On the Optimal Resolution of Inverse Kinematics for Redundant Manipulators Using a Topological Analysis

2020 ◽  
Vol 12 (3) ◽  
Author(s):  
Enrico Ferrentino ◽  
Pasquale Chiacchio
Keyword(s):  
Calculus Of Variations ◽  
Topological Analysis ◽  
Optimal Solution ◽  
Point Of View ◽  
Redundancy Resolution ◽  
Homotopy Classes ◽  
Transitional Point ◽  
Multiple Grids ◽  
Self Motion ◽  
Path Homotopy

Abstract The redundancy resolution schemes based on the optimization of an integral performance index are investigated from the topological point of view. The topological notions of self-motion manifold, C-path-homotopy and extended aspect are clarified in relation to the limitations of the necessary conditions of optimality provided by calculus of variations. On one hand, they do not guarantee the achievement of the optimal solution, and on the other hand, they translate into a two-point boundary value problem (TPBVP), whose resolution, under certain circumstances, may not lead to a feasible solution at all. In response to the limitations of calculus of variations, a dynamic-programming-inspired formalism is developed, which is based on the discretization of the state space and on its representation in the form of multiple grids. Building upon the topological analysis, effective algorithms are designed that are able to find the optimal solution in any condition, across all C-path homotopy classes and self-motion manifolds, with no limitation due to the passage through singularities. Moreover, if the grids are representative of the manipulator’s extended aspects, the topological notion of the transitional point can be used to reduce the computational complexity of the optimal redundancy resolution algorithm. The results are demonstrated on a canonical 4R planar robot in two different scenarios.

scholarly journals EFFICIENT ENGINEERING IN DEVELOPMENT OF CONSTRUCTION SECTOR COMPETITIVENESS

2021 ◽  
Vol 21 (3) ◽  
pp. 90-99
Author(s):  
O.N. Bekirova ◽  
◽  
S.A. Barkalov ◽  
M.S. Trifonova
Keyword(s):  
System Analysis ◽  
Consumer Preferences ◽  
Optimal Solution ◽  
Real Estate Market ◽  
Point Of View ◽  
Economic Conditions ◽  
Construction Sector ◽  
Construction Enterprise ◽  
Modern Economic ◽  
Optimal Construction

The COVID-19 pandemic has really become a real shock for the whole world. The way of life has changed not only for people, but also for companies in various industries. Today, the real estate market, like many other industries, is in conditions of economic instability. The study highlights the problems faced by the construction sector in the current conditions of the coronavirus pandem-ic. One of these problems is the sustainable competitiveness of construction and its compliance with new consumer preferences. Aim. The study of the influence of engineering solutions and other fac-tors on the competitiveness of construction in modern economic conditions, the definition of key criteria. Development and description of the decision-making methodology for choosing the optimal construction enterprise from the point of view of competitiveness. Materials and methods. The methods of system analysis, optimization methods, hierarchy analysis and decision theory are ap-plied in the work. Within the framework of the proposed methodology, the author's method of identifying key competitiveness criteria has been developed. Since the problem of choosing the optimal solution from among the alternatives is based on a multi-criteria approach, the use of this method is quite appropriate. The template for the formation of the methodology was identified based on the analy-sis of existing research in this area. Results. The author summarizes and supplements the criteria and factors affecting the competitiveness of construction organizations in the study. The author's method of making a decision on determining the optimal construction enterprise from the point of view of competitiveness based on the criteria considered by the author is presented. This technique includes several stages: 1) forming a goal; 2) formation of criteria by which organizations will be evaluated; 3) calculation of criteria for each organization and bringing them to a homogeneous type of data; 4) building a tree of goals and a matrix of priorities; 5) Determining the values of priority vectors for each organization under study. Conclusion. The total influence of criteria and engineering solutions on the competitiveness of construction is determined. In this regard, the implementation of the con-struction project should be carried out taking into account the strategic goals of the organization and binding to the identified criteria. The proposed methodology is developed for Russian construc-tion companies operating in modern economic conditions.

Multidisciplinary Optimization Design for Section Layout of Complex Umbilical Cables Based on Intelligent Algorithm

2015 ◽  
Author(s):  
Zhixun Yang ◽  
Jun Yan ◽  
Guojun Ma ◽  
Qingzhen Lu ◽  
Minggang Tang ◽  
...  
Keyword(s):  
Optimization Design ◽  
Oil And Gas ◽  
Power Transmission ◽  
Optimal Solution ◽  
Point Of View ◽  
Multidisciplinary Optimization ◽  
Intelligent Algorithm ◽  
Control Functions ◽  
Offshore Oil And Gas ◽  
Ocean Environment

