Hybrid LUT–CORDIC architecture on FPGA for efficient and accurate trigonometric computation in robot manipulators

Abstract

Although computational resources on robots are often limited, real-time, accurate computation of trigonometric functions is essential in robot manipulators, particularly for forward and inverse kinematics, dynamic analysis, trajectory planning, and motion control. The LUT method requires a large number of LUTs to improve accuracy. The accuracy of the CORDIC method is highly dependent on the number of computational latencies, which affects the computation speed. This paper combines two general approaches for computing trigonometric functions on robot manipulators that improve accuracy without increasing resource utilization and computational latencies. The design uses a 10-bit format (0.125° input resolution and 2^-10 output precision) and is implemented in VHDL on a Xilinx Artix-7 XC7A100T-CSG324 FPGA. Compared with a CORDIC-only baseline, the maximum absolute error is reduced from 0.083007812 to 0.009801151 for sine and from 0.079101563 to 0.008901377 for cosine, while MSE drops from 2.4031×10^-4 and 2.32974×10^-4 to 5.87754×10^-6 and 5.87862×10^-6, respectively. The hybrid core also reduces slice usage from 81 to 69 and shortens computation time from 35.271 ns to 30.627 ns, making it suitable for resource-constrained real-time robotic control.