A Rigorous Global Filtering Algorithm for Quadratic Constraints*

This article introduces a new filtering algorithm for handling systems of quadratic equations and inequations. Such constraints are widely used to model distance relations in numerous application areas ranging from robotics to chemistry. Classical filtering algorithms are based upon local consistencies and thus, are often unable to achieve a significant pruning of the domains of the variables occurring in quadratic constraint systems. The drawback of these approaches comes from the fact that the constraints are handled independently. We introduce here a global filtering algorithm that works on a tight linear relaxation of the quadratic constraints. The Simplex algorithm is then used to narrow the domains. Since most implementations of the Simplex work with floating point numbers and thus, are unsafe, we provide a procedure to generate safe linearizations. We also exploit a procedure provided by Neumaier and Shcherbina to get a safe objective value when calling the Simplex algorithm. With these two procedures, we prevent the Simplex algorithm from removing any solution while filtering linear constraint systems. Experimental results on classical benchmarks show that this new algorithm yields a much more effective pruning of the domains than local consistency filtering algorithms.*This article is an extended version of [23].     

Decentralized multi-robot allocation of tasks with temporal and precedence constraints

Abstract

We present an auction-based method for a team of robots to allocate and execute tasks that have temporal and precedence constraints. Temporal constraints are expressed as time windows, within which a task must be executed. The robots use our priority-based iterated sequential single-item auction algorithm to allocate tasks among themselves and keep track of their individual schedules. A key innovation is in decoupling precedence constraints from temporal constraints and dealing with them separately. We demonstrate the performance of the allocation method and show how it can be extended to handle failures and delays during task execution. We leverage the power of simulation as a tool to analyze the robustness of schedules. Data collected during simulations are used to compute well-known indexes that measure the risk of delay and failure in the robots’ schedules. We demonstrate the effectiveness of our method in simulation and with real robot experiments.     

装配配合约束自动获取技术研究

装配配合约束获取对于装配设计、装配工艺规划等多个领域的研究具有重要意义;现有的装配配合约束获取方法容易产生约束的遗漏和约束无效性；通过对自动获取配合约束技术进行研究，在充分利用CAD模型几何拓扑信息的基础上。提出了几何约束识别和配合验证相结合的装配配合约束自动获取箅法；实践证明，该方法可以显著地提高约束信息的获取效率、正确性和有效性。     

基于装配约束动态管理的虚拟拆卸

装配约束是虚拟拆卸环境下必须考虑的装配体的重要信息，提出虚拟拆卸过程中装配约束的动态管理机制，并实现了基于装配约束导航的虚拟拆卸。装配约束的动态管理包括虚拟环境下装配约束的获取、表达以及拆卸过程中装配约束的动态维护，即装配约束的动态解除和产生，文中用装配约束图表达零件间的装配约束，提出装配约束的间接解除方法，并实现了基于装配约束推理的零件可拆卸方向的推导。最后，通过一个简单装配体的拆卸实例，对文中方法进行了验证。     

对象族拓扑约束求解的研究

针对当前对象族模型在求解拓扑约束时存在的缺陷,提出一种求解拓扑约束的新方法,这种方法在求解拓扑约束时,把拓扑约束映射为布尔约束满足问题,通过用SAT求解器求解布尔约束来求解拓扑约束。实践证明,该方法不仅直接关联与拓扑约束指定的特征的语义,而且当模型中存在大量相交的特征时也是可行的,提高了拓扑约束求解的效率。     

Constrained stabilization problems for linear plants

Linear systems with magnitude and rate constraints on both the state and control variables are considered. For such systems, semi-global and global constrained stabilization problems are formulated when state feedback controllers are used. Necessary and sufficient conditions for the solvability of the formulated problems are developed. Moreover, design methodologies for such constrained stabilization problems are presented. An important aspect of our development here is a taxonomy of constraints to show clearly for what type of constraints what can or cannot be achieved.     