Umbilical which links the top floater and the subsea devices provides control functions through electrical cables and hydraulic remote transmission. They are treated as the “lifeline” of the subsea production system for offshore oil and gas exploitation. During operation, umbilical needs to undertake self-weight and periodical load due to the ocean environment. Meanwhile, the heat during power transmission in electric cable is released to the umbilical body, which influences the mechanical properties and optical transmission in the cable. However, there are a number of components and many kinds of sectional arrangement for the umbilical. So the sectional design with multiple components needs to be solved as a multidisciplinary optimization problem. From the mechanical point of view, the umbilical structure should be designed with more compacted and symmetric layout to obtain even probability of resistance to loads and reduce structural stress to improve its fatigue performance. Concerning thermal effect, these units should be arranged to dissipate the heat easily to avoid the influence on the functional and structural components. In this paper, compactedness, symmetry and temperature distribution are quantified through introducing corresponding indices. Then multidisciplinary optimization framework is established. Particle Swarm Optimization (PSO) intelligent algorithm is adopted to carry out the optimization to obtain the optimal solution, which is far superior to the initial design. The optimization design strategy is proved to be effective and efficient by some numerical examples, which provides reference for design of umbilical cables.

scholarly journals Assessment of direct and indirect effects of building developments on the environment

2019 ◽  
Vol 9 (1) ◽  
pp. 109-114
Author(s):  
Elżbieta Hanna Szafranko
Keyword(s):  
Complex Analysis ◽  
Objective Assessment ◽  
Optimal Solution ◽  
Point Of View ◽  
Nature Protection ◽  
Building Projects ◽  
Indicator Method ◽  
Considerable Impact ◽  
The One

AbstractAny building construction undertaking is inseparable from the environment in which it will be executed. Among all buildings, the most difficult ones from the point of view of nature protection are those which have been classified as having a considerable impact on the environment. Roads and road infrastructure are a particular case. Construction of roads or railroads and their subsequent long-term use lead to many changes in the environment. When planning such building projects, it is recommended to develop variant solutions in order to choose the one that would be least harmful to the environment, and then to submit them to an objective assessment. To facilitate the selection of an optimal solution, assessment indicators are developed. However, it needs to be remembered that a factor perceived as a negative one in the immediate assessment might generate positive consequences on a broader scale and vice versa. Hence, an assessment of the impacts on the environment caused by building projects should be viewed in the context of indirect (global) and direct (local) effects. This article will present a model analysis of the impacts caused by a fragment of a road, including local and global effects measured by the indicator method. This method has been developed by the author of this article, who believes that it enables the user to make a complex analysis, while the graphic presentation it involves, discussed in the conclusions to this paper, helps to decide easily which factors are decisive in the final assessment of the analysed project.

Multidisciplinary Optimization Design for the Section Layout of Umbilicals Based on Intelligent Algorithm

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Zhixun Yang ◽  
Qingzhen Lu ◽  
Jun Yan ◽  
Jinlong Chen ◽  
Qianjin Yue
Keyword(s):  
Optimization Design ◽  
Oil And Gas ◽  
Power Transmission ◽  
Production Systems ◽  
Optimal Solution ◽  
Point Of View ◽  
Multidisciplinary Optimization ◽  
Intelligent Algorithm ◽  
Control Functions ◽  
Electric Cables

Umbilicals, which link top floaters and subsea devices, provide control functions through electrical cables and hydraulic remote transmission. These cables are considered the “lifeline” of subsea production systems for offshore oil and gas exploitation. Umbilicals should undertake self-weight and periodic loading during operation because of the severe conditions of the ocean environment. Heat is released to the umbilical body during power transmission in electric cables, which influences the mechanical properties and optical transmission in the cable. However, several sectional arrangements can be applied to a number of umbilical components. Thus, sectional layout design with multiple components should be treated as a multidisciplinary optimization problem. From the mechanical point of view, the umbilical structure should be designed with compact and symmetric layout to obtain an even probability of resistance to loads and reduce structural stress, thereby improving fatigue performance. In terms of thermal effect, these electric cables should be arranged to dissipate heat easily and avoid influence on functional and structural components. This study quantifies compactness, symmetry, and temperature distribution by introducing corresponding indices. A multidisciplinary optimization framework is then established. Particle swarm optimization (PSO) intelligent algorithm is adopted to perform optimization and obtain the optimal solution, which is superior to the initial design. The optimization design strategy is proven effective and efficient by a case study, which provides a reference for umbilical design.

scholarly journals Investigation of Cyclicity of Kinematic Resolution Methods for Serial and Parallel Planar Manipulators

Robotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Maurizio Ruggiu ◽  
Andreas Müller
Keyword(s):  
Objective Function ◽  
Inverse Kinematics ◽  
Joint Space ◽  
Point Of View ◽  
Initial Configuration ◽  
Local Optimum ◽  
Closed Path ◽  
Redundancy Resolution ◽  
Projected Gradient Method ◽  
Inverse Kinematics Problem

Kinematic redundancy of manipulators is a well-understood topic, and various methods were developed for the redundancy resolution in order to solve the inverse kinematics problem, at least for serial manipulators. An important question, with high practical relevance, is whether the inverse kinematics solution is cyclic, i.e., whether the redundancy solution leads to a closed path in joint space as a solution of a closed path in task space. This paper investigates the cyclicity property of two widely used redundancy resolution methods, namely the projected gradient method (PGM) and the augmented Jacobian method (AJM), by means of examples. Both methods determine solutions that minimize an objective function, and from an application point of view, the sensitivity of the methods on the initial configuration is crucial. Numerical results are reported for redundant serial robotic arms and for redundant parallel kinematic manipulators. While the AJM is known to be cyclic, it turns out that also the PGM exhibits cyclicity. However, only the PGM converges to the local optimum of the objective function when starting from an initial configuration of the cyclic trajectory.

