Analysis of reachable workspace for spatial 3-cable under-constrained suspended cable driven parallel robots

2021 ◽  
pp. 1-42
Author(s):  
Yijia Peng ◽  
Wanghui Bu
Keyword(s):  
Linear Equations ◽  
Inequality Constraints ◽  
Parallel Robots ◽  
The Novel ◽  
Linear Inequality Constraints ◽  
Reachable Workspace ◽  
Linear Equality Constraints ◽  
Equilateral Triangles ◽  
Anchor Points ◽  
Branch And Prune

Abstract Workspace is an important reference for design of cable-driven parallel robots (CDPRs). Most current researches focus on calculating the workspace of redundant CDPRs. However, few literatures study the workspace of under-constrained CDPRs. In this paper, the static equilibrium reachable workspace (SERW) of spatial 3-cable under-constrained CDPRs is solved numerically since expressions describing workspace boundaries cannot be obtained in closed form. The analysis steps to solve the SERW are as follows. First, expressions which describe the SERW and its boundaries are proposed. Next, these expressions are instantiated through the novel anchor points model composed of linear equations, quadratic equations and limits of tension in cables. Then, based on the reformulated linearization technique (RLT), the constraint system is transformed into a system containing only linear equality constraints and linear inequality constraints. Finally, the framework of branch-and-prune (BP) algorithm is adopted to solve this system. The effect of the algorithm is verified by 2 examples. One is a special 3-cable CDPR in which the anchor points layouts both on the moving platform (MP) and on the base are equilateral triangles, followed by the method to extract the SERW boundary where cables do not interfere with each other. The other is a general case with randomly selected geometry arrangement. The presented method in this paper is universal for spatial 3-cable CDPRs with arbitrary geometry parameters.

UNIFORM INFERENCE IN A GENERALIZED INTERVAL ARITHMETIC CENTER AND RANGE LINEAR MODEL

2021 ◽  
pp. 1-43
Author(s):  
Yanqin Fan ◽  
Xuetao Shi
Keyword(s):  
Interval Arithmetic ◽  
Inequality Constraints ◽  
Coefficient Of Determination ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Linear Inequality Constraints ◽  
Linear Equality Constraints ◽  
Linear Equality ◽  
Random Intervals ◽  
Interval Valued

Via generalized interval arithmetic, we propose a Generalized Interval Arithmetic Center and Range (GIA-CR) model for random intervals, where parameters in the model satisfy linear inequality constraints. We construct a constrained estimator of the parameter vector and develop asymptotically uniformly valid tests for linear equality constraints on the parameters in the model. We conduct a simulation study to examine the finite sample performance of our estimator and tests. Furthermore, we propose a coefficient of determination for the GIA-CR model. As a separate contribution, we establish the asymptotic distribution of the constrained estimator in Blanco-Fernández (2015, Multiple Set Arithmetic-Based Linear Regression Models for Interval-Valued Variables) in which the parameters satisfy an increasing number of random inequality constraints.

Optimum Path Planning for Mechanical Manipulators

1981 ◽  
Vol 103 (2) ◽  
pp. 142-151 ◽  
Author(s):  
J. Y. S. Luh ◽  
C. S. Lin
Keyword(s):  
Path Planning ◽  
Feasible Solution ◽  
Computing Time ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Linear Inequality Constraints ◽  
Nonlinear Inequality ◽  
Angular Velocities ◽  
Nonlinear Inequality Constraints

To assure a successful completion of an assigned task without interruption, such as the collision with fixtures, the hand of a mechanical manipulator often travels along a preplanned path. An advantage of requiring the path to be composed of straight-line segments in Cartesian coordinates is to provide a capability for controlled interaction with objects on a moving conveyor. This paper presents a method of obtaining a time schedule of velocities and accelerations along the path that the manipulator may adopt to obtain a minimum traveling time, under the constraints of composite Cartesian limit on linear and angular velocities and accelerations. Because of the involvement of a linear performance index and a large number of nonlinear inequality constraints, which are generated from physical limitations, the “method of approximate programming (MAP)” is applied. Depending on the initial choice of a feasible solution, the iterated feasible solution, however, does not converge to the optimum feasible point, but is often entrapped at some other point of the boundary of the constraint set. To overcome the obstacle, MAP is modified so that the feasible solution of each of the iterated linear programming problems is shifted to the boundaries corresponding to the original, linear inequality constraints. To reduce the computing time, a “direct approximate programming algorithm (DAPA)” is developed, implemented and shown to converge to optimum feasible solution for the path planning problem. Programs in FORTRAN language have been written for both the modified MAP and DAPA, and are illustrated by a numerical example for the purpose of comparison.

scholarly journals A Quasi-Monte-Carlo-Based Feasible Sequential System of Linear Equations Method for Stochastic Programs with Recourse

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Changyin Zhou ◽  
Rui Su ◽  
Zhihui Jiang
Keyword(s):  
Monte Carlo ◽  
Linear Equations ◽  
Inequality Constraints ◽  
System Of Linear Equations ◽  
Active Constraint ◽  
Stochastic Programs ◽  
Quasi Monte Carlo ◽  
Sequential System ◽  
Constraint Set ◽  
A New Technique

