Proper Perturbation Research Articles

Sensitivity Analysis in Parametrized Convex Vector Optimization

This paper provides some results concerning sensitivity analysis in parametrized convex vector optimization. We consider three types of perturbation maps (i.e., perturbation map, proper perturbation map, and weak perturbation map) according to three kinds of solution concepts (i.e., minimality, proper minimality, and weak minimality with respect to a fixed ordering cone) for a vector optimization problem. As for general vector optimization, authors have already established the behavior of the above three types of perturbation maps by using the concept of contingent derivatives for set-valued maps in finite dimensional Euclidean spaces. In this paper we concentrate on convex vector optimization and provide quantitative properties of the perturbation maps under some convexity assumptions. Namely, we investigate the relationships between the contingent derivatives of the perturbation maps and those of the feasible set map in the objective space.

Sensitivity analysis in vector optimization

For a vector optimization problem that depends on a parameter vector, the sensitivity analysis of perturbation, proper perturbation, and weak perturbation maps is dealth with. Each of the perturbation maps is defined as a set-valued map which associates to each parameter value the set of all minimal, properly minimal, and weakly minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering cone. Using contingent cones in a finite-dimensional Euclidean space, we investigate the relationship between the contingent derivatives of the three types of perturbation maps and three types of minimal point sets for the contingent derivative of the feasible-set map in the objective space. These results provide quantitative informations on the behavior of the perturbation maps.

A fast approach for the robust trajectory planning of redunant robot manipulators

AbstractIn this article, a fast approach for robust trajectory planning, in the task space, of redundant robot manipulators is presented. The approach is based on combining an original method for obstacle avoidance by the manipulator configuration with the traditional potential field approach for the motion planning of the end‐effector. This novel method is based on formulating an inverse kinematics problem under an inexact context. This procedure permits dealing with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Furthermore, it is also shown that this formulation allows one to deal effectively with the local minimum problem frequently associated with the potential field approaches. The computation of the inverse kinematics problem is accomplished by numerically solving a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoinverse perturbation to deal with the singularities and/or the potential function local minima. These properties make the proposed approach suitable for redundant robots operating in real time in a sensor‐based environment. The developed algorithm is tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach compares favorably with the other approaches that have recently been proposed. © 1995 John Wiley & Sons, Inc.

Procedure for manipulator inverse kinematics computation and proper pseudoinverse perturbation

In this article, an efficient procedure for the proper pseudoinverse perturbation and the numerical inverse kinematics computation of robot manipulators is presented. The approach is based on solving a linear system of equations and using an original scheme for the appropriate perturbation of the pseudoinverse matrix in the next iteration. The resultant algorithm is tested on the simulation of an industrial robot manipulator. From the results obtained, it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.

Using parameters to increase smoothness of curves and surfaces generated by subdivision

Some recent subdivision schemes for curves and surfaces are viewed as perturbations of classical schemes for B-splines, and their convergence analysis is presented. It is shown that, under certain mild conditions, a small perturbation of a convergent subdivision scheme does not impair the smoothness of the limit function. Moreover, a proper perturbation can even increase the smoothness and thus provide a one-parameter class of schemes with better continuity properties.

Nearly circular shear mode cracks

In this paper we study the elasticity problems of a planar crack, lying in an infinite three-dimensional solid, the front of which differs only slightly from a circle. The crack system is subjected to loadings that induce shear mode stress intensity factors at the crack front. Quantities such as relative crack surface displacement, in-plane shear mode intensity factor K2 and anti-plane shear mode intensity factor K3 are derived in detail. The method used is based on a perturbation technique developed by Rice (J. Appl. Mech.52, 571–579 (1985)) of calculating the first-order variation of the elastic field of a crack when its front is perturbed from some regular reference geometry. The configurational stability problems of harmonic wave form perturbations of the front of a circular crack under axisymmetric shear loading are studied using the derived formulae. The shape that a planar crack under remote uniform shear loading would take so that the energy release rate distributes uniformly along the crack front is discussed by calculating proper perturbations on a circular crack that meets the above requirement.

Perturbation selection rules for multiphoton electronic spectroscopy of neutral alternant hydrocarbonsa)

A one-electron perturbation which is to significantly enhance a ‘‘forbidden’’ single-photon or multiphoton optical transition between any two states of an alternant hydrocarbon must satisfy pseudoparity selection rules in addition to the usual group theoretical selection rules. Pseudoparity predicts whether vibronic or inductive perturbations, e.g., will be successful, while group theory specifies the proper perturbation symmetries. A principal result is that for a given electronic transition, the roles of vibronic, and inductive perturbations are complementary. Their roles reverse depending on whether the transition requires an even or odd number of photons.

A unified view of bulk property theories for stochastic and periodic media

The response of a continuum characterized by two widely differing length scales, parameterized by the dimensionless ratioe, is considered in the context of the composite materials problem. The development of a bulk property theory appropriate in thee → 0 limit is examined both from the perspective of the deterministic homogenization literature and the smoothing method associated with statistical continuum theory and a unified framework established. The extension of bulk property theories through the development of ordered expansions in powers ofe is discussed and specifically related to analogous treatments in linear-gas relaxation theory. Finally, the projection operator techniques of homogenization and smoothing are compared to a proper two-scale perturbation analysis.