Analytical procedures for determining global minimum friction requirement for a six wheeled rover negotiating hard uneven terrain

2020 ◽  
pp. 095440622096113
Author(s):  
Sam Noble ◽  
K Kurien Issac
Keyword(s):  
Global Minimum ◽  
Iterative Algorithms ◽  
Global Minima ◽  
Local Optima ◽  
Uneven Terrain ◽  
Order Of Magnitude ◽  
Global Optima ◽  
Reaction Forces ◽  
Cubic Polynomial ◽  
Bounded Below

The problem of determining wheel torques of a rover, to minimize friction requirement, has been addressed by many researchers. We address it by trying to understand the ways in which local optima can occur, and on the basis of that understanding, develop analytical and non-iterative algorithms for determining global optima. The problem is posed in two variations, with normal reaction forces on wheels bounded below by (a) zero, and (b) a positive limit. In both cases, the nature of optima is studied comprehensively, and illustrated by solving examples. Explicit expressions are used to find roots of up to a cubic polynomial. Our algorithms are on the average about an order of magnitude faster than an SQP based general optimization solver, when the latter is started from random guesses. Moreover, our algorithms were able to reach global minima without fail for all examples solved, which number more than a thousand.

scholarly journals Metabolic cost of generating horizontal forces during human running

1999 ◽  
Vol 86 (5) ◽  
pp. 1657-1662 ◽  
Author(s):  
Young-Hui Chang ◽  
Rodger Kram
Keyword(s):  
Body Weight ◽  
Oxygen Consumption ◽  
Metabolic Cost ◽  
Ground Reaction Forces ◽  
Vertical Force ◽  
Order Of Magnitude ◽  
Reaction Forces ◽  
The Cost ◽  
Support Body Weight ◽  
Human Running

Previous studies have suggested that generating vertical force on the ground to support body weight (BWt) is the major determinant of the metabolic cost of running. Because horizontal forces exerted on the ground are often an order of magnitude smaller than vertical forces, some have reasoned that they have negligible cost. Using applied horizontal forces (AHF; negative is impeding, positive is aiding) equal to −6, −3, 0, +3, +6, +9, +12, and +15% of BWt, we estimated the cost of generating horizontal forces while subjects were running at 3.3 m/s. We measured rates of oxygen consumption (V˙o 2) for eight subjects. We then used a force-measuring treadmill to measure ground reaction forces from another eight subjects. With an AHF of −6% BWt,V˙o 2 increased 30% compared with normal running, presumably because of the extra work involved. With an AHF of +15% BWt, the subjects exerted ∼70% less propulsive impulse and exhibited a 33% reduction inV˙o 2. Our data suggest that generating horizontal propulsive forces constitutes more than one-third of the total metabolic cost of normal running.

scholarly journals Singular Points of Curves

2018 ◽  
Vol 25 (6) ◽  
pp. 692-710
Author(s):  
Artem D. Uvarov
Keyword(s):  
Iterative Process ◽  
Geometric Modeling ◽  
Global Minimum ◽  
Iterative Algorithms ◽  
Singular Points ◽  
Intersection Curve ◽  
Software Environment ◽  
Advantages And Disadvantages ◽  
Intersection Curves ◽  
Complex Cases

In this paper, we consider the key problem of geometric modeling, connected with the construction of the intersection curves of surfaces. Methods for constructing the intersection curves in complex cases are found: by touching and passing through singular points of surfaces. In the first part of the paper, the problem of determining the tangent line of two surfaces given in parametric form is considered. Several approaches to the solution of the problem are analyzed. The advantages and disadvantages of these approaches are revealed. The iterative algorithms for finding a point on the line of tangency are described. The second part of the paper is devoted to methods for overcoming the difficulties encountered in solving a problem for singular points of intersection curves, in which a regular iterative process is violated. Depending on the type of problem, the author dwells on two methods. The first of them suggests finding singular points of curves without using iterative methods, which reduces the running time of the algorithm of plotting the intersection curve. The second method, considered in the final part of the article, is a numerical method. In this part, the author introduces a function that achieves a global minimum only at singular points of the intersection curves and solves the problem of minimizing this function. The application of this method is very effective in some particular cases, which impose restrictions on the surfaces and their arrangement. In conclusion, this method is considered in the case when the function has such a relief, that in the neighborhood of the minimum point the level surfaces are strongly elongated ellipsoids. All the images given in this article are the result of the work of algorithms on methods proposed by the author. Images are built in the author’s software environment.

scholarly journals Bayesian inference of metal oxide ultrathin film structure based on crystal truncation rod measurements

