基于麻雀算法优化的LQR农机横向跟踪控制方法

摘要/Abstract

摘要：

路径跟踪在智能农机中至关重要。针对线性二次型调节器(LQR)的系数矩阵Q和R选取困难易造成跟踪精度不佳问题，提出一种基于麻雀算法优化的LQR农机横向跟踪控制方法。首先，以拖拉机二自由度车辆动力学为基础，构建横向跟踪误差模型，并采用前馈补偿的方式抑制稳态误差。其次，设定横向误差阈值，一旦超过该误差阈值，将采用麻雀算法对权重系数进行优化调整，以提高路径跟踪精度。最后，运用CarSim—Simulink平台进行联合仿真，通过3种不同曲率的单弯道路径和多弯道正弦路径对农机横向跟踪控制器进行精度测试，并与传统LQR控制器、传统MPC控制器、粒子群优化LQR控制器进行试验对比。结果表明，传统LQR控制器和传统MPC控制器以及粒子群优化LQR控制器在4条路径下平均横向误差分别为0.066 7 m、0.074 9 m、0.035 9 m，而具备麻雀优化功能的控制器平均横向误差最大为0.015 m，具有较好的跟踪效果。

关键词: 智能农机, 横向跟踪, LQR, 麻雀算法, 自适应权重, 粒子群优化

Abstract:

Path tracking plays an important role in intelligent agricultural machinery. To address the challenge of poor tracking accuracy caused by difficulties in selecting the coefficient matrices Q and R in a linear quadratic regulator (LQR), a lateral tracking control method for LQR agricultural machinery based on the sparrow algorithm was proposed. First, a lateral tracking error model was constructed using a two‑degree‑of‑freedom tractor dynamic model, with feedforward compensation employed to suppress steady‑state errors. Secondly, a lateral error threshold was then defined, beyond which the Sparrow algorithm optimized and adjusted the LQR weight coefficienst to improve the path tracking accuracy. Finally, the proposed method was evaluated through co‑simulation using the CarSim—Simulink platform. The precision of the agricultural machinery lateral tracking controller was tested on paths with three different curvatures, including single‑bend path and multi‑bend sinusoidal paths. The results were compared with traditional LQR, traditional MPC, and particle swarm optimization (PSO)—LQR controllers. Experimental results showed that the average lateral error of the traditional LQR, MPC, and PSO—LQR controllers across four path scenarios was 0.066 7 m, 0.074 9 m and 0.035 9 m, respectively. In contrast, the proposed sparrow algorithm‑optimized LQR controller achieved an average lateral error of 0.015 m, which significantly outperformed the other methods in tracking precision.

Key words: intelligent agricultural machinery, horizontal tracking, LQR, sparrow algorithm, adaptive weight, particle swarm optimization

中图分类号:

S220

魏世博, 吴翔, 王瞧, 牛群峰, 樊广晓. 基于麻雀算法优化的LQR农机横向跟踪控制方法[J]. 中国农机化学报, 2025, 46(6): 250-258.

Wei Shibo, Wu Xiang, Wang Qiao, Niu Qunfeng, Fan Guangxiao. Horizontal tracking control method of LQR agricultural machinery based on sparrow algorithm optimization[J]. Journal of Chinese Agricultural Mechanization, 2025, 46(6): 250-258.

参考文献

[ 1 ] 张俊杰, 张玮, 苗俊侠, 等. 智能农机发展推广应用的要点[J]. 南方农机, 2023, 54(1): 78-80.

[ 2 ] 杨涛, 李晓晓. 农机自动驾驶系统研究进展与行业竞争环境分析[J]. 中国农机化学报, 2021, 42(11): 222-231.

Yang Tao, Li Xiaoxiao. Research progress of agricultural machinery autopilot system and analysis of industry competition environment [J]. Journal of Chinese Agricultural Mechanization, 2021, 42(11): 222-231.

[ 3 ] Paden B, Cap M, Yong S Z, et al. A survey of motion planning and control techniques for self‑driving urban vehicles [J]. IEEE Transactions on Intelligent Vehicles, 2016, 1(1): 33-55.

[ 4 ] 翟长远, 杨硕, 王秀, 等. 农机装备智能测控技术研究现状与展望[J]. 农业机械学报, 2022, 53(4): 1-20.

Zhai Changyuan, Yang Shuo, Wang Xiu, et al. Status and prospect of intelligent measurement and control technology for agricultural equipment [J]. Transactions of the Chinese Society for Agricultural Machinery, 2022, 53(4): 1-20.

[ 5 ] 王林军, 吕耀平, 罗彬, 等. 三自由度并联机器人刚柔耦合动力学建模[J]. 中国农机化学报, 2016, 37(9): 208-212.

Wang Linjun, Lü Yaoping, Luo Bin, et al. Rigid‑flexible coupling dynamics modeling of 3—DOF parallel robots [J]. Journal of Chinese Agricultural Mechanization, 2016, 37(9): 208-212.

[ 6 ] 朱德泉, 陈启围, 宋宇, 等. 可调行距插秧机移箱机构运动学分析与优化[J]. 中国农机化学报, 2015, 36(5): 1-4.

