Redundant Constraints Research Articles

Joint reactions in rigid body mechanisms with dependent constraints

The problem of calculating joint reaction forces in rigid body mechanisms with dependent constraints is discussed. Two essentially different reasons of constraint dependency are considered: the existence of redundant constraints and singular configuration of the mechanism. It is known that if constraint equations are dependent, the constraint reaction forces cannot be uniquely determined. In this paper it is shown that despite the fact that all of the constraint reactions cannot be uniquely determined, selected single constraint reactions or selected groups of reactions can be specified uniquely. Conditions, which must be fulfilled to obtain unique values of selected reaction forces in the presence of dependent constraints, are presented and proven. The concept of direct sum, known from linear algebra, is exploited. These purely mathematical conditions form a basis for numerical methods that enable detection of constraints with uniquely solvable reactions. Three different numerical methods are proposed. These methods are confined to constraint Jacobian matrix analysis, thus they can be easily implemented in a multibody software. Finally, two examples of detection of constraints with uniquely solvable reactions are presented.

Synthesis of multi-degree of freedom, parallel flexure system concepts via freedom and constraint topology (FACT). Part II: Practice

In Part II of this paper we demonstrate how to use freedom and constraint topology (FACT) to synthesize concepts for the multi-degree of freedom, parallel precision flexure systems that fall within the scope of Part I. Several examples are provided to demonstrate how the Principle of Complementary Topologies and geometric entities from Part I are (i) relevant to flexure system characteristics, (ii) used to visualize the possible layout of flexure constraints to achieve a desired motion and (iii) used to select redundant constraints. A synthesis process is presented, and then used to visualize and construct a flexure system concept with the requisite kinematic characteristics and redundant constraints that provide increased stiffness, load capacity, and symmetry. The output of the process is a flexure concept that would then be modeled and refined by existing modeling and analysis methods.

Eliminating constraint drift in the numerical simulation of constrained dynamical systems

By means of the Udwadia–Kalaba approach we propose an explicit equation of constrained motion developed to simulate constrained dynamical systems without error accumulation due to constraint drift. The basic idea is to embed a small virtual force and a small virtual impulse to the equation of motion, in order to avoid the drift typically experienced in constrained multibody simulations. The embedded correction terms are selected to minimally alter the dynamics in an acceleration and kinetic energy norm sense. The formulation allows one to use a standard ODE solver, avoiding the need for iterative constraint stabilization. The equation is based on the pseudoinverse of a constraint matrix such that it can be used under redundant constraints and kinematic singularities. The proposed method takes into account the finite word-length of the computational environment, and also accommodates possibly inconsistent initial conditions.

A novel method for predicting and using distance constraints of high accuracy for refining protein structure prediction

The principal bottleneck in protein structure prediction is the refinement of models from lower accuracies to the resolution observed by experiment. We developed a novel constraints-based refinement method that identifies a high number of accurate input constraints from initial models and rebuilds them using restrained torsion angle dynamics (rTAD). We previously created a Bayesian statistics-based residue-specific all-atom probability discriminatory function (RAPDF) to discriminate native-like models by measuring the probability of accuracy for atom type distances within a given model. Here, we exploit RAPDF to score (i.e., filter) constraints from initial predictions that may or may not be close to a native-like state, obtain consensus of top scoring constraints amongst five initial models, and compile sets with no redundant residue pair constraints. We find that this method consistently produces a large and highly accurate set of distance constraints from which to build refinement models. We further optimize the balance between accuracy and coverage of constraints by producing multiple structure sets using different constraint distance cutoffs, and note that the cutoff governs spatially near versus distant effects in model generation. This complete procedure of deriving distance constraints for rTAD simulations improves the quality of initial predictions significantly in all cases evaluated by us. Our procedure represents a significant step in solving the protein structure prediction and refinement problem, by enabling the use of consensus constraints, RAPDF, and rTAD for protein structure modeling and refinement.

