This article is concerned with the design of impulsive observers with variable update intervals for Lipschitz nonlinear systems with delays in state. Discontinuous Lyapunov function/funtional approaches are developed to analyse the stability of error dynamics. Delay-independent sufficient conditions for uniform exponential stability of the error dynamics over variable update intervals are derived in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the observer gain matrix can be solved numerically with an LMI-based optimisation algorithm. Numerical examples are provided to show the efficiency of the proposed approach.     

PDE-based event-triggered containment control of multi-agent systems with input delay under spatial boundary communication

This article studies the containment control problem for multi-agent systems with input delay under spatial boundary communication by employing an event-based approach. Firstly, the collective dynamics of multi-agent systems are described as parabolic partial differential equations (PDEs). Applying the integral transformation method developed in PDEs, the delayed parabolic PDEs are transformed into a series of new coupled PDE-PDE systems. Then, by taking the spatial boundary communication scheme into account and using the local boundary information, two boundary containment control protocols together with a dynamic event-triggered scheme (DETS) are designed, such that the states of all followers converge to a convex hull formed by multiple leader agents with and without input delay. The optimal protocols are given by minimizing the 2-norm of the designed control gain matrix, and the exclusion of the Zeno behavior is analyzed. Finally, a numerical simulation example is provided to support the main results.     

Impulsive motion of multibody systems

This article uses the piecewise model and Kane’s method to present a procedure for studying impulsive motion of multibody systems. Impulsive motion occurs when the system is subject to either impulsive forces or impulsive constraints, or when subjected to both simultaneously. The Appellian classification of impulsive constraints and the corresponding equations of impulsive motion of the multibody system are discussed. The governing equations are derived based upon multibody formulation procedures developed by Huston. Constraint impulses associated with finite and impulsive constraints are incorporated into impact dynamical equations through the impulsive Lagrange multipliers. The kinetic energy change of the scleronomic multibody system due to the impact is derived. Newton’s impact law is treated as an impulsive constraint equation to study single-point frictionless collision between two multibody systems. Several examples are used to demonstrate and validate the procedure.     

Symplectic spatial integration schemes for systems of balance equations

A method to generate geometric pseudo-spectral spatial discretization schemes for hyperbolic or parabolic partial differential equations is presented. It applies to the spatial discretization of systems of conservation laws with boundary energy flows and/or distributed source terms. The symplecticity of the proposed spatial discretization schemes is defined with respect to the natural power pairing (form) used to define the port-Hamiltonian formulation for the considered systems of balance equations. The method is applied to the resistive diffusion model, a parabolic equation describing the plasma dynamics in tokamaks. A symplectic Galerkin scheme with Bessel conjugated bases is derived from the usual Galerkin method, using the proposed method. Besides the spectral and energetic properties expected from the symplecticity of the method, it is shown that more accurate approximation of eigenfunctions and reduced numerical oscillations result from this choice of conjugated approximation bases. Finally, the obtained numerical results are validated against experimental data from the tokamak Tore Supra facility.     

空间多体机械系统耦合动力学的键合图法

为提高多能域耦合空间多体系统动力学分析的效率及可靠性,提出了键合图法．从能量守恒的基本原理出发,讨论了键合图中的多通口元件MTF所具有的特性．以此为基础阐述了建立空间多体机械系统键合图模型的一般方法及其动力学原理．将运动副约束反力视做未知势源加在系统键合图模型相应的0-结处,有效地解决了微分因果关系及非线性结型结构所带来的十分困难的代数问题,推导出便于计算机自动生成的系统状态方程及运动副约束反力方程的统一公式,实现了计算机自动建模与仿真．实际算例表明了所述方法的有效性．     

Cooperative output regulation of multi-agent systems with switched leader dynamics

In this paper, the cooperative output regulation problem for heterogeneous multi-agent systems is addressed by considering a switched leader dynamics. The switched leader dynamics consists of multiple linear models and a switching rule governing the switches among them. A switched leader is capable of generating various sophisticated reference signals for more complicated multi-agent coordination tasks. A novel distributed hybrid impulsive switching control scheme is proposed to achieve cooperative output regulation. Distributed switching stability is established using the average dwell-time technique with multiple Lyapunov functions. Moreover, the associated distributed control synthesis conditions are formulated in terms of linear matrix inequalities plus linear matrix equations. As a result, both switching rules for the leader and distributed switching protocols for the followers can be jointly synthesised via efficient semi-definite programming. An example has been used to demonstrate the effectiveness of the proposed approach.     

Control of nonholonomic systems with extended base space dynamics

This paper extends certain results in Reference 1 to a more general class of nonholonomic systems with extended base space dynamics. This extension is important in applications for which control actuator dynamics are significant. These nonlinear control systems are referred to as nonholonomic control systems owing to certain nonintegrability assumptions which are made. The class of systems considered in this paper are characterized by general nonlinear base space dynamics that are input-output decouplable. Controllability results for this class of nonholonomic control systems are presented.