复杂陈述式仿真模型的相容性分析

模型的相容性分析是复杂产品多领域建模面临的一个关键问题.研究了陈述式基于方程仿真模型的方程系统过约束或欠约束判定、检测与修正策略.首先,将方程系统表示为二部图,通过二部图分解判定模型的相容性,并分离出方程系统的过约束和欠约束部分.然后,通过检测、判定与缩减过程,自动判别出过约束或欠约束发生的大致范围,并给出修正方案.所提出的策略与算法能够显著地提高用户发现与排除过约束或欠约束问题的效率,已在多领域物理系统混合建模与仿真平台MWorks中实现.     

Joint Reaction Forces in Multibody Systems with Redundant Constraints

Redundant constraints are defined as those constraints which can be removed without changing the kinematics of the mechanism. They are usually eliminated from the mathematical model of a multibody system. For a given mechanism the set of redundant constraints can be chosen in many ways. Rigid body systems with redundant constraints do not have a unique solution to the problem of joint reaction forces calculation. If redundant constraints are present in the mechanical system, then the system is statically undetermined. If in the case of dynamics problem the constraints are consistent, all of them are frictionless and we are interested only in positions, velocities and accelerations of the bodies, then the calculation of joint reaction forces is not necessary. In many cases, however, e.g. when we want to take into account friction in joints, the calculation of joint reaction forces cannot be avoided. In some rigid body systems, despite the redundant constraints existence, reaction forces in selected joints can be uniquely determined. The paper presents three methods of finding the constraints for which reaction forces can be uniquely determined using rigid body model. Three different techniques of Jacobian matrix analysis are used.     

A leg proprioception based 6 DOF odometry for statically stable walking robots

This article presents a 3D odometry algorithm for statically stable walking robots that only uses proprioceptive data delivered by joint angle and joint torque sensors embedded within the legs. The algorithm intrinsically handles each kind of emerging statically stable gait and is independent of predefined gait patterns. Additionally, the algorithm can be equally applied to stiff robots as well as to robots with compliant joints. Based on the proprioceptive information a 6 degrees of freedom (DOF) pose estimate is calculated in three steps. First, point clouds, represented by the foot positions with respect to the body frame at two consecutive time steps, are matched and provide a 6 DOF estimate for the relative body motion. The obtained relative motion estimates are summed up over time giving a 6 DOF pose estimate with respect to the start frame. Second, joint torque measurement based pitch and roll angle estimates are determined. Finally in a third step, these estimates are used to stabilize the orientation angles calculated in the first step by data fusion employing an error state Kalman filter. The algorithm is implemented and tested on the DLR Crawler, an actively compliant six-legged walking robot. For this specific robot, experimental data is provided and the performance is evaluated in flat terrain and on gravel, at different joint stiffness settings and for various emerging gaits. Based on this data, problems associated with the odometry of statically stable walking robots are identified and discussed. Further, some results for crossing slopes and edges in a complete 3D scenario are presented.     

A new constructive approach to constraint-based geometric design

In the paper, a new constructive approach to solving geometric constraints in 2-D space is presented. Constraints are employed on lines and points only, but more sophisticated geometric elements like Bézier curves and ellipses can also be constrained by mapping them onto auxiliary lines and points. The algorithm is based on local propagation, but first, the problem is transformed into a form that guarantees success of employing this simple technique. The most important steps are substitution of complex constraints with sets of simpler ones and insertion of redundant constraints by solving triangles and determining sums and differences of adjacent angles. In this way, various well-constrained problems with a few exceptions are solved, over-constrained scenes and input data contradictory to some well-known mathematical theorems are detected, and the algorithm is proved successful in many under-constrained cases as well.     

Solving Interval Constraints by Linearization in Computer-Aided Design

Current parametric CAD systems require geometric parameters to have fixed values. Specifying fixed parameter values implicitly adds rigid constraints on the geometry, which have the potential to introduce conflicts during the design process. This paper presents a soft constraint representation scheme based on nominal interval. Interval geometric parameters capture inexactness of conceptual and embodiment design, uncertainty in detail design, as well as boundary information for design optimization. To accommodate under-constrained and over-constrained design problems, a double-loop Gauss-Seidel method is developed to solve linear constraints. A symbolic preconditioning procedure transforms nonlinear equations to separable form. Inequalities are also transformed and integrated with equalities. Nonlinear constraints can be bounded by piecewise linear enclosures and solved by linear methods iteratively. A sensitivity analysis method that differentiates active and inactive constraints is presented for design refinement.     

