Inverse kinematics solution of a new circumferential drilling machine for aircraft assembly

Robotica ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 98-117 ◽  
Author(s):  
Weidong Zhu ◽  
Biao Mei ◽  
Yinglin Ke
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Inverse Kinematics ◽  
Geodesic Distance ◽  
Error Function ◽  
Optimization Method ◽  
Distance Functions ◽  
Drilling Machine ◽  
Orientation Error ◽  
Joint Coordinates

SUMMARYInverse kinematics solutions are the basis for position and orientation control of automated machines in their Cartesian workspace. This paper presents an efficient and robust inverse kinematics algorithm for a new circumferential drilling machine for aircraft fuselage assembly. After a brief introduction to the circumferential drilling machine and its forward kinematics, the paper discusses the nonlinear optimization method for solving inverse kinematics problems. The objective function is defined as a weighted combination of a position error function and an orientation error function. By representing orientation error as the geodesic distance between two points on a unit sphere, the paper proposes to define the orientation error function by using faithful geodesic distance functions, which are accurate approximations to the geodesic distance when it is small. For increased efficiency, robustness, and easy setting of initial values, the inverse kinematics problem is decomposed into two subproblems. The revolute joint coordinates are obtained by nonlinear optimization, and the prismatic joint coordinates are calculated with closed-form formulas. Numerical experiments show that the objective function defined with faithful geodesic distance functions is effective, and the proposed algorithm is efficient, robust, and accurate. The algorithm has been successfully integrated into the control system of the circumferential drilling machine. Preliminary drilling experiments show that the position accuracy of drilled holes is within ±0.5 mm, which is acceptable for the assembly of large aircrafts.

scholarly journals Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1452
Author(s):  
Cristian Mateo Castiblanco-Pérez ◽  
David Esteban Toro-Rodríguez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Programming Model ◽  
Distribution Networks ◽  
Optimization Method ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Balance ◽  
Continuous Version ◽  
Discrete Part

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

scholarly journals Research on the inverse kinematics of manipulator using an improved self-adaptive mutation differential evolution algorithm

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110144
Author(s):  
Qianqian Zhang ◽  
Daqing Wang ◽  
Lifu Gao
Keyword(s):  
Differential Evolution ◽  
Objective Function ◽  
Inverse Kinematics ◽  
Differential Evolution Algorithm ◽  
Weight Coefficient ◽  
Adaptive Mutation ◽  
Feasible Region ◽  
Serial Manipulators ◽  
De Algorithm ◽  
Self Adaptive

To assess the inverse kinematics (IK) of multiple degree-of-freedom (DOF) serial manipulators, this article proposes a method for solving the IK of manipulators using an improved self-adaptive mutation differential evolution (DE) algorithm. First, based on the self-adaptive DE algorithm, a new adaptive mutation operator and adaptive scaling factor are proposed to change the control parameters and differential strategy of the DE algorithm. Then, an error-related weight coefficient of the objective function is proposed to balance the weight of the position error and orientation error in the objective function. Finally, the proposed method is verified by the benchmark function, the 6-DOF and 7-DOF serial manipulator model. Experimental results show that the improvement of the algorithm and improved objective function can significantly improve the accuracy of the IK. For the specified points and random points in the feasible region, the proportion of accuracy meeting the specified requirements is increased by 22.5% and 28.7%, respectively.

Nonlinear Optimal Design of Dynamic Mechanical Systems

1992 ◽  
Author(s):  
T. E. Potter ◽  
K. D. Willmert ◽  
M. Sathyamoorthy
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Iteration Process ◽  
Optimization Method ◽  
Linear Constraints ◽  
Sum Of Squares ◽  
Function Evaluation ◽  
Deformation Analysis ◽  
Nonlinear Constraints ◽  
Quadratic Constraints

Abstract Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraints and revises the Gauss nonlinearly constrained method for quadratic constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that when the iteration process terminates, these conditions are automatically satisfied. Although the technique was developed for mechanism problems, it is applicable to any optimization problem having the form of a sum of squares objective function subjected to nonlinear constraints.

A More Effective Formulation of the Path Generation Mechanism Synthesis Problem

1994 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Error Function ◽  
Mathematical Optimization ◽  
Optimization Methods ◽  
Complex Nature ◽  
Mechanism Synthesis ◽  
Structural Error ◽  
Crank Angle ◽  
The Common ◽  
Selection Of

Abstract Use of mathematical optimization methods for synthesis of path-generating mechanisms has had only limited success due to the very complex nature of the commonly used Structural Error objective function. The complexity arises, in part, because the objective function represents not only the error in the shape of the coupler curve, but also the error in location, orientation and size of the curve. Furthermore, the common introduction of timing (or crank angle), done generally to facilitate selection of corresponding points on the curve for calculating structural error, has little practical value and unnecessarily limits possible solutions. This paper proposes a new objective function, based on Fourier Descriptors, which allows search for coupler curve of the desired shape without reference to location, orientation, or size. The proposed objective function compares overall shape properties of curves rather than making point-by-point comparison and therefore does not requires prescription of timing. Experimental evidence is provided to show that it is much easier to search the space of the proposed objective function compared to the structural error function.

Prediction of Performance and Design via Optimization of Ducted Propellers Subject to Non-axisymmetric Inflows

2005 ◽  
Author(s):  
Spyros A. Kinnas ◽  
Hanseong Lee ◽  
Hua Gu ◽  
Yumin Deng
Keyword(s):  
Nonlinear Optimization ◽  
Pressure Coefficient ◽  
Optimization Method ◽  
Least Square ◽  
Maximum Efficiency ◽  
Design Parameters ◽  
Blade Design ◽  
Constrained Nonlinear Optimization ◽  
Nonlinear Optimization Method ◽  
Ducted Propellers

Recently developed methods at UT Austin for the analysis of open or ducted propellers are presented, and then coupled with a constrained nonlinear optimization method to design blades of open or ducted propellers for maximum efficiency satisfying the minimum pressure constraint for fully wetted case, or the specified maximum allowable cavity area for cavitating case. A vortex lattice method (named MPUF3A) is applied to analyze the unsteady cavitating performance of open or ducted propellers subject to non-axisymmetric inflows. A finite volume method based Euler solver (named GBFLOW) is applied to predict the flow field around the open or ducted propellers, coupled with MPUF-3A in order to determine the interaction of the propeller with the inflow (i.e. the effective wake) or with the duct. The blade design of open or ducted propeller is performed by using a constrained nonlinear optimization method (named CAVOPT-BASE), which uses a database of computed performance for a set of blade geometries constructed from a base-propeller. The performance is evaluated using MPUF-3A and GBFLOW. CAVOPT-BASE approximates the database using the least square method or the linear interpolation method, and generates the coefficients of polynomials based on the design parameters, such as pitch, chord, and camber. CAVOPT-BASE finally determines the optimum blade design parameters, so that the propeller produces the desired thrust for the given constraints on the pressure coefficient or the allowed amount of cavitation.

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

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