滑模变结构控制趋近运动边界特性研究北大核心CSCD

为对滑模变结构控制趋近运动阶段状态变量的范数边界特性进行分析,以一类非线性模型作为研究对象,采用2种典型趋近律设计滑模控制调节器,基于广义Gronwall-Bellman引理对趋近运动阶段状态变量范数的边界特性进行分析,给出状态变量范数的约束关系式,该范数的边界可利用趋近律参数的选取进行调节,使得滑模到达时状态变量在滑模态稳定域内,滑模运动指数稳定。利用MATLAB/Simulink对所得调节器进行仿真。仿真结果表明,在趋近运动阶段,对于满足给定初始条件的状态变量,其范数严格单调递减,满足分析得到的约束关系,在趋近运动结束进入滑模运动阶段后,系统能指数稳定在平衡状态。     

一个五维受控混沌系统的动力学行为

用状态反馈的方法对L櫣系统的混沌运动进行控制,在L櫣系统中增加两个新的状态变量,获得了一个五维的受控混沌系统,该系统有复杂的动力学行为.计算了系统的Lyapunov指数、功率谱和相轨迹.数值模拟表明：通过改变控制参数,可以将系统的周期运动改变为混沌运动、混沌运动改变为周期运动.     

基于变维度状态空间的增量启发式路径规划方法研究

在移动机器人路径规划中需要考虑运动几何约束,同时,由于它经常工作于动态、时变的环 境中,因此,还必须保证路径规划算法的效率.本文提出了一种基于变维度状态空间的增量启发式路径规划 方法,该方法既能满足移动机器人的运动几何约束,又能保证规划算法的效率.首先,设计了变维度状态空间, 在机器人周围的局部区域考虑运动几何约束组织高维状态空间,其他区域组织低维状态空间;然后,基于变维 度状态空间,提出了一种增量启发式路径规划方法,该方法在新的规划进程中可以使用以前的规划结果,仅对 机器人周围的局部区域进行重搜索,从而能保证算法的增量性及实时性;最后,通过仿真计算和机器人实验验 证了算法的有效性.     

有多余坐标的可控完整力学系统的自由运动与初始运动

对于完整力学系统,若选取的参数不是完全独立的,则称为有多余坐标的完整系统.本文研究有多余坐标的可控力学系统的自由运动与初始运动.首先,需由d′Alembert Lagrange原理并利用Lagrange乘子法建立有多余坐标完整系统的运动微分方程;其次,由约束系统自由运动的定义,令所有乘子为零,得到系统实现自由运动的条件.第三,如果给定运动的初始条件和控制参数,就可以研究系统的初始运动.文末,举例并说明方法和结果的应用.     

基于运动序列分割的运动捕获数据关键帧提取

采用线性时不变系统把高维运动数据映射到低维状态空间;在低维状态空间中,定义了姿态之间的相似性度量;并采用误差平方和准则对时序的低维数据点集进行运动分割,分割点上的运动姿态被定义为关键帧．实验结果表明：该算法能够较好地提取出运动序列中的关键帧,并且这些关键帧能够很好地概括原始运动序列的内容．     

带状态约束的疏浚最优控制问题转化方法

疏浚作业系统追求疏浚产量最大化,同时需要保证横移土壤切削过程和泥浆管道输送过程稳定安全的运行,可归结为带状态不等式约束的线性二次型最优跟踪控制问题。针对该问题,提出一种系统状态空间增维的转化方法,引入辅助状态变量和控制变量,将状态不等式约束转化为等式约束,并构建具有控制安全性的等价疏浚系统。仿真结果表明,该方法能够较好地提高泥浆浓度,同时又可以限制系统中主要状态量长时间的过载运行,从而有效增强挖泥船疏浚施工的安全性与平稳性。     

基于偏微分方程约束的机器人群集运动控制系统设计

为充分发挥机器人群集的协作优势,克服单机器人能力不足问题,利用偏微分方程约束理论,设计机器人群集运动控制系统。扩大机器人群集间通信网络范围,改装机器人传感器、运动控制器和驱动电机设备。在硬件设备的支持下,考虑机械结构、运动与动力工作原理,建立机器人群集数学模型。分配机器人群集运动任务,利用偏微分方程规划机器人群集编队运动路径,设置规划路径作为机器人群集运动的约束条件。从位置和姿态角两个方面计算运动控制量,通过控制指令的生成与转换,实现系统的机器人群集运动控制功能。通过系统测试实验得出结论：与传统运动控制系统相比,在优化设计系统的控制下,机器人群集的运动跟踪控制误差为13cm,机器人群集运动过程中产生的碰撞次数得到明显减少,即优化设计系统具有良好的控制效果。     

