Linear complementarity, linear and nonlinear programming

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Linear complementarity, linear and nonlinear programming

01 Jan 1988-

About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.

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Using simulation for planning and design of robotic systems with intermittent contact

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Jeff Trinkle¹, Stephen Berard¹•Institutions (1)

Rensselaer Polytechnic Institute¹

01 Jan 2009

TL;DR: Four new time-stepping methods are introduced and a new non-recursive nonlinear filter is presented using the model of these systems, which allows us to estimate the system's parameters, which is a necessary requirement for using simulation for planning and design.

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Abstract: For robotic systems to automatically plan and execute manipulation tasks involving intermittent contact, one must be able to accurately predict the motions of the manipulated objects. Not surprisingly, many of the important manipulation problems that could yield to closed-form analysis have been solved and studied thoroughly. Problems characterized by intermittent contact are one particularly important type of robotics problem for which research must rely on simulation techniques. Due to the intermittency of contact and the presence of stick-slip frictional behavior, dynamic models of such multibody systems are inherently (mathematically) nonsmooth, and are thus difficult to integrate accurately or quickly. Commercially available software tools have a difficult time simulating systems with unilateral constraints, that is constraints where touching bodies are allowed to touch or separate, but not interpenetrate. Users expect to spend considerable effort in a trial-and-error search for good simulation parameters to obtain believable, not necessarily accurate, results. Even the seemingly simple problem of a sphere rolling on a horizontal plane under only the influence of gravity is challenging for commercial simulators. The correct handling of unilateral contact constraints is one of the most difficult challenges left for many commercial simulation software packages. This thesis relates to the use of simulation for planning and design of robotics systems with intermittent contact. As previously noted, such systems arise in many applications, including automated manufacturing, health care, and personal robotics. The relationship between these seemingly unrelated application areas is forged by the desire of interactive robotic devices situated in an unstructured world. A better understanding of the dynamics, especially the contact dynamics, will allow us to improve the autonomy of these systems. In the first part of this work, we introduce four new time-stepping methods, which were constructed for a variety of reasons, including accuracy, performance, and design. Next, we developed a simulation software package (dubbed daVinci Code) that implements these new methods. This software tool facilitates the simulation, analysis, and virtual design of multibody systems with intermittent frictional unilateral contact. Next, a study on the applicability of our time-stepping method is presented. We performed a numerical study on the accuracy of our methods, and experimentally validated our time-stepper on a system composed of a vibrating rigid plate and interacting part. With the accuracy of our time-stepper verified for this system, we were able to study the inverse problem of designing new plate motions to generate a desired part motion. Lastly, we present our initial results of a new non-recursive nonlinear filter using our model of these systems. This filter allows us to estimate the system's parameters, which is a necessary requirement for using simulation for planning and design. The filtering problem is particularly challenging, since the underlying mathematical model is nonsmooth.

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15 citations

Journal Article•DOI•

A Time‐Stepping Algorithm for Stiff Mechanical Systems with Unilateral Constraints

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K. Funk¹, Friedrich Pfeiffer¹•Institutions (1)

Technische Universität München¹

01 Mar 2003-Pamm

TL;DR: In this paper, a stable implicit first-order time-stepping method for simulation of stiff mechanical systems with unilateral constraints and Coulomb friction is presented, which ensures that the unilateral constraints are fulfilled directly on the displacement level.

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Abstract: This paper presents a stable implicit first order time-stepping method for the simulation of stiff mechanical systems with unilateral constraints and Coulomb friction. It ensures that the unilateral constraints are fulfilled directly on the displacement level. The resulting linear complementarity problem is formulated in a very compact nonstandard way. A modified form of Lemke's algorithm is presented to solve it.

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15 citations

Journal Article•DOI•

On singular N0-matrices and the class Q

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S. K. Neogy¹, A. K. Das¹•Institutions (1)

Indian Statistical Institute¹

01 Feb 2011-Linear Algebra and its Applications

TL;DR: In this article, the authors studied singular N 0 -matrices with Q-property and showed that the class of N and N 0-matrices arises in the theory of global univalence of functions, multivariate analysis and complementarity theory.

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15 citations

Journal Article•DOI•

Complementarity framework for non‐linear dynamic analysis of skeletal structures with softening plastic hinges

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Mettupalayam V. Sivaselvan¹•Institutions (1)

University of Colorado Boulder¹

15 Apr 2011-International Journal for Numerical Methods in Engineering

TL;DR: In this article, an algorithm for the incremental state update of elasto-plastic systems with softening is described, which uses a complementary pivoting technique and is based on casting the incremental update as a complementarity problem.

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Abstract: In this paper, we describe an algorithm for the incremental state update of elasto-plastic systems with softening. The algorithm uses a complementary pivoting technique and is based on casting the incremental state update as a complementarity problem. In developing the algorithm, we take advantage of the special features of solid and structural mechanics problems to achieve good computational performance, and hence the ability to compute numerical solutions to practical size problems. For example, the notion of a tangent stiffness matrix arises. Numerical examples using models of skeletal structures are presented to demonstrate the practicability of the algorithm. The numerical examples also raise some interesting questions about multiplicity of the solutions. Copyright © 2010 John Wiley & Sons, Ltd.

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15 citations

Cites methods from "Linear complementarity, linear and ..."

...For example, in References [30, 34] the PATH solver [7] for complementarity problems is used, and Krabbenhoft et al. [4] use an interior point algorithm for optimization....
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...We first obtain all the solutions of this MCP by enumerating the 212 complementary cones [6], and compare these with the solutions obtained using Approaches 1–4....
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...For example, techniques to approximate the yield function in plasticity by piecewise planar surfaces are discussed in References [37, 38]....
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...For example, multiplicity of solutions to the state update problem is explored in Reference [30] for quasibrittle fracture analysis, and in References [31, 32] for skeletal structures with softening....
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...We refer the reader to References [13, 16–23] as examples of recent work related to the latter two classes....
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Analyse und Synthese elektromechanischer Systeme

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Olaf Enge

03 Mar 2005

15 citations

Cites background from "Linear complementarity, linear and ..."

...durch Abbildung des NCP auf äquivalente Punktmengen [161])....
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...Der Lemke-Algorithmus und ähnliche Verfahren werden in den Standardwerken [25, 26, 161] aber z....
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...Der Lemke-Algorithmus und ähnliche Verfahren werden in den Standardwerken [25, 26, 161] aber z.B. auch bei Seyfferth [212] ausführlich beschrieben....
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...Dieses Problem kann als ein LCP in Standardform ([26], [161]) formuliert werden....
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...Auch für NCP sind neben der oben erwähnten Linearisierung (und Lösung mittels LCP) noch andere Lösungsverfahren bekannt (z.B. durch Abbildung des NCP auf äquivalente Punktmengen [161])....
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Linear complementarity, linear and nonlinear programming

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Cites methods from "Linear complementarity, linear and ..."

Cites background from "Linear complementarity, linear and ..."

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