A two-stage stochastic quadratic programming problem with inequality constraints is considered. By quasi-Monte-Carlo-based approximations of the objective function and its first derivative, a feasible sequential system of linear equations method is proposed. A new technique to update the active constraint set is suggested. We show that the sequence generated by the proposed algorithm converges globally to a Karush-Kuhn-Tucker (KKT) point of the problem. In particular, the convergence rate is locally superlinear under some additional conditions.

scholarly journals A NOVEL SIMPLE-BASED PRESSURE-ENTHALPY COUPLING SCHEME FOR ENGINE FLOW PROBLEMS

2012 ◽  
Vol 17 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Maximilian Emans ◽  
Zoran Žunič ◽  
Branislav Basara ◽  
Sergey Frolov
Keyword(s):  
Linear Equations ◽  
Computing Time ◽  
Simple Algorithm ◽  
Variable Density ◽  
Coupling Scheme ◽  
The Novel ◽  
Simple Method ◽  
Flow Problems ◽  
Novel Method ◽  
Coupling Terms

A novel method in CFD derived from the SIMPLE algorithm is presented. Instead of solving the linear equations for each variable and the pressurecorrection equation separately in a so-called segregated manner, it relies on the solution of a linear system that comprises the discretisation of enthalpy and pressurecorrection equation which are linked through physical coupling terms. These coupling terms reflect a more accurate approximation of the density update with respect to thermodynamics (compared to standard SIMPLE method). We show that the novel method is a reasonable extension of existing CFD techniques for variable density flows based on SIMPLE. The novel method leads to a reduction of the number of iterations of SIMPLE which translates in many – but not in all – cases to a reduction in computing time. We will therefore demonstrate practical advantages and restrictions in terms of computational efficiency for industrial CFD applications in the field of piston engine simulations.

FAST MAXIMUM ENTROPY ALGORITHM FOR ILL-POSED PROBLEMS

1994 ◽  
Vol 05 (06) ◽  
pp. 987-995 ◽  
Author(s):  
S.V. MESHKOV ◽  
D.V. BERKOV
Keyword(s):  
Maximum Entropy ◽  
Inequality Constraints ◽  
Quantum Systems ◽  
Quadratic Functional ◽  
Strongly Correlated ◽  
Imaginary Time ◽  
Linear Inequality Constraints ◽  
Ill Posed ◽  
Correlated Quantum Systems ◽  
Maxent Approach

The fast algorithm of the Maximum Entropy (MaxEnt) numerical solution of the linear inverse problem is described. The minimization of a general functional intrinsic to the MaxEnt approach is reduced to an iteration procedure with each step being a constrained least-squares problem (minimization of a quadratic functional with linear inequality constraints). The algorithm is structurally simple and can be assembled from blocks available in standard program libraries. The algorithm is tested on “toy” tasks with exponential kernel, as well as on practical problems of the recovery of the spectral density of strongly correlated quantum systems from the imaginary time Green’s functions obtained by Monte Carlo.

scholarly journals Mathematical model for determining rational machining conditions for flat grinding with the wheel periphery on machines with a rectangular table

2018 ◽  
Vol 224 ◽  
pp. 01112
Author(s):  
Dmitriy L. Skuratov ◽  
Dmitriy G. Fedorov ◽  
Dmitriy V. Evdokimov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Linear Inequality ◽  
Inequality Constraints ◽  
Machining Time ◽  
Functional Parameters ◽  
Linear Inequality Constraints ◽  
Machining Quality ◽  
Machining Conditions ◽  
Grinding Operations

A mathematical model is presented for determining the rational machining conditions for flat grinding operations by the rim of a wheel on machines with a rectangular table consisting of a linear objective function and linear inequality constraints. As the objective function, the equation, determining the main machining time, was used. And constraints which are related to the functional parameters and parameters determining the machining quality and the kinematic capabilities of the machine were used as inequality constraints.

A Reference Governor for Nonlinear Systems Based on Quadratic Programming

2016 ◽  
Author(s):  
Nan I. Li ◽  
Ilya Kolmanovsky ◽  
Anouck Girard
Keyword(s):  
Nonlinear Systems ◽  
Quadratic Programming ◽  
Optimization Problem ◽  
Inequality Constraints ◽  
Closed Loop System ◽  
Linear Inequality Constraints ◽  
And Control ◽  
Bounded Disturbance ◽  
State And Control Constraints ◽  
Reference Governor

The reference governor modifies set-point commands to a closed-loop system in order to enforce state and control constraints. In this paper, we describe an approach to reference governor implementation for nonlinear systems, which is based on bounding (covering) the response of a nonlinear system by the response of a linear model with a set-bounded disturbance input. Such a design strategy is of interest as it reduces the online optimization problem to a convex quadratic programming (QP) problem with linear inequality constraints, thereby permitting standard QP solvers to be used. A numerical example is reported.

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