关于具有几何约束的三次代数曲线插值

给定四点pi(xi，yi)(i=1，2，3，4)以逆时针方向构成一简单四边形并在两端点p1和p4处给定两直线L1和L2。张三元等人提出和研究了一种通过上述四点并与L1和L2相切的代数曲线插值并建立了一些新的结果，作者进一步研究了这些代数曲线并给出了三次曲线C(λ)具有通过四点pi(xi，yi)(i=1，2，3，4)的连续凸曲线分支的充分且必要条件，也研究了当四边形不在控制区域上的其它情形。     

A Framework for Optimal Correction of Inconsistent Linear Constraints

The problem of inconsistency between constraints often arises in practice as the result, among others, of the complexity of real models or due to unrealistic requirements and preferences. To overcome such inconsistency two major actions may be taken: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as model correction is the problem we address in this paper in the context of linear constraints over the reals. The correction of the right hand side alone, which is very close to a fuzzy constraints approach, was one of the first proposals to deal with inconsistency, as it may be mapped into a linear problem. The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, that provide corrections with quite rigid patterns, the optimization of the important Frobenius norm was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global minimizer.     

配对组合测试中参数约束问题研究

给出了配对组合测试参数约束分类方法及相关定义。重点对有2值型约束的情况进行了研究,得出有2值型约束存在时虽然所需覆盖的配对数减少,但测试集不一定减小的结论;给出有2值型约束时测试集的最小下限,并证明之。最后介绍了能够有效解决配对组合测试参数约束问题的HPC_IPO约束控制算法。     

Algorithmic Power from Declarative Use of Redundant Constraints

Interval constraints can be used to solve problems in numerical analysis. In this paper we show that one can improve the performance of such an interval constraint program by the declarative use of constraints that are redundant in the sense of not needed to define the problem. The first example shows that computation of an unstable recurrence relation can be improved. The second example concerns a solver of nonlinear equations. It shows that, by adding as redundant constraints instances of Taylor's theorem, one can obtain convergence that appears to be quadratic.     

On Derivation of Motion Equations for Systems with Non-Holonomic High-Order Program Constraints

The paper develops and discusses the generalization of modeling methods for systems with non-holonomic constraints. The classification of constraints has been revisited and a concept of program constraints introduced. High-order non-holonomic constraints (HONC), as presented in examples, are the generalization of the constraint concept and may, as a constraint class, include many of motion requirements that are put upon mechanical systems. Generalized program motion equations (GPME) that have been derived in the paper can be applied to systems with HONC. Concepts of virtual displacements and a generalized variational principle for high-order constraints are presented. Classical modeling methods for non-holonomic systems based on Lagrange equations with multipliers, Maggi, Appell–Gibbs, Boltzman–Hamel, Chaplygin and others are peculiar cases of GPME. The theory has been illustrated with examples of high-order constraints. Motion equations have been derived for a system subjected to a constraint that programmed a trajectory curvature profile. Efficiency, advantages and disadvantages of GPME have been discussed.     

一种新的几何约束系统参数取值范围的计算方法

在利用参数化CAD系统进行图形设计的过程中,通过修改图形对象的可变参数重新生成图形是最常见的一种操作。但用户在改变参数的过程中,由于事先并不知道有效的参数值,也没有任何引导信息,导致了用户只能盲目地不断输入参数值,通过反复输入参数值来满足约束关系的需要。该文将结构约束引入参数有效取值范围求解的范畴,并提出了确定一类常用的二维参数化CAD模型中参数的有效范围的计算方法和算法。算法复杂度为O(n2) 。     

Reasoning about synchronization in GALS systems

Correct design of interface circuits is crucial for the development of System-on-Chips (SoC) using off-the-shelf IP cores. For correct operation, an interface circuit must meet strict synchronization timing constraints, and also respect sequencing constraints between events dictated by interfacing protocols and rational clock relations. In this paper, we propose a technique for automatically analyzing the interaction between independently specified synchronization constraints and sequencing constraints between events. We show how this analysis can be used to derive delay constraints for correct operation of interface circuits in a GALS system. Our methodology allows an SoC designer to mix and match different interfacing protocols, rational clock relations and synchronization constraints for communication between a pair of modules, and automatically explore their implications on correct interface circuit design.     

