Improved singular robust inverse solutions of redundant serial manipulators

To address the Jacobian matrix approximation error, which usually exists in the iterative solving process of the classic singular robust inverse method, the correction coefficient α is introduced, and the improved singular robust inverse method is the result. On this basis, the constant improved singular robust method and the intelligent improved singular robust inverse method are proposed. In addition, a new scheme, combining particle swarm optimization and artificial neural network training, is applied to obtain real-time parameters. The stability of the proposed methods is verified according to the Lyapunov stability criteria, and the effectiveness is verified in the application examples of spatial linear and curve trajectories with a seven-axis manipulator. The simulation results show that the improved singular robust inverse method has better optimization performance and stability. In the allowable range, the terminal error is smallest, and there is no lasting oscillation or large amplitude. The least singular value is largest, and the joint angular velocity is smallest, exactly as expected. The derivative of the Lyapunov function is negative definite. Comparing the two extended methods, the constant improved singular robust method performs better in terms of joint angular velocity and least singular value optimization, and the intelligent improved singular robust inverse method can achieve a smaller terminal error. There is little difference between their overall optimization effects. However, the adaptability of the real-time parameters makes the intelligent improved singular robust inverse method the first choice for kinematic control of redundant serial manipulators.

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Extended singular robust inverse solution of redundant serial manipulators

Advances in Mechanical Engineering ◽

10.1177/1687814020907731 ◽

2020 ◽

Vol 12 (2) ◽

pp. 168781402090773

Author(s):

Jingyu Sun ◽

Yanjun Liu ◽

Chen Ji

Keyword(s):

Angular Velocity ◽

Inverse Method ◽

Approximation Error ◽

Coefficient Matrix ◽

Correction Coefficient ◽

Serial Manipulators ◽

Damping Matrix ◽

Selection Principles ◽

Allowable Range ◽

Simulation Results

We propose the use of a damping matrix β to replace the unified damping coefficient λ in the singular robust inverse method, allowing for adjustment of the manipulator’s singularity for different joints separately. In addition, the correction coefficient matrix α is employed to eliminate the Jacobian matrix approximation error, which usually exists in the iterative control solving process; the extended singular robust inverse method is thereby proposed. This article contains analyses of the singularities caused by three methods and how they result in larger values of the manipulator terminal error and joint angular velocity; additionally, the semi-empirical selection principles of β and α are given. The stability of the proposed method is investigated with the Lyapunov stability criteria, and its effectiveness is verified for spatial linear and curve trajectories with 7-axis and 10-axis redundant serial manipulators. The simulation results show that the proposed method exhibits improved optimization performance and stability, and the terminal error is stable and within the allowable range. The least singular value is larger and the joint angular velocity is the lowest, which is the expected outcome. Furthermore, the simulation results for the 10-axis manipulator also indicate the generality of the proposed method.

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Online Real-Time Monitoring System Through Using Adaptive Angular-Velocity VKF Order Tracking

Volume 1: 24th Conference on Mechanical Vibration and Noise, Parts A and B ◽

10.1115/detc2012-70506 ◽

2012 ◽

Cited By ~ 1

Author(s):

Ting-Chi Yeh ◽

Min-Chun Pan

Keyword(s):

Angular Velocity ◽

Real Time ◽

Monitoring System ◽

Condition Monitoring ◽

Theoretical Derivation ◽

Periodic Loading ◽

Order Tracking ◽

Computation Scheme ◽

Condition Monitoring System ◽

Operation Status

When rotary machines are running, acousto-mechanical signals acquired from the machines are able to reveal their operation status and machine conditions. Mechanical systems under periodic loading due to rotary operation usually respond in measurements with a superposition of sinusoids whose frequencies are integer (or fractional integer) multiples of the reference shaft speed. In this study we built an online real-time machine condition monitoring system based on the adaptive angular-velocity Vold-Kalman filtering order tracking (AV2KF_OT) algorithm, which was implemented through a DSP chip module and a user interface coded by the LabVIEW®. This paper briefly introduces the theoretical derivation and numerical implementation of computation scheme. Experimental works justify the effectiveness of applying the developed online real-time condition monitoring system. They are the detection of startup on the fluid-induced instability, whirl, performed by using a journal-bearing rotor test rig.