三维几何约束系统的等价性分析

针对过约束、完整约束和欠约束三维几何约束系统的求解问题,提出了等价性分析方法.该方法基于三维几何约束系统的内在等价性,充分挖掘几何领域知识,依据拆解约束闭环、缩减约束闭环和析出约束闭环等原则,采用等价约束替换来处理几何约束闭环问题,优化几何约束图的结构,实现几何约束系统的优化分解.最后用多个实例验证了该方法的正确性和有...     

快速判定几何约束奇异性的切面扰动法

针对冗余奇异和分支奇异的判定问题,提出一种新的切面扰动的判定方法.该方法将奇异的雅可比矩阵分为独立构型空间和奇异空间,变量沿独立构型空间的切面扰动,计算更新的雅克比矩阵的秩,依据秩亏的变化可以快速、稳定地判定约束奇异性.该算法克服了残量扰动法的数值迭代、计算量大和不稳定的缺点,并且在参数化特征造型系统InteSolid中得到验证.     

Enumeration of optimal pin-jointed bistable compliant mechanisms with non-crossing members

An optimization approach is presented for enumerating pin-jointed bistable compliant mechanisms. In the first stage, the statically determinate trusses with non-crossing members containing a given set of nodes and some pre-defined members are regarded as minimally rigid framework or a Laman framework, and are enumerated without repetitions by the graph enumeration algorithm. In the second stage, the nodal locations and the cross-sectional areas are optimized under mechanical constraints, where the snapthrough behavior is extensively utilized to produce a pin-jointed bistable compliant mechanism. In the numerical examples, many bistable compliant mechanisms are generated to show the effectiveness of the proposed method.     

Optimization of singular problems

A new optimization method is presented that optimizes singular structures. An example of a singular problem is deleting an inefficient member from a structure. As the member is deleted, the stresses in the member may increase above the allowables. When a member is deleted the nature of the analysis changes because the member stiffness becomes zero. This causes a local optima because stress constraints prevent inefficient members from zeroing. The problem is reformulated using the percent method so that the appropriate stress constraints are deleted as the member is deleted. Several examples show that the global optimal design is reached. Other methods to reach the global optima are appropriate only if the optimal structure is statically determinate. The percent optimization is also useful for optimization of discrete problems.     

空间机器人捕获航天器操作的避撞柔顺复合自抗扰控制

讨论空间机器人在轨捕获非合作航天器过程避免关节受冲击力矩破坏的避撞柔顺控制问题.在机械臂与关节电机之间配置一种弹簧类柔顺装置——旋转型串联弹性执行器(RSEA),其作用在于:1)在捕获碰撞阶段,可通过其内置弹簧的变形吸收碰撞产生的能量;2)在镇定运动阶段,结合避撞柔顺策略适时开、关电机,以保证关节所受冲击力矩受限在安全范围.首先,应用拉格朗日方法和牛顿-欧拉法分别得到捕获前空间机器人及目标航天器系统动力学方程;然后,结合整个系统动量守恒关系,捕获操作后速度约束关系及力的传递规律,建立捕获后两者形成联合体系统的动力学方程;最后,针对失稳的联合体系统提出一种基于复合误差的避撞柔顺自抗扰控制方案以实现其镇定控制.系统数值仿真结果表明了上述避撞柔顺策略的有效性.     

Power system control with minimum eigenvalue sensitivity to operating conditions

Power system dynamics around an operating point can be represented by a multi-input linear time invariant state equation . When an unrestricted rank constant state feedback matrix F is used for exact pole assignment in a multi-input linear system there are degrees of freedom available for optimising additional criteria if necessary. In this paper it is shown how this design freedom can be utilized to minimize the sensitivity of the closed loop poles to variations in the matrix A (due to changes in operating conditions of Power system).

The advantage of using a controller of unrestricted rank over a unity rank controller is shown.     

三维装配约束推理的球面几何和球面机构法

分析了装配姿态约束和位置约束的可解耦性,提出求解姿态约束的球面几何和球面机构法.将姿态约束的组合分为可操作和不可操作的情形,可操作的情形利用简单的球平面中平移、旋转和刚性变换推理,快速地判定冗余约束和求解约束;不可操作的情形利用球面四杆机构求解.该方法具有很强的几何解释性和可操作性,降低求解复杂度.该方法在自主研发的CAD浏览器系统InteVue中实现.     

Rigid body mode and spurious mode in the dual boundary element formulation for the Laplace problems

In this paper, the general formulation for the static stiffness is analytically derived using the dual integral formulations. It is found that the same stiffness matrix is derived by using the integral equation no matter what the rigid body mode and the complementary solutions are superimposed in the fundamental solution. For the Laplace problem with a circular domain, the circulant was employed to derive the stiffness analytically in the discrete system. In deriving the static stiffness, the degenerate scale problem occurs when the singular influence matrix can not be inverted. The Fredholm alternative theorem and the SVD updating technique are employed to study the degenerate scale problem mathematically and numerically. The direct treatment in the matrix level is achieved to deal with the degenerate scale problems instead of using a modified fundamental solution. The addition of a rigid body term in the fundamental solution is found to shift the zero singular value for the singular matrix without disturbing the stiffness.     

