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Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

NONLINEAR DYNAMICS 2020年第3期102卷 1611-1626页

作者： Dabiri, Arman Poursina, Mohammad Machado, J. A. Tenreiro Southern Illinois Univ Edwardsville Dept Mech & Mechatron Engn Edwardsville IL 62026 USA Univ Agder Dept Sci & Engn N-4879 Grimstad Norway Polytech Inst Porto Inst Engn Dept Elect Engn Rua Dr Antonio Bernardino de Almeida 431 P-4249015 Porto Portugal

In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.

关键词： Multibody dynamics Closed-chain system Open-chain system LQR Optimal control divide and conquer algorithm Computed-torque control Fractional control PID Parallel computing

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A Robust divide and conquer algorithm for Progressive Medial Axes of Planar Shapes

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2016年第12期22卷 2522-2536页

作者： Liu, Yong-Jin Yu, Cheng-Chi Yu, Min-Jing Tang, Kai Kim, Deok-Soo Tsinghua Univ Dept Comp Sci & Technol TNList Beijing Peoples R China Hong Kong Univ Sci & Technol Dept Mech & Aerosp Engn Hong Kong Hong Kong Peoples R China Hanyang Univ Voronoi Diagram Res Ctr Seoul South Korea Hanyang Univ Sch Mech Engn Seoul South Korea

The medial axis is an important shape representation that finds a wide range of applications in shape analysis. For large-scale shapes of high resolution, a progressive medial axis representation that starts with the lowest resolution and gradually adds more details is desired. In this paper, we propose a fast and robust geometric algorithm that computes progressive medial axes of a large-scale planar shape. The key ingredient of our method is a novel structural analysis of merging medial axes of two planar shapes along a shared boundary. Our method is robust by separating the analysis of topological structure from numerical computation. Our method is also fast and we show that the time complexity of merging two medial axes is O(n log n(v)), where n is the number of total boundary generators, n(v) is strictly smaller than n and behaves as a small constant in all our experiments. Experiments on large-scale polygonal data and comparison with state-of-the-art methods show the efficiency and effectiveness of the proposed method.

关键词： Progressive medial axes shape hierarchy and evolution topology-oriented algorithm divide and conquer algorithm

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An improved divide-and-conquer algorithm for the banded matrices with narrow bandwidths

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第10期71卷 1933-1943页

作者： Liao, Xiangke Li, Shengguo Cheng, Lizhi Gu, Ming Natl Univ Def Technol Coll Comp Changsha 410073 Hunan Peoples R China Natl Univ Def Technol Sci & Technol Parallel & Distributed Proc Lab Changsha 410073 Hunan Peoples R China Natl Univ Def Technol State Key Lab High Performance Comp Changsha 410073 Hunan Peoples R China Natl Univ Def Technol Coll Sci Changsha 410073 Hunan Peoples R China Univ Calif Berkeley Dept Math Berkeley CA 94720 USA

In this paper we propose a novel divide-and-conquer (DC) algorithm to compute the SVD of banded matrices, and further accelerate it by using rank-structured matrix techniques, especially the hierarchically semiseparable (HSS) matrix. The DC algorithm for the symmetric banded eigenvalue problem can also be accelerated similarly. For matrices with few deflations, the banded DC algorithms require more flops than the classical DC algorithm, and thus they are suitable for narrowly banded matrices. While, if there exist many deflations, the banded DC algorithms can be faster than the classical ones for matrices with relatively large bandwidths. Numerous experiments have been done to test the proposed algorithms. Some of the tested matrices are from construction and some are from real applications. Comparing with the DC algorithm in Intel MKL, our proposed algorithms can be hundreds times faster for matrices with narrow bandwidths or many deflations. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： divide and conquer algorithm Banded matrices SVD HSS matrices Eigenvalue problem

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Ensuring High Visibility of Passive Markers at Fixed Camera Gain Using divide and conquer Method

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IEEE ROBOTICS AND AUTOMATION LETTERS 2024年第11期9卷 9741-9748页

作者： Retinger, Marek Michalski, Jacek Kozierski, Piotr Drapikowski, Pawel Poznan Univ Tech Inst Robot & Machine Intelligence PL-60965 Poznan Poland