Zhu Dequan, Chen Qiwei, Song Yu, et al. Kinematic analysis and optimization of box moving mechanism for row space adjustable transplanter [J]. Journal of Chinese Agricultural Mechanization, 2015, 36(5): 1-4.

[ 7 ] 陈慧岩, 陈舒平, 龚建伟. 智能汽车横向控制方法研究综述[J]. 兵工学报, 2017, 38(6): 1203-1214.

Chen Huiyan, Chen Shuping, Gong Jianwei. A review on the research of lateral control for intelligent vehicles [J]. Acta Armamentarii, 2017, 38(6): 1203-1214.

[ 8 ] Zafter B， Kursad G. Intelligent‑PID with PD feedforward trajectory tracking control of an autonomous underwater vehicle [J]. Machines, 2023, 11(2): 300.

[ 9 ] He J, Meng Y, You J, et al. Trajectory tracking control method based on adaptive higher order sliding mode [J]. Applied Sciences, 2022, 12(16): 7955.

[10] Szepe T, Assal S F M. Pure pursuit trajectory tracking approach: Comparison and experimental validation [J]. International Journal of Robotics and Automation, 2012, 27(4): 355.

[11] AbdElmoniem A, Osama A, Abdelaziz M, et al. A path‑tracking algorithm using predictive Stanley lateral controller [J]. International Journal of Advanced Robotic Systems, 2020, 17(6): 1729881420974852.

[12] Hu K, Cheng K. Trajectory planning for an articulated tracked vehicle and tracking the trajectory via an adaptive model predictive control [J]. Electronics, 2023, 12(9): 1988.

[13] 黄海洋, 张建, 王宇, 等. 基于多点预瞄最优控制的智能车辆路径跟踪[J]. 汽车技术, 2018(10): 6-9.

[14] 化祖旭. 自动驾驶汽车路径跟踪控制算法综述[J]. 装备制造技术, 2021(6): 100-103.

[15] 王荣本, 张荣辉, 储江伟, 等. 区域交通智能车辆控制器优化设计和品质分析[J]. 农业机械学报, 2007(1): 22-25, 48.

[16] 李爽, 徐延海, 陈静, 等. 基于弧长预瞄的车辆侧向跟踪控制研究[J]. 汽车工程, 2019, 41(6): 668-675.

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（上接第 258页）

[17] 邓召文, 易强, 高伟, 等. 四轮转向汽车闭环LQR控制仿真研究[J]. 机械设计与制造, 2022(1): 20-25.

Deng Zhaowen, Yi Qiang, Gao Wei, et al. Study and simulation on closed‑loop LQR control for four‑wheel steering vehicle [J]. Machinery Design & Manufacture, 2022(1): 20-25.

[18] 陈亮, 秦兆博, 孔伟伟, 等. 基于最优前轮侧偏力的智能汽车LQR横向控制[J]. 清华大学学报(自然科学版), 2021, 61(9): 906-912.

Chen Liang, Qin Zhaobo, Kong Weiwei, et al. Lateral control using LQR for intelligent vehicles based on the optimal front‑tire lateral force [J]. Journal of Tsinghua University (Science and Technology), 2021, 61(9): 906-912.

[19] Qian Y, Wang Z, Liang W, et al. Research on automatic parking system based on linear quadratic regulator [J]. Engineering Computations: International Journal for Computer‑Aided Engineering and Software, 2022, 39(3): 1161-1179.

[20] 毛婷婷, 薛金林. 自动驾驶履带车辆的变曲率路径的跟踪控制策略研究[J]. 机械科学与技术, 2024, 43(9): 1493-1504.

Mao Tingting, Xue Jinlin. Study on optimal speed planning hybrid lateral control under curvature based on LQR—MPC [J]. Mechanical Science and Technology for Aerospace Engineering, 2024, 43(9): 1493-1504.

[21] 刘飞飞, 陈臻阳, 彭辉辉, 等. 基于多模态控制的智能车辆路径跟踪[J]. 制造业自动化, 2020, 42(6): 99-102.

Liu Feifei, Chen Zhenyang, Peng Huihui, et al. Intelligent vehicle path tracking based on multi‑modal control [J]. Manufacturing Automation, 2020, 42(6): 99-102.

[22] 马思群, 王兆强, 韩博, 等. 改进的LQR横向路径跟踪控制器[J]. 机械科学与技术, 2024, 43(1): 130-140.

Ma Siqun, Wang Zhaoqiang, Han Bo, et al. An improved lateral path tracking controller based on linear quadratic regulator [J]. Mechanical Science and Technology for Aerospace Engineering, 2024, 43(1): 130-140.

[23] Wang Z, Sun K, Ma S, et al. Improved linear quadratic regulator lateral path tracking approach based on a real‑time updated algorithm with fuzzy control and cosine similarity for autonomous vehicles [J]. Electronics, 2022, 11(22): 3703.

[24] Xue J, Shen B. A novel swarm intelligence optimization approach: Sparrow search algorithm [J]. Systems Science & Control Engineering, 2020, 8(1): 22-34.

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