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J. Hefei Univ. Tech. (Nat. Sci.)

合肥工业大学学报(自然科学版)

JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE)

Competent Authorities: Ministry of Education of the People's Republic of China

Sponsor by: Hefei University of Technology

ISSN 1000-1646, CN 34-1001/N

Design and implementation of a space motion equation fast solver

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空间运动方程快速求解器设计与实现

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Jan.2024, Vol.47 No.1: 54-61

DOI: 10.3969/j.issn.1003-5060.2024.01.009

Authors

WANG Xiaolei, HUANG Zhangqian, FANG Xu, SONG Yukun

(School of Microelectronics, Hefei University of Technology, Hefei 230601, China)

Abstract and Keywords

Abstract: Based on the classical Runge-Kutta method of order four(RK-4) and the fourth-order Adams predictor-corrector method(Adams-4), a field programmable gate array(FPGA)-implemented space motion equation fast solver(SMEFS) with dynamically configurable data paths is proposed. SMEFS adopts a foldable structure. With the help of efficient task mapping and precise state management, the dynamic configuration of data paths is realized by resource reusing and dynamic configuring connections between operators, the solutions of space motion equations can be obtained quickly by SMEFS, and hardware resources are saved effectively. The experimental results of the performance evaluation of SMEFS for solving large-scale space motion equations using the relevant data of a certain type of launch vehicle show that the solutions of five-degree-of-freedom space motion equations in the launch coordinate system can be obtained quickly and reliably by SMEFS. The average speedup compared to the software solutions is 12.765 and the maximum relative error of the solutions is less than $ 9 \times 10^{-5} $. Therefore, SMEFS has good acceleration effect and high calculation reliability.

Keywords: classical Runge-Kutta method of order four(RK-4); fourth-order Adams predictor-corrector method(Adams-4); space motion equation; folding technology; field programmable gate array(FPGA)

作者信息

王晓蕾，黄章骞，房旭，宋宇鲲

（合肥工业大学微电子学院，安徽合肥230601）

摘要和关键词

摘要: 文章基于四阶经典龙格库塔法(classical Runge-Kutta method of order four, RK-4)和四阶 Adams 预测校正法(fourth-order Adams predictor-corrector method, Adams-4)，提出一种现场可编程逻辑门阵列(field programmable gate array, FPGA)实现的数据路径可动态配置的空间运动方程快速求解器(space motion equation fast solver, SMEFS)。SMEFS 采用折叠式结构，借助高效的任务映射和精准的状态管理，通过资源复用和动态配置运算器内部连接关系实现数据路径的动态配置，快速求解空间运动方程，并有效节省硬件资源。采用某型运载火箭的相关数据对 SMEFS 进行大批量空间运动方程求解的性能评估，实验结果表明 SMEFS 能够快速可靠地求解发射坐标系下的五自由度空间运动方程，与软件求解的平均加速比为 12.765，求解结果最大相对误差小于 $ 9 \times 10^{-5} $，具备较好的加速效果和较高的计算可靠性。

关键词: 四阶经典龙格库塔法(RK-4)；四阶 Adams 预测校正法(Adams-4)；空间运动方程；折叠技术；现场可编程逻辑门阵列(FPGA)

Funding

国家重点研发计划资助项目（2018YFB2202604）

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