The letter presents a novel solution to determine exposure and threshold values for cameras in motion capture systems without excessive interaction with the user. The solution is based on the divide and conquer method, which ensures a fast and efficient search of the values. As the results have shown, users without specialist knowledge can significantly improve the tracking capabilities of the motion capture system, especially for smaller passive markers. The tests have proved that for spherical markers with a diameter of 7.9 mm, the full time tracking capabilities can be ensured based on the settings determined with the proposed method, what is difficult to achieve with the default settings. Moreover, the cameras utilisation can be increased, which should have a positive effect on the overall tracking quality. This makes it possible to use smaller and lighter-weight markers, which is desirable for small flying units with payload capacity of a few grams only. The primary tests were performed in the laboratory equipped with 12 OptiTrack Prime(x) 13W cameras. The dedicated programming interfaces (Motive API and Camera SDK) were used. The validation tests included a DJI Tello EDU unit with four markers attached. In addition to analysis and considerations, the document includes pseudocodes that clearly explain the idea behind the algorithms and allow for an easy implementation of the solution.

关键词： Cameras Indexes Robot vision systems Motion capture Tracking Accuracy Software algorithms Visual tracking methods and tools for robot system design motion capture divide and conquer algorithm

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Least Squares Model Averaging for Distributed Data

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JOURNAL OF MACHINE LEARNING RESEARCH 2023年第1期24卷 1-59页

作者： Zhang, Haili Liu, Zhaobo Zou, Guohua Shenzhen Polytech Univ Inst Appl Math Shenzhen 518055 Peoples R China Shenzhen Univ Inst Adv Study Shenzhen 518060 Peoples R China Capital Normal Univ Sch Math Sci Beijing 100048 Peoples R China

divide and conquer algorithm is a common strategy applied in big data. Model averaging has the natural divide-and-conquer feature, but its theory has not been developed in big data scenarios. The goal of this paper is to fill this gap. We propose two divide-and conquer-type model averaging estimators for linear models with distributed data. Under some regularity conditions, we show that the weights from Mallows model averaging criterion converge in L-2 to the theoretically optimal weights minimizing the risk of the model averaging estimator. We also give the bounds of the in-sample and out-of-sample mean squared errors and prove the asymptotic optimality for the proposed model averaging estimators. Our conclusions hold even when the dimensions and the number of candidate models are divergent. Simulation results and a real airline data analysis illustrate that the proposed model averaging methods perform better than the commonly used model selection and model averaging methods in distributed data cases. Our approaches contribute to model averaging theory in distributed data and parallel computations, and can be applied in big data analysis to save time and reduce the computational burden.

关键词： consistency distributed data divide and conquer algorithm Mallows' criterion model averaging optimality

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Optimizing Parallelization Strategies for the Big-Means Clustering algorithm 14th

Optimizing Parallelization Strategies for the Big-Means Cl...

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14th International Conference on Optimization and Applications, OPTIMA 2023

作者： Mussabayev, Ravil Mussabayev, Rustam Department of Mathematics University of Washington Padelford Hall C-138 SeattleWA98195-4350 United States Huawei Russian Research Institute Smolenskaya Square 5 Moscow121099 Russia Institute of Information and Computational Technologies Laboratory for Analysis and Modeling of Information Processes Pushkin str. 125 Almaty050010 Kazakhstan

ISBN: (纸本)9783031487507

This study focuses on the optimization of the Big-means algorithm for clustering large-scale datasets, exploring three distinct parallelization strategies. We conducted extensive experiments to assess the computational efficiency, scalability, and clustering performance of each approach, revealing their benefits and limitations. The paper also delves into the trade-offs between computational efficiency and clustering quality, examining the impacts of various factors. Our insights provide practical guidance on selecting the best parallelization strategy based on available resources and dataset characteristics, contributing to a deeper understanding of parallelization techniques for the Big-means algorithm. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Big data Clustering Decomposition divide and conquer algorithm Global optimization K-means K-means++ Minimum sum-of-squares Unsupervised learning

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How to Use K-means for Big Data Clustering?