Adaptive Motion/Force Tracking Control for a Class of Mobile Manipulators

In this paper, modeling and adaptive motion/force tracking control is considered for a class of mobile manipulators under the holonomic and affine constraints with the presence of uncertainties and disturbances. Based on a suitable reduced dynamic model, adaptive controllers are proposed to ensure that the states of a closed‐loop system asymptotically track desired trajectories while the constraint force remains bounded by tuning design parameters. Detailed simulation results confirm the effectiveness of the control strategy.     

A note on stress-constrained truss topology optimization

The purpose of this brief note is to demonstrate that general-purpose optimization methods and codes should not be discarded when dealing with stress-constrained truss topology optimization. By using a disaggregated formulation of the considered problem, such methods may find also “singular optima”, without using perturbation techniques like the ε-relaxed approach. Received February 19, 2002     

Constraint Techniques for Authoring Multimedia Documents

Authoring a multimedia document requires to specify both its spatial layout and its temporal organization, i.e. when and where objects such as pictures, texts and videos appear/disappear on /from the screen and when objects such as audios and videos start/end to play. In this paper, we present some benefits authors can gain when using an authoring tool in which constraints are used to specify these two kinds of information. We describe our experience in building Madeus, a constraint-based environment to design multimedia documents and we point out technical problems that still need to be solved to more completely satisfy author requirements.     

基于仿真和知识的广义动态约束网络技术

针对并行协同设计中的参数不确定性,将普通的约束网络扩展为广义动态约束网络,以对设计中的不确定性信息进行管理.建立了包含领域级约束和知识级约束的广义动态约束网络模型;提出了基于仿真分析和自适应响应面法的领域级约束建模的有效方法,并提出模糊-粗糙集算法,对仿真结果进行数据挖掘,实现了知识级约束获取;基于模板技术给出了广义动态约束网络中各种约束的统一表示方法;构造了有效的约束冲突求解策略和一致性求解算法,求出一致性设计区间.最后通过设计实例验证了文中方法的有效性.     

基于柔性约束满足的企业集成协调方法

冲突是企业中常见的现象,对于企业集成这样一个几乎涉及企业所有方面的活动,更是会出现各种各样的冲突。论文提出采用约束满足的方式作为解决企业集成过程中冲突的消解方式。同时引入决策者对约束满足的偏好信息,对传统的约束满足问题进行扩展,利用柔性约束满足求解的思路,分层解决冲突问题,并将该方法应用于实际研究中,取得了较好的效果。     

特征向量变换求解装配约束的表示方法

基于装配零件的匹配特征的解析求解方法,利用装配特征的特征向量之间转换来确定零件之间的装配方向和相互位置关系．分析了平面之间共面、角度和平行约束,圆柱面之间同轴约束和圆锥面之间的重合等约束关系;并对几种常用的装配约束关系进行归类,给出了求解旋转矩阵和平移矩阵的统一的求解方法．文中方法同样适用于装配特征与装配体全局坐标轴倾斜情况．应用实例验证了该方法的有效性．     

Optimization of frame structures with flexible joints

In the traditional approach to analysing and optimizing frame structures, joints are assumed to be rigid. Research has shown, however, that flexibility in the joints of a structure has a great effect on its behaviour. In this paper we present a formal method for optimizing frame structures to account for joint flexibilities and their design parameter sensitivities. We also present a simplified method that accounts for joint flexibility in the initial configuration, but neglects sensitivities to the design parameters. In a case study on an automotive sub-frame structure we compare optimization results using the traditional rigid joint model and the flexible joint methods proposed here. Results suggest that the simplified flexible joint method is more accurate than the traditional rigid joint model, and provides a more conservative design than the full flexible joint method while saving physical and computational effort. Received January 18, 1999