具有不确定性的非线性切换系统的约束预测控制

针对一类具有不确定性和变量约束的非线性切换系统, 提出了一种基于Lyapunov函数的预测控制方法, 其中状态约束分为两种情况: 1)要求状态变量在所有时刻都满足约束(称为硬约束); 2)允许状态在某些时刻超出约束(称为软约束). 主要思想是: 对切换系统的每一个子系统, 在输入和状态均受约束的情况下, 设计基于Lyapunov函数的有界控制器和预测控制器, 在两者之间适当切换, 得到初始稳定区域的描述并使得子闭环系统保持稳定. 对整个切换系统, 设计适当的切换律以保证: 1)在切换时刻, 闭环系统的状态处在切入系统的稳定区域内; 2)切入模块的Lyapunov函数是非增的, 从而可保证稳定性. 在状态变量的约束是软约束时, 对每一子模块首先设计一个控制策略, 尽快将状态控制到初始稳定区域, 然后再利用稳定区域内的控制律使系统稳定.     

一类非线性金融系统的数值研究

利用数值模拟的方法研究了一类非线性金融系统的动力学行为.建立了由生产、资金、股份、劳动力四个部分构成的一类非线性金融系统的动力学模型.首先运用四维微分方程来描述由利率、投资需求、价格指数和平均利润率构成的四个状态变量随时间的变化,然后将金融系统简化为四维自治微分方程组.通过对四维自治微分方程组进行数值模拟发现了非线性金融系统的动力学特性,从数值模拟获得的三维相图反映了金融系统的非线性特性.从数值模拟结果发现,在特定的条件下非线性金融系统存在周期运动和混沌运动.除此之外,还观察到参数的改变对四维自治金融系统的非线性特性有着显著的影响.     

基于状态空间表示法的机械产品概念设计

分析了机械工程系统的功能关系。确立待设计系统的状态变量，利用键合图的基础元件建立状态空间转换矩阵，根据机械系统中能量传递建立系统状态空间模型，采用状态空间变换操作，产生多个设计方案，并结合电动静脉注射器设计说明其应用。     

Null Space Integration Method for Constrained Multibody Systems with No Constraint Violation

A method for integrating equations of motion of constrained multibodysystems with no constraint violation is presented. A mathematical model,shaped as a differential-algebraic system of index 1, is transformedinto a system of ordinary differential equations using the null-spaceprojection method. Equations of motion are set in a non-minimal form.During integration, violations of constraints are corrected by solvingconstraint equations at the position and velocity level, utilising themetric of the system's configuration space, and projective criterion to thecoordinate partitioning method. The method is applied to dynamicsimulation of 3D constrained biomechanical system. The simulation resultsare evaluated by comparing them to the values of characteristicparameters obtained by kinematic analysis of analyzed motion based onmeasured kinematic data.     

Constrained motion planning of nonholonomic systems

This paper addresses the constrained motion planning problem for nonholonomic systems represented by driftless control systems with output. The problem consists in defining a control function driving the system output to a desirable point at a given time instant, whereas state and control variables remain over the control horizon within prescribed bounds. The state and control constraints are handled by extending the control system with a pair of state equations driven by the violation of constraints, and adding regularizing perturbations. For the regularized system a Jacobian motion planning algorithm is designed, called imbalanced. Solutions of example constrained motion planning problems for the rolling ball illustrate the theoretical concepts.     

Dynamics and Motion Planning of Trident Snake Robot

The trident snake robot is a mechanical device that serves as a demanding testbed for motion planning and control algorithms of constrained non-holonomic systems. This paper provides the equations of motion and addresses the motion planning problem of the trident snake with dynamics, equipped with either active joints (undulatory locomotion) or active wheels (wheeled locomotion). Thanks to a partial feedback linearization of the dynamics model, the motion planning problem basically reduces to a constrained kinematic motion planning. Two kinds of constraints have been taken into account, ensuring the regularity of the feedback and the collision avoidance between the robot’s arms and body. Following the guidelines of the endogenous configuration space approach, two Jacobian motion planning algorithms have been designed: the singularity robust Jacobian algorithm and the imbalanced Jacobian algorithm. Performance of these algorithms have been illustrated by computer simulations.     

Dynamics of Flexible Multibody Systems with Non-Holonomic Constraints: A Finite Element Approach

In this article it is shown how non-holonomic constraints can beincluded in the formulation of the dynamic equations of flexiblemultibody systems. The equations are given in state space formwith the degrees of freedom, their derivatives and the kinematiccoordinates as state variables, which circumvents the use ofLagrangian multipliers. With these independent state variables forthe system the derivation of the linearized equations of motion isstraightforward. The incorporation of the method in a finiteelement based program for flexible multibody systems is discussed.The method is illustrated by three examples, which show, amongother things, how the linearized equations can be used to analysethe stability of a nominal steady motion.     