An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation

This paper presents an efficient hybrid method for dynamic analysis of a flexible multibody system. This hybrid method is the combination of a penalty and augmented Lagrangian formulation with the mass-orthogonal projections method based on the absolute nodal coordinate formulation (ANCF). The characteristic of the ANCF that the mass matrix is constant and both Coriolis and centrifugal terms vanish in the equations of motion make the proposed method computationally efficient. Within the proposed method, no additional unknowns, such as the Lagrange multipliers in the Newmark method, are introduced, and the number of equations does not depend on the number of constraint conditions. Furthermore, conventional integration stabilization methods, such as Baumgarte’s method. are unnecessary. Therefore, the proposed method is particularly suitable for systems with redundant constraints, singular configurations, or topology changes. Comparing results from different methods in terms of efficiency and accuracy has shown that the proposed hybrid method is efficient and has good convergence characteristics for both stiff and flexible multibody systems.

The Elimination of Redundant Constraints in Surprisal Analysis of Unimolecular Dissociation and Other Endothermic Processes

It is well understood that energy rich polyatomic molecules do not dissociate promptly because the number, P, of their energy states far exceeds the number, N, of the decay channels. In the simplest RRK theory, the fraction N/P is the probability of dissociation. We discuss the distribution of the decay rates of maximal entropy and conclude that it is governed by at most N linearly independent constraints, N < P, or, more typically, N << P. This mathematical requirement already severely restricts the number of constraints. Beyond it however, on physical grounds, one constraint, or at most a few, may be dominant. We discuss why just one constraint, or a few but less than N, can be sufficient to describe the product state distribution.

An Exact Approach to the One-Dimensional Facility Layout Problem

The one-dimensional facility layout problem is concerned with arranging n departments of given lengths on a line, while minimizing the weighted sum of the distances between all pairs of departments. The problem is NP-hard because it is a generalization of the minimum linear arrangement problem. In this paper, a 0-1 quadratic programming model consisting of only O(n2) 0-1 variables is proposed for the problem. Subsequently, this model is cast as an equivalent mixed-integer program and then reduced by preprocessing. Next, additional redundant constraints are introduced and linearized in a higher space to achieve an equivalent mixed 0-1 linear program, whose continuous relaxation provides an approximation of the convex hull of solutions to the quadratic program. It is shown that the resulting mixed 0-1 linear program is more efficient than previously published mixed-integer formulations. In the computational results, several problem instances taken from the literature were efficiently solved to optimality. Moreover, it is now possible to efficiently solve problems of a larger size.

Propagating systems of dense linear integer constraints

In interval propagation approaches to solving nonlinear constraints over reals it is common to build stronger propagators from systems of linear equations. This, as far as we are aware, is not pursued for integer finite domain propagation. In this paper we show how we use interval Gauss---Jordan elimination to build stronger propagators for an integer propagation solver. In a similar fashion we present an interval Fourier elimination preconditioning technique to generate redundant linear constraints from a system of linear inequalities. We show how to convert the resulting interval propagators into integer propagators. This allows us to use existing integer solvers. We give experiments that show how these preconditioning techniques can improve propagation performance on dense systems.

A redundant Klee–Minty construction with all the redundant constraints touching the feasible region

We have previously shown, by redundant Klee–Minty constructions, that the central path may arbitrarily closely visit every vertex of the Klee–Minty cube. In those constructions, the redundant constraints are far away from the feasible region. In this paper, we provide a construction in which all redundant constraints touch the feasible region.