2017 ◽  
Vol 50 (6) ◽  
pp. 1611-1616 ◽  
Author(s):  
Masato Anada ◽  
Yoshinori Nakanishi-Ohno ◽  
Masato Okada ◽  
Tsuyoshi Kimura ◽  
Yusuke Wakabayashi
Keyword(s):  
Bayesian Inference ◽  
Structural Parameters ◽  
Film Structure ◽  
Perovskite Oxide ◽  
Local Optima ◽  
Domain Structures ◽  
Crystal Truncation Rod ◽  
Global Optima ◽  
Optimum Model ◽  
Simulated Annealing Procedure

Monte Carlo (MC)-based refinement software to analyze the atomic arrangements of perovskite oxide ultrathin films from the crystal truncation rod intensity is developed on the basis of Bayesian inference. The advantages of the MC approach are (i) it is applicable to multi-domain structures, (ii) it provides the posterior probability of structures through Bayes' theorem, which allows one to evaluate the uncertainty of estimated structural parameters, and (iii) one can involve any information provided by other experiments and theories. The simulated annealing procedure efficiently searches for the optimum model owing to its stochastic updates, regardless of the initial values, without being trapped by local optima. The performance of the software is examined with a five-unit-cell-thick LaAlO3film fabricated on top of SrTiO3. The software successfully found the global optima from an initial model prepared by a small grid search calculation. The standard deviations of the atomic positions derived from a dataset taken at a second-generation synchrotron are ±0.02 Å for metal sites and ±0.03 Å for oxygen sites.

scholarly journals Chaotic Fitness Dependent Optimizer for Planning and Engineering Design

2021 ◽  
Author(s):  
Hardi M. Mohammed ◽  
Tarik A. Rashid
Keyword(s):  
Chaotic Maps ◽  
Task Assignment ◽  
Swarm Optimization ◽  
Local Optima ◽  
Tent Map ◽  
Engineering Problems ◽  
Global Optima ◽  
Specific Limitation ◽  
Task Assignment Problem ◽  
Better Than

Abstract Fitness Dependent Optimizer (FDO) is a recent metaheuristic algorithm that mimics the reproduction behavior of the bee swarm in finding better hives. This algorithm is similar to Particle Swarm Optimization (PSO) but it works differently. The algorithm is very powerful and has better results compared to other common metaheuristic algorithms. This paper aims at improving the performance of FDO, thus, the chaotic theory is used inside FDO to propose Chaotic FDO (CFDO). Ten chaotic maps are used in the CFDO to consider which of them are performing well to avoid local optima and finding global optima. New technic is used to conduct population in specific limitation since FDO technic has a problem to amend population. The proposed CFDO is evaluated by using 10 benchmark functions from CEC2019. Finally, the results show that the ability of CFDO is improved. Singer map has a great impact on improving CFDO while the Tent map is the worst. Results show that CFDO is superior to GA, FDO, and CSO. Both CEC2013 and CEC2005 are used to evaluate CFDO. Finally, the proposed CFDO is applied to classical engineering problems, such as pressure vessel design and the result shows that CFDO can handle the problem better than WOA, GWO, FDO, and CGWO. Besides, CFDO is applied to solve the task assignment problem and then compared to the original FDO. The results prove that CFDO has better capability to solve the problem.

Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction

2018 ◽  
Vol 25 (1) ◽  
pp. 248-256
Author(s):  
Camila de Lima ◽  
Elias Salomão Helou
Keyword(s):  
Projection Operator ◽  
Tomographic Reconstruction ◽  
Computational Cost ◽  
Iterative Algorithms ◽  
Incremental Algorithm ◽  
Back Projection ◽  
Tomographic Images ◽  
Incremental Methods ◽  
Order Of Magnitude ◽  
Synchrotron Light

Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughlyO(N3) floating point operations (flops) forN×Npixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator toO(N2logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost ofO(N2logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data.

scholarly journals The Intermediate Phase in Ternary GexAsxSe1–2x Glasses

2002 ◽  
Vol 754 ◽  
Author(s):  
Tao Qu ◽  
D.G. Georgiev ◽  
P. Boolchand ◽  
M. Micoulaut
Keyword(s):  
Differential Scanning Calorimetry ◽  
Power Law ◽  
Global Minimum ◽  
Composition Range ◽  
Intermediate Phase ◽  
Power Laws ◽  
Mode Frequency ◽  
Scanning Calorimetry ◽  
Modulated Differential Scanning Calorimetry ◽  
Order Of Magnitude

ABSTRACTMelt-quenched AsxGexSe1–2x glasses over the composition range, 0 < x < 0.26, are examined in Raman scattering, T-modulated Differential Scanning Calorimetry (MDSC), and 119Sn Mossbauer spectroscopy measurements. The non-reversing enthalpy near Tg, ΔHnr(x), accessed from MDSC shows a global minimum (∼ 0) in the xc(1) = 0.09 < x < xc(2) = 0.16 range, and increases by an order of magnitude both at x < xc(1) and at x > xc(2). Raman mode frequency of corner-sharing Ge(Se1/2)4 tetrahedra studied as a function of x, also shows three distinct regimes (or power-laws, p) that coincide with ΔHnr(x) trends. These regimes are identified with mechanically floppy (x < xc(1)), intermediate (xc(1) < x < xc(2)), and stressed-rigid (x > xc(2)) phases. The Raman elasticity power-law in the intermediate phase, p1 = 1.04(3), and in the stressed rigid phase, p2= 1.52(5), suggest effective dimensionalities of d = 2 and 3 respectively.