Controllability of kinematic control systems on stratifiedconfiguration spaces

This paper considers nonlinear kinematic controllability of a class of systems called stratified. Roughly speaking, such stratified systems have a configuration space which can be decomposed into sub-manifolds upon which the system has different sets of equations of motion. For such systems, considering the controllability is difficult because of the discontinuous form of the equations of motion. The main result in this paper is a controllability test, analogous to Chow's theorem, is based upon a construction involving distributions, and the extension thereof to robotic gaits     

On the constraints violation in forward dynamics of multibody systems

It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton–Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical solution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as a function of the Moore–Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian, and the coordinate partitioning method.     

Unscented model predictive control of chance constrained nonlinear systems

This paper introduces an unscented model predictive approach for the control of constrained nonlinear systems under uncertainty. The main contribution of this paper is related to incorporation of statistical linearization, rather than commonly used analytical linearization, of the process and measurement models to provide a closer approximation of belief space propagation. Specifically, the state transition is approximated using an unscented transform to obtain a Gaussian belief space. This approximation allows for realization of closed-form solutions, which are otherwise available to linear systems only. Subsequently, the proposed approach is used to develop a model predictive motion control scheme that yields optimal control policies in presence of nonholonomic constraints as well as state estimation and collision avoidance chance constraints. As an example, successful kinematic control of a two-wheeled mobile robot is demonstrated in unstructured environments. Finally, the superiority of the proposed unscented model predictive control (MPC) over the traditional linearization-based MPC is discussed.     

Elimination of Constraint Violation and Accuracy Aspects in Numerical Simulation of Multibody Systems

Multibody systems are often modeled as constrained systems, and theconstraint equations are involved in the dynamics formulations. To makethe arising governing equations more tractable, the constraint equationsare differentiated with respect to time, and this results in unstablenumerical solutions which may violate the lower-order constraintequations. In this paper we develop a methodology for numerically exactelimination of the constraint violations, based on appropriatecorrections of the state variables (after each integration step) withoutany modification in the motion equations. While the elimination ofviolation of position constraints may require few iterations, theviolation of velocity constraints is removed in one step. The totalenergy of the system is sometimes treated as another measure of theintegration process inaccuracy. An improved scheme for one-stepelimination of the energy constraint violation is proposed as well. Theconclusion of this paper is, however, that the energy conservation is ofminor importance as concerns the improvement of accuracy of numericalsimulations. Some test calculations are reported.     

Robust optimization of constrained mechanical system with joint clearance and random parameters using multi-objective particle swarm optimization

Joint clearance and uncertainty are inevitable in mechanical systems due to design tolerance, abrasion, manufacture error, assembly error and imperfections. In this study, kinematic analysis and robust optimization of constrained mechanical systems with joint clearance and random parameters were performed. Joint clearance was modeled by Lankarani-Nikravesh contact force model, and probability space was applied for characterizing uncertain parameters. A kinematic analysis method based on Baumgarte approach and confidence region method was presented to predict kinematic error of the mechanical system. Slider-crank mechanism, an illustrative example was presented to show the influence of clearance and uncertainty on the kinematic accuracy. Then, a novel multi-objective robust optimization methodology was presented for kinematic accuracy robust optimization design of the constrained mechanical system. In this approach, a multi-objective robust optimization model derived from 95% confidence region is constructed to reduce the effects of clearance and parameter uncertainty on 95% confidence region of kinematic error. The robust optimization model is a double-loop process. A multi-objective robust optimization strategy, combing Kriging surrogate model, multi-objective particle swarm optimization, confidence region and Monte Carlo methods, was proposed to search the design variables for minimizing the optimization objectives derived from confidence region while balancing computational accuracy and efficiency of the optimization process. The optimal results of the slider-crank mechanism demonstrated the validity and feasibility of the proposed robust optimization method.     

On the robust control of two manipulators holding a rigid object

In this paper, a control architecture is developed for the closed chain motion of two six-joint manipulators holding a rigid object in a three-dimensional workspace. Dynamic and kinematic constraints are combined with the equations of motion of the manipulators to obtain a dynamical model of the entire system in the joint space. Reduced-order dynamic equations are then developed with regard to the position and force control variables. Robust control laws are then determined such that the force and position control design is decoupled. The control laws that will be discussed are: a robust position tracking controller that yields an exponentially stable position tracking error result, and a robust force tracking controller that yields adjustable bounds on the force tracking error.