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Least singular value and condition number of a square random matrix with i.i.d. rows

Statistics & Probability Letters ◽

10.1016/j.spl.2021.109070 ◽

2021 ◽

pp. 109070

Author(s):

M. Gregoratti ◽

D. Maran

Keyword(s):

Condition Number ◽

Random Matrix ◽

Singular Value ◽

Least Singular Value

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A real-time robust method of system error registration based on the sorting of doubly linked list

2016 35th Chinese Control Conference (CCC) ◽

10.1109/chicc.2016.7554167 ◽

2016 ◽

Cited By ~ 1

Author(s):

Xu Zhang ◽

Hong Liu ◽

Jiangong Wang ◽

Haidong Wu ◽

Feng Li ◽

...

Keyword(s):

Real Time ◽

Robust Method ◽

System Error ◽

Linked List

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Three Revised Kalman Filtering Models for Short-Term Rail Transit Passenger Flow Prediction

Mathematical Problems in Engineering ◽

10.1155/2016/9717582 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 17

Author(s):

Pengpeng Jiao ◽

Ruimin Li ◽

Tuo Sun ◽

Zenghao Hou ◽

Amir Ibrahim

Keyword(s):

Real Time ◽

Nonparametric Regression ◽

Kalman Filtering ◽

Rail Transit ◽

Correction Coefficient ◽

Short Term ◽

Transit System ◽

Filtering Method ◽

Passenger Flow ◽

Model Based

Short-term prediction of passenger flow is very important for the operation and management of a rail transit system. Based on the traditional Kalman filtering method, this paper puts forward three revised models for real-time passenger flow forecasting. First, the paper introduces the historical prediction error into the measurement equation and formulates a revised Kalman filtering model based on error correction coefficient (KF-ECC). Second, this paper employs the deviation between real-time passenger flow and corresponding historical data as state variable and presents a revised Kalman filtering model based on Historical Deviation (KF-HD). Third, the paper integrates nonparametric regression forecast into the traditional Kalman filtering method using a Bayesian combined technique and puts forward a revised Kalman filtering model based on Bayesian combination and nonparametric regression (KF-BCNR). A case study is implemented using statistical passenger flow data of rail transit line 13 in Beijing during a one-month period. The reported prediction results show that KF-ECC improves the applicability to historical trend, KF-HD achieves excellent accuracy and stability, and KF-BCNR yields the best performances. Comparisons among different periods further indicate that results during peak periods outperform those during nonpeak periods. All three revised models are accurate and stable enough for on-line predictions, especially during the peak periods.

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A Real-Time Algorithm for Constrained Nonlinear Receding Horizon Control Based on Off-Line Singular Value Decomposition

Transactions of the Institute of Systems Control and Information Engineers ◽

10.5687/iscie.25.126 ◽

2012 ◽

Vol 25 (5) ◽

pp. 126-133

Author(s):

Keita Akayama ◽

Toshiyuki Ohtsuka

Keyword(s):

Singular Value Decomposition ◽

Real Time ◽

Time Algorithm ◽

Singular Value ◽

Receding Horizon Control ◽

Receding Horizon ◽

Value Decomposition ◽

Nonlinear Receding Horizon Control

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Construction of a Rotation Acquisition System using Arduino and Scada Supervisory Software

International Journal for Innovation Education and Research ◽

10.31686/ijier.vol9.iss11.3486 ◽

2021 ◽

Vol 9 (11) ◽

pp. 173-182

Author(s):

Adeilson Nascimento de Sousa ◽

Laudileni Olenka ◽

Jorge Luis Nepomuceno de Lima ◽

Viviane Barrozo da Silva ◽

Antonio Carlos Duarte Ricciotti ◽

...

Keyword(s):

Angular Velocity ◽

Data Acquisition ◽

Open Source ◽

Real Time ◽

Graphical Representation ◽

Data Acquisition System ◽

Linear Velocity ◽

Acquisition System ◽

Instantaneous Values

This work presents the development and implementation of a System for Acquisition of Rotations composed of an open-source Arduino electronic prototyping platform and a Supervision and Data Acquisition System (SCADA). This system obtains instantaneous values for frequency, linear velocity, and angular velocity, and the graphical representation of said instantaneous values is in real-time. Thus, the proposed system is a mediator of learning for the teaching of Circular Movement Uniform, with theoretical/practical interaction essential in classes for understanding the content.

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