Computational development of Jacobian matrices for complex spatial manipulators

Goehler, Craig M.; Murray, Wendy M.

doi:10.1016/j.advengsoft.2012.01.002

Cited by 5 publications

(3 citation statements)

References 8 publications

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“…The classical linearization method is to build the equation using the Jacobian matrix. 26 If it is divided by time, we can obtain the corresponding speed linear relationship as follows…”

Section: Preliminariesmentioning

confidence: 99%

Improved singular robust inverse solutions of redundant serial manipulators

Sun

Liu

Chen

2020

International Journal of Advanced Robotic Systems

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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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“…The classical linearization method is to build the equation using the Jacobian matrix. 26 If it is divided by time, we can obtain the corresponding speed linear relationship as follows…”

Section: Preliminariesmentioning

confidence: 99%

Improved singular robust inverse solutions of redundant serial manipulators

Sun

Liu

Chen

2020

International Journal of Advanced Robotic Systems

View full text Add to dashboard Cite

show abstract

“…The common method of linearization is to establish the equation with the Jacobian matrix. 23 If divided by time, the linear relationship of the corresponding velocity can be obtained as follows…”

Section: Preliminariesmentioning

confidence: 99%

Extended singular robust inverse solution of redundant serial manipulators

Sun

Liu

Chen

2020

Advances in Mechanical Engineering

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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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“…With the help of symbolic partial derivation and new modified metrics solve and reduce momentous computation time in MatLab. [15] Chembrammel and Kesavadas suggest matrix estimation of a Jacobian method. That method used for real-time implementation of kinematics and dynamics in complex planar and spatial robots with changes in the structure [16].…”

Section: Parallel Manipulatormentioning

confidence: 99%

An Application of Jacobian Matrix in Kinematic of Multi-loop Spatial Mechanism

2019

IJITEE

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Mechanism is an intended to turn input motion into a required set of output motion and forces. Now a days the spatial mechanism is widely used in various industrial applications like parallel kinematic machines as a robot manipulator. The main aim of the review paper is to use the Jacobian matrix into the kinematic analysis. From the review papers analysis, it has been concluded that the Kinematic analysiswith help of Jacobian matrix performed various Multi-loop Spatial Mechanism settings for Kinematic geometry, its topology and to carried out displacement modelling. It also used to Kinematic Design, synthesis and optimization. Finally, Comparison of existing methods for Kinematic Singularities with Jacobian in Parallel Manipulator.

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Computational development of Jacobian matrices for complex spatial manipulators

Cited by 5 publications

References 8 publications

Improved singular robust inverse solutions of redundant serial manipulators

Improved singular robust inverse solutions of redundant serial manipulators

Extended singular robust inverse solution of redundant serial manipulators

An Application of Jacobian Matrix in Kinematic of Multi-loop Spatial Mechanism

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