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PATTERN RECOGNITION 2023年第1期137卷

作者： Mussabayev, Rustam Mladenovic, Nenad Jarboui, Bassem Mussabayev, Ravil Inst Informat & Computat Technol Lab Anal & Modeling Informat Proc Pushkin Str 125 Alma Ata 050010 Kazakhstan Univ Washington Dept Math Padelford Hall C-138 Seattle WA 98195 USA Higher Coll Technol Dept Ind Management St 19 Abu Dhabi 25026 U Arab Emirates

K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of data. Therefore, it is crucial to improve K-means by scaling it to big data using as few of the following computational resources as possible: data, time, and algorith-mic ingredients. We propose a new parallel scheme of using K-means and K-means++ algorithms for big data clustering that satisfies the properties of a "true big data" algorithm and outperforms the classical and recent state-of-the-art MSSC approaches in terms of solution quality and runtime. The new approach naturally implements global search by decomposing the MSSC problem without using additional meta -heuristics. This work shows that data decomposition is the basic approach to solve the big data clustering problem. The empirical success of the new algorithm allowed us to challenge the common belief that more data is required to obtain a good clustering solution. Moreover, the present work questions the es-tablished trend that more sophisticated hybrid approaches and algorithms are required to obtain a better clustering solution.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： Big data Clustering Minimum sum -of -squares divide and conquer algorithm Decomposition K -means K -means plus plus Global optimization Unsupervised learning

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Least squares model averaging for distributed data

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 10235-10293页

作者： Haili Zhang Zhaobo Liu Guohua Zou Institute of Applied Mathematics Shenzhen Polytechnic University Shenzhen China Institute for Advanced Study Shenzhen University Shenzhen China School of Mathematical Sciences Capital Normal University Beijing China

divide and conquer algorithm is a common strategy applied in big data. Model averaging has the natural divide-and-conquer feature, but its theory has not been developed in big data scenarios. The goal of this paper is to fill this gap. We propose two divide-and-conquer-type model averaging estimators for linear models with distributed data. Under some regularity conditions, we show that the weights from Mallows model averaging criterion converge in L2 to the theoretically optimal weights minimizing the risk of the model averaging estimator. We also give the bounds of the in-sample and out-of-sample mean squared errors and prove the asymptotic optimality for the proposed model averaging estimators. Our conclusions hold even when the dimensions and the number of candidate models are divergent. Simulation results and a real airline data analysis illustrate that the proposed model averaging methods perform better than the commonly used model selection and model averaging methods in distributed data cases. Our approaches contribute to model averaging theory in distributed data and parallel computations, and can be applied in big data analysis to save time and reduce the computational burden.

关键词： consistency distributed data divide and conquer algorithm Mallows' criterion model averaging optimality

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Linear expectile regression under massive data

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Fundamental Research 2021年第5期1卷 574-585页

作者： Shanshan Song Yuanyuan Lin Yong Zhou Department of Statistics Chinese University of Hong KongHongKongChina Academy of Statistics and Interdisciplinary Sciences East China Normal UniversityShanghaiChina

In this paper,we study the large-scale inference for a linear expectile regression *** mitigate the computational challenges in the classical asymmetric least squares(ALS)estimation under massive data,we propose a communication-efficient divide and conquer algorithm to combine the information from sub-machines through confidence *** resulting pooled estimator has a closed-form expression,and its consistency and asymptotic normality are established under mild ***,we derive the Bahadur representation of the ALS estimator,which serves as an important tool to study the relationship between the number of submachines K and the sample *** studies including both synthetic and real data examples are presented to illustrate the finite-sample performance of our method and support the theoretical results.

关键词： divide and conquer algorithm Expectile regression (Asymptotic)confidence distribution Massive data

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A divide and conquer algorithm for constrained multibody system dynamics based on augmented Lagrangian method with projections-based error correction

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NONLINEAR DYNAMICS 2012年第1期70卷 871-889页

作者： Malczyk, Pawel Fraczek, Janusz Warsaw Univ Technol Fac Power & Aeronaut Engn Inst Aeronaut & Appl Mech PL-00665 Warsaw Poland

This paper presents a new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed approaches treat tree topology mechanisms or multibody systems which contain kinematic closed loops in a uniform manner and can handle problems with rank deficient Jacobian matrices. Test case results indicate good accuracy performance dependent on the expense put in the iterative correction of constraint equations. Good numerical properties and robustness of the algorithms are observed when handling systems with single and coupled kinematic loops, redundant constraints, which may repeatedly enter singular configurations.

关键词： divide and conquer algorithm Augmented Lagrangian method Mass-orthogonal projections Parallel computing

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