Integrated design of supply chain networks with three echelons, multiple commodities and technology selection

We consider a strategic supply chain design problem with three echelons, multiple commodities and technology selection. We model the problem as a tri-echelon, capacitated facility location problem that decides on the location of plants and warehouses, their capacity and technology planning, the assignment of commodities to plants and the flow of commodities to warehouses and customer zones. We use a mixed-integer programming formulation strengthened by valid but redundant constraints and apply Lagrangean relaxation to decompose the problem by echelon. Lagrangean relaxation provides a lower bound that is calculated using an interior-point cutting plane method. Feasible solutions are generated using a primal heuristic that uses the solution of the subproblems. Unlike common practice in the literature, the decomposition does not aim at getting easy subproblems, but rather at getting subproblems that preserve most of the characteristics of the original problem. Not only does this provide a sharp lower bound but also leads to a simple and efficient primal heuristic. We can afford to have relatively difficult subproblems because the interior-point cutting plane method used to solve the Lagrangean dual makes clever and selective choices of the Lagrangean multipliers leading to fewer calls to the subproblems. Computational results indicate the efficiency of the approach in providing a sharp bound and in generating feasible solutions that are of high quality.

Smoothing Lipschitz functions

This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties of f. Depending on the assumptions about the distribution of the random noise, smoothing is reduced to a standard quadratic or a linear programming problem. We discuss an efficient algorithm which eliminates the redundant inequality constraints. Numerical experiments illustrate applicability and efficiency of the method. This approach provides an efficient new tool of multivariate scattered data approximation.

Identifying redundant linear constraints in systems of linear matrix inequality constraints

Semidefinite programming has been an interesting and active area of research for several years. In semidefinite programming one optimizes a convex (often linear) objective function subject to a system of linear matrix inequality constraints. Despite its numerous applications, algorithms for solving semidefinite programming problems are restricted to problems of moderate size because the computation time grows faster than linear as the size increases. There are also storage requirements. So, it is of interest to consider how to identify redundant constraints from a semidefinite programming problem. However, it is known that the problem of determining whether or not a linear matrix inequality constraint is redundant or not is NP complete, in general. In this paper, we develop deterministic methods for identifying all redundant linear constraints in semidefinite programming. We use a characterization of the normal cone at a boundary point and semidefinite programming duality. Our methods extend certain redundancy techniques from linear programming to semidefinite programming.

A simpler and tighter redundant Klee–Minty construction

By introducing redundant Klee-Minty examples, we have previously shown that the central path can be bent along the edges of the Klee-Minty cubes, thus having 2 n 2 sharp turns in dimension n. In those constructions the redundant hyperplanes were placed parallel with the facets active at the optimal solution. In this paper we present a simpler and more powerful construction, where the redundant constraints are parallel with the coordinate-planes. An important consequence of this new construction is that one of the sets of redundant hyperplanes is touching the feasible region, and N, the total number of the redundant hyperplanes is reduced by a factor of n 2 , further

Constraint-based beautification and dimensioning of 3D polyhedral models reconstructed from 2D sketches

3D models reconstructed from 2D sketches are inaccurate because of the inherent inaccuracies in the input and the reconstruction method. It is therefore necessary to “beautify” them before use in CAD systems. We present a method that detects geometric constraints, such as parallel and orthogonal faces, present in the reconstructed model and then selects a subset that constrains the object sufficiently and consistently. The subset selection algorithm first prioritizes the constraints depending on their type and then uses a novel method, based on quasi-Newton optimization, to detect and eliminate redundant and inconsistent constraints. The remaining constraints then define the dimensions of the model fully and consistently. Results from our implementation show that the method can beautify and dimension recovered 3D models correctly at acceptable speed.

Robust preliminary analysis of large-scale linear model for optimal industrial investments

Which equipment should be bought for a given sum to increase the profit of an industrial enterprize with a known specification of production within given limits? This problem is described as a large-scale linear program (LP) of a specific structure. An effective preliminary analysis for this structure was proposed in Ioslovich and Makarenkov [On methods of dimensionality reduction in linear programming, Econ. Math. Methods Moscow (in Russian) 11(3) (1975) 316–324] which aimed to reduce the size of the problem by detection of the redundant and active constraints. In this paper a robust system is considered, dealing with box-constrained uncertainties in the input coefficients. The analysis is based on robust evaluations of bounds for primal and dual constraints. A robust evaluation of uncertain duals presented in [I. Ioslovich, P.-O. Gutman, Robust redundancy determination and evaluation of the dual variables of linear programming problems in the presence of uncertainty, 1, in, V. Kucera, M. Sebek (Eds.), Proceedings of 3rd IFAC Symposium on Robust Control Design (ROCOND 2000), IFAC, Prague, Czech Republic, Elsevier Science, Amsterdam, 2000, paper 115] is essentially used.

