Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

Yang, Chengxiang; Zheng, Shutao; Jin, Jun; Zhu, Shengqi; Han, Junwei

doi:10.1007/s11771-010-0630-1

Cited by 39 publications

(20 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, genetic algorithms [39][40][41][42], neuronal methods [43,44] and interval analysis methods [15,45] have to be mentioned. In fact, the most common numerical procedures for fast determination of the manipulator platform's pose are iterative techniques such as Newton-Raphson algorithms, see References [11,[46][47][48][49][50]. Here, the inverse kinematic equations are used together with a pose estimate for iteratively solving these equations with a multi-dimensional Newton-Raphson algorithm.…”

Section: Numerical Solutionmentioning

confidence: 99%

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Schulz

2019

Robotics

View full text Add to dashboard Cite

In this paper, we experimentally evaluate the performance of a sensor concept for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism by using solely the linear actuators’ orientations. At first, we review classical methods for solving the direct kinematics problem of parallel mechanisms and discuss their disadvantages on the example of the general planar 3-RPR parallel mechanism, a planar parallel robot with two translational and one rotational degrees of freedom, where P denotes active prismatic joints and R denotes passive revolute joints. In order to avoid these disadvantages, we present a sensor concept together with an analytical formulation for solving the direct kinematics problem of a general planar 3-RPR parallel mechanism where the number of possible assembly modes can be significantly reduced when the linear actuators’ orientations are used instead of their lengths. By measuring the orientations of the linear actuators, provided, for example, by inertial measurement units, only two assembly modes exist. Finally, we investigate the accuracy of our direct kinematics solution under static as well as dynamic conditions by performing experiments on a specially designed prototype. We also investigate the solution formulation’s amplification of measurement noise on the calculated pose and show that the Cramér-Rao lower bound can be used to estimate the lower bound of the expected variances for a specific pose based exclusively on the variances of the linear actuators’ orientations.

show abstract

Section: Numerical Solutionmentioning

confidence: 99%

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Schulz

2019

Robotics

View full text Add to dashboard Cite

show abstract

“…As shown in Eq. (27), for the Stewart platform, there is only the second type kinematic singularity, when det(J )=0. Such singularities can be further classified into three categories are adjusted, namely, architecture singularity, configuration singularity and formulation singularity [24,25].…”

Section: Dynamics Verification Experimentsmentioning

confidence: 99%

Dynamics Verification Experiment of the Stewart Parallel Manipulator

Shao

Tang

Wang

2015

International Journal of Advanced Robotic Systems

View full text Add to dashboard Cite

As the basis of dynamic analysis and driving force calculation, dynamic models and dynamic parameters are important issues in mechanical design and control. In this paper, a dynamics verification experiment, which covers both dynamic models and dynamic parameters as a whole, is carried out on the typical Stewart parallel manipulator. First, the complete dynamic model of the Stewart manipulator is derived, considering the force sensors. The Newton-Euler method with clear physical meaning is adopted to facilitate understanding and parameter definitions. The dynamic parameters are deduced based on the established three-dimensional virtual prototype and adjusted with actual measurements. The recorded trajectory, instead of the theory trajectory, is adopted to calculate the theoretical limb forces. The practical limb forces are measured using pull pressure sensors. Finally, the dynamic model and identified parameters are verified by comparing the limb forces obtained using the above two approaches. Experiment results show that theoretical and practical limb forces coincide well, with a small maximum RMS (root mean square) error of 1.516N and forces ranging from 10N to 40N. Additionally, the established dynamics verification algorithm, which involves dynamic modelling, a parameter identification approach and a data analysis method, are generic and practical, and can be flexibly applied to the dynamic analysis of other parallel manipulators.

show abstract

“…Equation (13) describes three vector equations which totally form a system of 12 variables (q ac 1 , q ac 2 , q ac 3 , x p , y p , z p , h, u, k, b 1 , b 2 , b 3 ) and nine equations. In the forward kinematics problem of 3-PSP parallel robot, the displacement of three active prismatic joints (q ac 1 , q ac 2 , q ac 3 ) are known as inputs to the problem and the other variables should be computed by solving the system of Equation (13). Therefore, the unknowns of this problem are,…”

Section: Each Leg Of the Robot Is Part Of A Closed Kinematic Chain Whmentioning

confidence: 99%

“…In fact, for some initial guesses the algorithm may diverge, resulting in a decrease in performance. Various methods like the robust NewtonRaphson, [11] the global Newton-Raphson, [12] and the modified global Newton-Raphson [13] are proposed to overcome this limitation. Although the divergence problem is somehow resolved in these methods, the algorithms will take a long time to converge if the initial guess falls away from exact solution.…”

Section: Introductionmentioning

confidence: 99%

An improved hybrid method for forward kinematics analysis of parallel robots

Kardan

Akbarzadeh

2015

Advanced Robotics

View full text Add to dashboard Cite

This paper combines a new structure of artificial neural networks (ANNs) with a 3rd-order numerical algorithm and proposes an improved hybrid method for solving forward kinematics problem (FKP) of parallel manipulators. In this method, an approximate solution of the FKP is first generated by the neural network. This solution is next considered as an initial guess for the 3rd-order numerical technique which solves the nonlinear forward kinematics equations and obtains the answer with a desired level of accuracy. To speed up the method, a new structure is proposed for designing the ANN which is called Same Class One Network. In this structure, the outputs of the ANN are classified into classes of similar variables with an individual network designed for each class. The proposed method is then applied to a planar 3-RPR parallel manipulator and a spatial 3-PSP parallel robot. The results show that using this method will lead to a 55% reduction in required iterations and a 20% reduction in the FKP analysis time, while maintaining a high level of solution accuracy.

show abstract

Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

Cited by 39 publications

References 20 publications

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Performance Evaluation of a Sensor Concept for Solving the Direct Kinematics Problem of General Planar 3-RPR Parallel Mechanisms by Using Solely the Linear Actuators’ Orientations

Dynamics Verification Experiment of the Stewart Parallel Manipulator

An improved hybrid method for forward kinematics analysis of parallel robots

Contact Info

Product

Resources

About