Revealing matrices of linear differential systems of arbitrary order

If the leading matrix of a linear differential system is nonsingular, then its determinant is known to bear useful information about solutions of the system. Of interest is also the frontal matrix. However, each of these matrices (we call them revealing matrices) may occur singular. In the paper, a brief survey of algorithms for transforming a system of full rank to a system with a nonsingular revealing matrix of a desired type is given. The same transformations can be used to check whether the rank of the original system is full. A Maple implementation of these algorithms (package EGRR) is discussed, and results of comparison of estimates of their complexity with actual operation times on a number of examples are presented.     

基于刚体运动与弹性运动的机械系统动力学建模研究

讨论了具有刚体运动与柔性变形的机械系统的动力学建模,将刚体自由度与弹性变形自由度看作广义坐标,利用有限元法对具有刚性运动与弹性变形的机械系统的运动与变形进行了描述,得到了以刚体位移与弹性变形位移表示的单元的广义惯性力;从应力应变入手,得到了表示单元弹性变形与几何非线性变形的结构刚度矩阵与几何非线性刚度矩阵,使用Kane方程推导了弹性连杆机构的单元运动方程,这种建模方法,可以使用在任意结构的机械系统。     

Singularity Analysis of Geometric Constraint Systems

Singularity analysis in an important subject of the geometric constraint satisfaction problem.In this paper,three kinds of singularities are described and corresponding identifcation methods are presented for both under0constrained systems and over-constrained systems,Another special but common singularity for under-constrained geometric systems,pseudo-singularity,is analyzed.Pseudo-singularity is caused by a variety of constraint mathching of under-constrained systems and can be removed by improving constraint distribution.To avoid pseudo-singularity and decide redundant constraints adaptively,a differentiaiton algorithm is proposed in the paper.Its corrctness and effciency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.     

A constructive approach to solving 3-D geometric constraint systems using dependence analysis

Solving geometric constraint systems in 3-D is much more complicated than that in 2-D because the number of variables is larger and some of the results valid in 2-D cannot be extended for 3-D. In this paper, we propose a new DOF-based graph constructive method to geometric constraint systems solving that can efficiently handle well-, over- and under-constrained systems based on the dependence analysis. The basic idea is that the solutions of some geometric elements depend on some others because of the constraints between them. If some geometric elements depend on each other, they must be solved together. In our approach, we first identify all structurally redundant constraints, then we add some constraints to well constrain the system. And we prove that the order of a constraint system after processing under-constrained cases is not more than that of the original system multiplied by 5. After that, we apply a recursive searching process to identify all the clusters, which is shown to be capable of getting the minimum order-reduction result of a well-constrained system. We also briefly describe the constraint evaluation phase and show the implementation results of our method.     

A linear quadrilateral shell element with fast stiffness computation

A new quadrilateral shell element with 5/6 nodal degrees of freedom is presented. Assuming linear isotropic elasticity a Hellinger–Reissner functional with independent displacements, rotations and stress resultants is used. Within the mixed formulation the stress resultants are interpolated using five parameters for the membrane forces as well as for the bending moments and four parameters for the shear forces. The hybrid element stiffness matrix resulting from the stationary condition is integrated analytically. This leads to a part obtained by one point integration and a stabilization matrix. The element possesses the correct rank, is free of locking and is applicable within the whole range of thin and thick shells. The in-plane and bending patch tests are fulfilled and the computed numerical examples show that the convergence behaviour of the stress resultants is very good in comparison to comparable existing elements. The essential advantage is the fast stiffness computation due to the analytically integrated matrices.     

Effects of planar element formulation and numerical integration order on checkerboard material layouts

The effects of selected planar finite element formulations, and their associated integration schemes, on the stiffness of a checkerboard material layout are investigated. Standard 4-node bilinear elements, 8- and 9-node quadratic elements, as well as 4-node elements with drilling degrees of freedom are considered. Integration schemes evaluated include popular Gauss quadrature rules, as well as modified 5- and 8-point integration schemes. It is shown that, although checkerboarding may be slightly alleviated when using elements with drilling degrees of freedom, the homogenized checkerboard stiffness is identical to that of standard bilinear elements. This is significant since elements with drilling degrees of freedom are derived from an 8-node parent element. We do however demonstrate that modified reduced integration schemes, applied to quadratic elements, effectively reduce the stiffness of a checkerboard material layout. Furthermore, the proposed schemes effectively suppress spurious zero energy modes which may occur on the element level in topology optimization.