Super-High Dimension Complex Functions Optimization Using Adaptive Particle Swarm Optimizer

2012 ◽  
Vol 532-533 ◽  
pp. 1830-1835
Author(s):  
Ying Zhang ◽  
Bo Qin Liu ◽  
Han Rong Chen
Keyword(s):  
High Dimension ◽  
Large Scale ◽  
Particle Swarm ◽  
Search Space ◽  
Scale Space ◽  
Global Optimum ◽  
Particle Swarm Optimizer ◽  
Local Optima ◽  
Complex Functions ◽  
Global Optima

Due to the existence of large numbers of local and global optima of super-high dimension complex functions, general Particle Swarm Optimizer (PSO) methods are slow speed on convergence and easy to be trapped in local optima. In this paper, an Adaptive Particle Swarm Optimizer(APSO) is proposed, which employ an adaptive inertia factor and dynamic changes strategy of search space and velocity in each cycle to plan large-scale space global search and refined local search as a whole according to the fitness change of swarm in optimization process of the functions, and to quicken convergence speed, avoid premature problem, economize computational expenses, and obtain global optimum. We test the proposed algorithm and compare it with other published methods on several super-high dimension complex functions, the experimental results demonstrate that this revised algorithm can rapidly converge at high quality solutions.

scholarly journals Quantum-Inspired Wolf Pack Algorithm to Solve the 0-1 Knapsack Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yangjun Gao ◽  
Fengming Zhang ◽  
Yu Zhao ◽  
Chao Li
Keyword(s):  
Knapsack Problem ◽  
Global Search ◽  
Knapsack Problems ◽  
High Dimensional ◽  
Second Step ◽  
Local Optima ◽  
Global Optima ◽  
High Level ◽  
Search Capability ◽  
Statistical Results

This paper proposes a Quantum-Inspired wolf pack algorithm (QWPA) based on quantum encoding to enhance the performance of the wolf pack algorithm (WPA) to solve the 0-1 knapsack problems. There are two important operations in QWPA: quantum rotation and quantum collapse. The first step enables the population to move to the global optima and the second step helps to avoid the trapping of individuals into local optima. Ten classical and four high-dimensional knapsack problems are employed to test the proposed algorithm, and the results are compared with other typical algorithms. The statistical results demonstrate the effectiveness and global search capability for knapsack problems, especially for high-level cases.

scholarly journals OPTIMASI ALGORITMA ALGA UNTUK MENINGKATKAN LAJU KONVERGENSI

2017 ◽  
Vol 2 (1) ◽  
pp. 68-82
Author(s):  
Hari Santoso ◽  
Lukman Fakih Lidimilah
Keyword(s):  
Convergence Rate ◽  
Design Optimization ◽  
Pressure Vessel ◽  
Complexity Analysis ◽  
Selection Process ◽  
Three Dimensional ◽  
Helical Motion ◽  
Algorithm Optimization ◽  
Local Optima ◽  
Global Optima

Artificial AlgaeAlgorithm (AAA) is an optimization algorithm that has advantages of swarm algorithm model and evolution model. AAA consists of three phases of helical movement phase, reproduction, and adaptation. Helical movement is a three-dimensional movement with the direction of x, y, and z which is very influential in the rate of convergence and diversity of solutions. Helical motion optimization aims to increase the convergence rate by moving the algae to the best colony in the population. Algae Algorithm Optimization (AAA ') was tested with 25 objective functions of CEC'05 and implemented in case of pressure vessel design optimization. The results of the CEC'05 function test show that there is an increase in convergence rate at AAA ', but at worst condition of AAA' becomes less stable and trapped in local optima. The complexity analysis shows that AAA has the complexity of O (M3N2O) and AAA 'has the complexity of O (M2N2O) with M is the number of colonies, N is the number of algae individuals, and O is the maximum of the evaluation function. The results of the implementation of pressure vessel design optimization show that AAA's execution time increased 1,103 times faster than AAA. The increase in speed is due to the tournament selection process in AAA performed before the helical motion, whereas in AAA 'is done if the solution after movement is no better than before. At its best, AAA 'found a solution 4.5921 times faster than AAA. At worst, AAA 'stuck on local optima because helical movement is too focused on global best that is not necessarily global optima.  

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