Optimal control for antiplane frictional contact problems involving nonlinearly elastic materials of Hencky type

2017 ◽  
Vol 23 (3) ◽  
pp. 308-328 ◽  
Author(s):  
Andaluzia Matei ◽  
Sorin Micu ◽  
Constantin Niţǎ
Keyword(s):  
Optimal Control ◽  
Frictional Contact ◽  
Variational Equation ◽  
Optimal Solution ◽  
Contact Problems ◽  
Point Of View ◽  
Friction Laws ◽  
Convergence Results ◽  
Positive Exponent ◽  
Nonlinearly Elastic

We consider an antiplane contact problem modeling the friction between a nonlinearly elastic body of Hencky type and a rigid foundation. We discuss the well-posedness of the model by considering two friction laws. Firstly, Tresca’s law is used to describe the friction force and leads to a variational inequality. Alternatively, a regularizing power law with a positive exponent r is considered and gives, from the mathematical point of view, a variational equation. In both contexts, we address a boundary optimal control problem by minimizing, on a nonconvex set, a cost functional with two arguments. We show the existence of at least one optimal pair for each problem. Finally, we deliver some convergence results proving that the optimal solution of the regular problem tends, when r goes to zero, to an optimal solution of the first one.

scholarly journals INCREASING THE EFFICIENCY OF MULTIMODAL TRANSPORTATION WITH ALTERNATIVE USE OF DIFFERENT TYPES OF TRANSPORT

2021 ◽  
Vol 23 (2(79)) ◽  
pp. 96-104
Author(s):  
S.V. KOTENKO ◽  
V.A. KASIANOVA ◽  
M.V. SHAMIN
Keyword(s):  
Optimal Solution ◽  
Freight Transportation ◽  
Point Of View ◽  
Objective Functions ◽  
Measurement Scales ◽  
Multimodal Transportation ◽  
Different Types ◽  
Cargo Transportation ◽  
The Impact ◽  
Efficiency And Reliability

Topicality. The urgency of the study is due to the fact that in Ukraine the volume of cargo transportation using multimodal technologies is growing. Therefore, increasing the efficiency of multimodal transportation using the latest methods of their optimization is timely. This is especially true for those modes of transport whose share in total freight turnover is relatively small. Aim and tasks.The main purpose of the study is to develop theoretical and applied provisions and algorithms for finding the optimal solution for several target functions with different measurement scales to increase the efficiency of multimodal transportation, in particular, with the alternative use of different modes of transport. To achieve this goal, the following tasks arose: to study the impact of the monopolization of the transportation market by certain modes of transport on the reliability and efficiency of transportation; solving the problem of optimization of freight transportation from the national or general industry point of view; study of the importance of the development of inland water transport to increase the efficiency and reliability of multimodal transport; creating an algorithm for finding the optimal solution for several target functions. Research results.Theoretical and applied positions of search of the optimum decision on several target functions with different scale of measurement for increase of efficiency of multimodal transportations, including, at alternative use of different types of transport are investigated. The study proved that the choice of only one of the traditional target functions of transport companies - the cost or time of transportation does not guarantee its effectiveness without assessing the risks of transportation of goods. An algorithm for selecting the optimal solution for several objective functions is proposed. To do this, we used the method of finding the extremum of each of them by its own nontrivial subset. It is proved that these sets, in the general case, are not identical, so to find a solution for several objective functions complicated by their different dimensions, the principle of compromise must be used.The study established a significant degree of monopolization of the transportation market by certain modes of transport and indicated that to solve the problem of optimization of freight transportation from the national or general industry point of view requires equalization of disparities in freight turnover by mode of transport.Conclusion.Analysis of the results of the study allows us to draw the following conclusions: to use the resource to increase the efficiency and reliability of cargo transportation, especially for multimodal transportation technologies, it is necessary to equalize the disproportions of cargo turnover by types of cargo transportation to avoid monopolization of the transport market. To increase the efficiency of transportation, the latest algorithm for selecting the optimal solution for several target functions is proposed. The introduction of this algorithm to optimize multimodal transportation in scientific and practical problems will allow to take into account the risks and find a compromise solution in complex problems of finding solutions for the transportation of goods.

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