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FPGA-based hardware implementation of arctangent and arccosine functions for the inverse kinematics of robot manipulator

Ying-Shieh Kung (Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiwan)
Ming-Kuang Wu (Department of Mechanical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiwan)
Hai Linh Bui Thi and (Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiwan)
Tz-Han Jung (Department of Electrical Engineering, Southern Taiwan University of Science and Technology, Tainan, Taiwan)
Feng-Chi Lee (Mechanical and System Research Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan)
Wen-Chuan Chen (Mechanical and System Research Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan)

Engineering Computations

ISSN: 0264-4401

Article publication date: 28 October 2014

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Abstract

Purpose

The inverse kinematics in robot manipulator have to handle the arctangent and arccosine function. However, the two functions are complicated and need much computation time so that it is difficult to be realized in the typical processing system. The purpose of this paper is to solve this problem by using Field Programmable Gate Array (FPGA) to speed up the computation power.

Design/methodology/approach

The Taylor series expansion method is firstly applied to transfer arctangent and arccosine function to a polynomial form. And Look-Up Table (LUT) is used to store the parameters of the polynomial form. Then the behavior of the computation algorithm is described by Very high-speed IC Hardware Description Language (VHDL) and a co-simulation using ModelSim and Simulink is applied to evaluate the correctness of the VHDL code.

Findings

The computation time of arctangent and arccosine function using by FPGA need only 320 and 420 ns, respectively, and the accuracy is <0.01°.

Practical implications

Fast computation in arctangent and arccosine function can speed up the motion response of the real robot system when it needs to perform the inverse kinematics function.

Originality/value

This is the first time such to combine the Taylor series method and LUT method in the computation the arctangent and arccosine function as well as to implement it with FPGA.

Keywords

Acknowledgements

The financial support provided by Industrial Technology Research Institute (ITRI) is gratefully acknowledged.

Citation

Kung, Y.-S., Wu, M.-K., Linh Bui Thi and, H., Jung, T.-H., Lee, F.-C. and Chen, W.-C. (2014), "FPGA-based hardware implementation of arctangent and arccosine functions for the inverse kinematics of robot manipulator", Engineering Computations, Vol. 31 No. 8, pp. 1679-1690. https://doi.org/10.1108/EC-11-2012-0290

Publisher

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Emerald Group Publishing Limited

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