Removing propagation redundant constraints in redundant modeling

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logically implied by others in the problem model. However, some redundant constraints are propagation redundant and hence do not contribute additional propagation information to the constraint solver. Redundant constraints arise naturally in the process of redundant modeling where two models of the same problem are connected and combined through channeling constraints. In this paper, we give general theorems for proving propagation redundancy of one constraint with respect to channeling constraints and constraints in the other model. We illustrate, on problems from CSPlib (http://www.csplib.org), how detecting and removing propagation redundant constraints in redundant modeling can speed up search by several order of magnitudes.

Integrated Production-Inventory-Distribution System Design with Risk Pooling: Model Formulation and Heuristic Solution

In this paper, we consider a multiproduct two-echelon production-inventory-distribution system design model that captures risk-pooling effects by consolidating the safety-stock inventory of the retailers at distribution centers (DCs). We propose a model that determines plant and DC locations, shipment levels from plants to the DCs, safety-stock levels at DCs, and the assignment of retailers to DCs by minimizing the sum of fixed facility location costs, transportation costs, and safety-stock costs. The model is formulated as a nonlinear mixed-integer programming problem and linearized using piecewise-linear functions. The formulation is strengthened using redundant constraints. Lagrangean relaxation is applied to decompose the problem by echelon. A lower bound is provided by the Lagrangean relaxation, while a heuristic is proposed that uses the solution of the subproblems to construct an overall feasible solution. Computational results reveal that the Lagrangean relaxation provides a sharp lower bound and a heuristic solution that is within 5% of the optimal solution.

On the generalized Wolf problem: Preprocessing of nonnegative large-scale linear programming problems with group constraints

Nonnegative large-scale linear programming problems with group constraints are extremely important for different applications in economics, technology, and other spheres. In this paper, we describe a new approach to preprocessing of these problems so that to reduce their dimensions considerably by defining and removing redundant constraints and variables.

Deadline constrained cyclic scheduling on pipelined dedicated processors considering multiprocessor tasks and changeover times

This paper presents a scheduling technique used to optimize computation speed of loops running on architectures that may include pipelined dedicated processors. The problem under consideration is to find an optimal periodic schedule satisfying the timing constraints. Motivated by FPGA (Field-Programmable Gate Array) architecture we formulate a problem of cyclic scheduling on one dedicated processor where tasks are constrained by the precedence delays. Further we generalize this result to the set of dedicated processors. We also show how the set of constraints in both problems can be extended by start time related deadlines, multiprocessor tasks, changeover times and minimization of data transfers. We prove that this problem is NP-hard by reduction from Bratley’s scheduling problem 1 | r j , d ˜ j | C max and we suggest a solution based on ILP (Integer Linear Programming) that allows one to minimize the completion time. Besides this, we suggest elimination of redundant constraints and binary variables in a integer linear programming model which leads to a speedup of the scheduling algorithm. Finally, experimental results are shown on an application of recursive least square filter and benchmarks.

3216 肘拘束を利用した冗長マニピュレータ型レスキューロボットに関する研究(J25-3 メカニカルシステムとその知能化(3),J25 メカニカルシステムとその知能化)

3216 肘拘束を利用した冗長マニピュレータ型レスキューロボットに関する研究(J25-3 メカニカルシステムとその知能化(3),J25 メカニカルシステムとその知能化)