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.
An inverse kinematics IP (Intellectual Property) for six-axis articulated manipulator is investigated in this paper. Firstly, the formulation of the inverse kinematics for six-axis articulated manipulator is derived. Secondly, the computation algorithm and its hardware implementation of some key trigonometric functions are described. Thirdly, the IP design of inverse kinematics is illustrated and VHDL (Very high speed IC Hardware Description Language) is used to describe the overall behavior of the proposed IP. Additionally, VHDL code will apply the parameterized function to increase the code flexibility and the FSM (Finite state machine) is used to reduce the hardware resource usage. Finally, to verify the correctness of the proposed inverse kinematics IP, a co-simulation work is constructed by ModelSim and Simulink. The inverse kinematics hardware IP is run by ModelSim and Simulink models is taken as a test bench that generates stimulus to ModelSim and display the output response. Under this design, computing the inverse kinematics algorithm can be completed within several micro-second.
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