[1]宁一高,赵轩*,周猛,等.考虑多源不确定性的同轴两轮车轨迹跟踪控制[J].长安大学学报(自然科学版),2026,46(2):168-179.[doi:10.19721/j.cnki.1671-8879.2026.02.012]
　NING Yi-gao,ZHAO Xuan*,ZHOU Meng,et al.Trajectory tracking control of coaxial two-wheeled vehicles considering multiple uncertain sources[J].Journal of Chang’an University (Natural Science Edition),2026,46(2):168-179.[doi:10.19721/j.cnki.1671-8879.2026.02.012]
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考虑多源不确定性的同轴两轮车轨迹跟踪控制()
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长安大学学报（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
第46卷
期数:
2026年2期
页码:
168-179
栏目:
汽车与机械工程
出版日期:
2026-04-18

文章信息/Info

Title:
Trajectory tracking control of coaxial two-wheeled vehicles considering multiple uncertain sources
文章编号:
1671-8879(2026)02-0168-12
作者:
宁一高; 赵轩*; 周猛; 房熙博
(长安大学 汽车学院,陕西 西安 710018)
Author(s):
NING Yi-gao;  ZHAO Xuan*;  ZHOU Meng;  FANG Xi-bo
(School of Automobile, Chang'an University, Xi'an 710018, Shaanxi, China)
关键词:
汽车工程;  控制器;  区间二型模糊逻辑;  同轴两轮车;  RBF神经网络;  轨迹跟踪
Keywords:
automotive engineering;  controller;  interval type-2 fuzzy logic;  coaxial two-wheeled vehicles;  RBF neural network;  trajectory tracking
分类号:
U469
DOI:
10.19721/j.cnki.1671-8879.2026.02.012
文献标志码:
A
摘要:
为使同轴两轮车在车辆自身和外部环境的多源不确定性条件下仍能实现精确轨迹跟踪控制,提出一种基于区间二型模糊逻辑(IT2FL)和径向基函数(RBF)神经网络的同轴两轮车轨迹跟踪控制方案。利用拉格朗日方程推导车辆动力学模型,通过误差变换将同轴两轮车对参考轨迹的跟踪转化为对期望纵向速度和转向角速度的跟踪问题,从而将车辆系统解耦为欠驱动纵向子系统和全驱动转向子系统进行控制。分别基于IT2FL和RBF神经网络设计纵向子系统和转向子系统控制器,实现同轴两轮车的车身平衡以及纵向与转向的协调跟踪控制,并采用哈密顿-雅可比不等式和李雅普诺夫稳定性理论证明闭环系统的稳定性和跟踪误差的收敛特性。在此基础上,将所提方法与2种现有方法(基于一型模糊逻辑和无RBF神经网络自适应的前馈控制方法以及基于线性二次型调节器和滑模控制的方法)在相同初始条件下进行对比仿真试验。研究结果表明:对比方法在内部参数摄动和外部未知干扰的多源不确定性条件下难以实现有效轨迹跟踪控制,其最大车身倾角速度和最大位置偏差分别达0.32 rad·s-1和3.37 m,而提出方法能够克服相关不确定性影响,车身倾角速度和位置偏差除了初始时的波动外分别不超过0.12 rad·s-1和0.22 m,可有效实现对参考轨迹的鲁棒跟踪,验证了所提方法的可行性和优势。
Abstract:
To make the coaxial two-wheeled vehicle realize a precise trajectory tracking control under multiple uncertain sources from the vehicle itself and external environment, a trajectory tracking control scheme based on interval type-2 fuzzy logic(IT2FL)and radial basis function(RBF)neural network was proposed. Specifically, the vehicle dynamics model was deduced by Lagrangian equation, and the trajectory tracking problem was transformed to be a problem of desired longitudinal velocity and steering angular velocity tracking through errors transform. The whole vehicle system was decoupled into an actuated steering subsystem and an underactuated longitudinal subsystem to be controlled separately. The longitudinal and steering subsystem controllers were designed by IT2FL and RBF neural network, separately, and the stabilization of the vehicle body and the coordination between longitudinal and steering tracking control were realized. The closed-loop system's stability and convergence of tracking error were demonstrated based on Hamilton-Jacobi inequality in the sense of Lyapunov stability theory. On that basis, comparative simulation experiments were conducted under the same initial conditions for the proposed method and existing two methods(the method based on type-1 fuzzy logic and feedforward control without adaptive RBF as well as the method based on linear quadratic regulator and sliding mode control). Research results show the trajectory tracking control of coaxial two-wheeled vehicles cannot be implemented with comparison methods in uncertain condition, and the maximum tilt angle velocity and position errors reach 0.32 rad·s-1 and 3.37 m, respectively. But the robust tracking control can be realized with the proposed method, related uncertain influences can be overcome effectively, and the maximum tilt angle velocity and position error are less than 0.12 rad·s-1 and 0.22 m except the initial fluctuation caused by the existence of initial tilt angle, respectively, thus the feasibility and superior performance of the proposed method are validated.4 tabs, 6 figs, 32 refs.

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备注/Memo

备注/Memo:
收稿日期:2025-08-01
基金项目:国家自然科学基金项目(52402492,52372375); 中国博士后科学基金项目(2023M730358); 陕西省自然科学基础研究计划项目(2024JC-YBQN-0564)
作者简介:宁一高(1990-),男,陕西宝鸡人,讲师,工学博士,博士后,从事车辆动力学与控制、智能车辆方面的研究,E-mail:ningyigao@chd.edu.cn。
通信作者:赵 轩(1983-),男,陕西汉中人,教授,工学博士,博士后,E-mail:zh
更新日期/Last Update: 2026-04-20