Real-time solution of the forward kinematics for a parallel haptic device using a numerical approach based on neural networks

Liu, Guanyang; Wang, Yan; Zhang, Yuru; Xie, Zheng

doi:10.1007/s12206-015-0543-x

Cited by 19 publications

(12 citation statements)

References 29 publications

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“…without suffering the problem of multi-solution. Besides, they are more suitable in practice because the methods are simple and can be extended to various structures of parallel robots [10]- [13]. But the convergence performance is a key issue, e.g., convergence ability and convergence speed, impacting the behavior of control systems.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the initial value is limited within a certain domain by ANNs so that the efficiency of calculation can be improved. In the iteration procedure, frequent calculation of the Jacobian matrix and its inverse is time-consuming but it has attracted little attention [10]. On this account, we introduce simplified Newton iteration [23] with the fixed inverse of Jacobian to reduce the amount of calculation in each iteration.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Numerical Method for Forward Kinematics of Parallel Robots

Zhu

Zhang

2019

IEEE Access

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Solving the forward kinematics of parallel robots efficiently is important for real-time applications. However, it remains a difficult problem due to its high nonlinearity. This paper combines artificial neural networks and the Global Newton-Raphson with Monotonic Descent (GNRMD) algorithm to decrease the training sets of neural networks while avoiding divergence problem. Furthermore, simplified Newton iteration is introduced to reduce the duration of solution time. The proposed method is demonstrated taking a Stewart platform as an example and the nonlinear equations are established with the geometrical method. Based on the continuous characteristic of real-time applications, the result of the previous solution cycle is used as the initial value of the current solution cycle. Moreover, a threshold adjusting the effective scope of GNRMD algorithm and simplified Newton iteration is set to balance the efficiency and number of iteration. The performance of the algorithm is verified in the environment of Microsoft Visual Studio 2013 based on the continuous feedback of the Stewart platform. Besides, it is compared with GNRMD algorithm and a higher-order numerical method. The results indicate that the proposed algorithm can improve the efficiency of solving the forward kinematics problem. INDEX TERMS Parallel robots, forward kinematics, numerical method, real-time application.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Numerical Method for Forward Kinematics of Parallel Robots

Zhu

Zhang

2019

IEEE Access

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“…2 Indeed, the forward kinematic problem (FKP) of a parallel robots has multiple solutions and there is no standard technique to calculate them. 3 Even though particular FKP solutions may exist, their calculation is rather time consuming 4 and finding a complete solution becomes more complex with the number of degrees of freedom (DOF) of the end-effector. Also, numerical problems may be encountered even for robots with very simple architectures.…”

Section: Introductionmentioning

confidence: 99%

Estimation of camera-space manipulation parameters by means of an extended Kalman filter: Applications to parallel robots

González¹,

González-Galván²,

Maya³

et al. 2019

International Journal of Advanced Robotic Systems

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Parallel robots have a growing range of applications due to their appealing characteristics (high speed and acceleration, increased rigidity, etc.). However, several open problems make it difficult to model and control them. Low computational-cost algorithms are needed for high speed tasks where high accelerations are required. This article develops the nonlinear camera-space manipulation method and makes use of an extended Kalman filter (EKF) for the estimation of the camera-space manipulation parameters. This is presented as an alternative to the traditional method which can be time consuming while reaching convergence. The proposed camera-space manipulation parameter identification was performed in positioning tasks for a parallel manipulator and the experimental results are reported. Results show that it is possible to estimate the set of camera-space manipulation parameters by means of an extended Kalman filter. Using the proposed Kalman filter method we observed a significant reduction of the computational effort when estimating the camera-space manipulation parameters. However, there was no significant reduction of the robot’s positioning error. The proposed extended Kalman filter implementation requires only 2 ms to update the camera-space manipulation parameters compared to the 85 ms required by the traditional camera-space manipulation algorithm. Such time reduction is beneficial for the implementation of the method for a wide range of high speed and industrial applications. This article presents a novel use of an extended Kalman filter for the real-time estimation of the camera-space manipulation parameters and shows that it can be used to increase the positioning accuracy of a parallel robot.

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“…On the contrary, the elimination process of the analytical method is very complex which may introduce an imaginary root. In addition, a lot of intelligent algorithms were proposed recently, such as particle swarm optimization [19], hybrid immune algorithm [20], and neural network algorithm [21].…”

Section: Introductionmentioning

confidence: 99%

A Parallel Ranging-Based Relative Position and Orientation Measurement Method for Large-Volume Components

2018

Journal of Sensors

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In this paper, a novel relative position and orientation (R-P&O) measurement method for large-volume components is proposed. Based on the method, the parallel distances between the cooperative point pairs (CPPs) are collected by multiple pairs of wireless ranging sensors which are installed on respective components and finally turned into the R-P&O. Accordingly, a measurement model is built and an algorithm is designed to solve the model, in which the radial basis function neural network (RBFNN) produces a preliminary solution by offline training and the differential evolution (DE) strategy finds the accurate solution by online heuristic searching. Furthermore, the crucial parameters and the performance of the algorithm are analyzed through simulating a virtual alignment process which proves that the RBFNN-DE algorithm can quickly and accurately find the global optimal solution in the whole effective workspace. Besides the theory study, a ranging device based on ultrasound has been developed along with a calibration method. Depending on the device, an experiment of actual alignment is implemented to verify the algorithm. Experimental results indicate that the error of R-P&O is no more than 4.1 mm and 0.32° when the ranging error is 0.1 mm, compared with the measurement result of indoor GPS (iGPS).

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Real-time solution of the forward kinematics for a parallel haptic device using a numerical approach based on neural networks

Cited by 19 publications

References 29 publications

An Efficient Numerical Method for Forward Kinematics of Parallel Robots

An Efficient Numerical Method for Forward Kinematics of Parallel Robots

Estimation of camera-space manipulation parameters by means of an extended Kalman filter: Applications to parallel robots

A Parallel Ranging-Based Relative Position and Orientation Measurement Method for Large-Volume Components

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