Trajectory tracking algorithm for mobile robots based on geometric model predictive control

doi:10.11772/j.issn.1001-9081.2024091273

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (9): 3026-3035.DOI: 10.11772/j.issn.1001-9081.2024091273

• Frontier and comprehensive applications • Previous Articles

Trajectory tracking algorithm for mobile robots based on geometric model predictive control

Songjian GU¹^,², Fuxiang WU², Xiangyang GAO², Mengjie YANG³, Yibing ZHAN⁴, Jun CHENG²()

^1.Key Laboratory of Advanced Manufacturing and Automation Technology （Guilin University of Technology），Guilin Guangxi 541006，China
^2.Shenzhen Institute of Advanced Technology，Chinese Academy of Sciences，Shenzhen Guangdong 518005，China
^3.Shine Technology Company Limited，Kunming Yunnan 650000，China
^4.JD Explore Academy，Beijing 100000，China

Received:2024-09-06 Revised:2024-11-29 Accepted:2024-12-02 Online:2025-01-15 Published:2025-09-10
Contact: Jun CHENG
About author:GU Songjian， born in 1998， M.S. candidate. His research interests include mobile robot control， embedded systems.
WU Fuxiang， born in 1984， Ph. D.， associate professor. His research interests include multimodal deep learning， image generation.
GAO Xiangyang， born in 1982， M. S.， senior engineer. His research interests include intelligent robots， embedded systems.
YANG Mengjie， born in 1982， senior engineer. His research interests include artificial intelligence， smart cities， intelligent parks.
ZHAN Yibing， born in 1990， Ph. D.， associate research fellow. His research interests include multimodal learning， graph neural networks， large models.
Supported by:
National Key Innovation 2030 — “New Generation Artificial Intelligence” Major Project(2021ZD0111700);National Natural Science Foundation of China(U21A20487);Yunnan Science & Technology Project(202305AF150152)

基于几何模型预测控制的移动机器人轨迹跟踪算法

古松健¹^,², 吴福祥², 高向阳², 杨梦杰³, 詹忆冰⁴, 程俊²()

^1.广西高校先进制造与自动化技术重点实验室（桂林理工大学），广西桂林 541006
^2.中国科学院深圳先进技术研究院，广东深圳 518055
^3.盛云科技有限公司，昆明 650000
^4.京东探索研究院，北京 100000

通讯作者: 程俊
作者简介:古松健（1998—），男，广东茂名人，硕士研究生，主要研究方向：移动机器人控制、嵌入式系统
吴福祥（1984—），男，广东梅州人，副教授，博士，CCF会员，主要研究方向：多模态深度学习、图像生成
高向阳（1982—），男，陕西咸阳人，高级工程师，硕士，主要研究方向：智能机器人、嵌入式系统
杨梦杰（1982—），男，云南蒙自人，高级工程师，主要研究方向：人工智能、智慧城市、智慧园区
詹忆冰（1990—），男，湖北荆门人，副研究员，博士，主要研究方向：多模态学习、图神经网络、大模型
基金资助:
国家科技创新2030—“新一代人工智能”重大项目(2021ZD0111700);国家自然科学基金资助项目(U21A20487);云南省科技人才与平台计划（院士专家工作站）(202305AF150152)

Abstract

Abstract:

To address the pose deviation issues faced by Wheeled Mobile Robots （WMRs） during trajectory tracking due to inaccurate positioning and unknown disturbances， an Enhanced Particle Swarm Optimization Mixer （EPSO-Mixer） algorithm based on Geometric Model Predictive Control （GMPC） was proposed， aiming to enhance trajectory tracking performance of WMRs. Firstly， an Enhanced Particle Swarm Optimization （EPSO） algorithm was proposed on the basis of Particle Swarm Optimization （PSO） to accelerate convergence and improve optimization capabilities. Secondly， EPSO was used to improve GMPC by selecting optimal tracking parameters according to the current deviation level， so as to reduce trajectory tracking errors effectively. Finally， by integrating the Multi-Layer Perceptron Mixer （MLP-Mixer） architecture， EPSO-Mixer algorithm was proposed， thereby further enhancing search capability for the global optimum and generating more adaptive control strategies. Simulation results show that compared with nonlinear model predictive control and classic GMPC algorithms， EPSO-Mixer GMPC improves trajectory tracking performance of WMRs under pose deviation conditions effectively with errors reduced by 8.0% - 82.3% and mitigating vibration issues during motion significantly. These results indicate that EPSO-Mixer algorithm provides more effective control strategies， thereby reducing the complexity and time cost of parameter adjustment， and enhancing the adaptability of trajectory tracking control significantly.

Key words: Wheeled Mobile Robot (WMR), trajectory tracking, Particle Swarm Optimization (PSO), Multi-Layer Perceptron Mixer (MLP-Mixer), Geometric Model Predictive Control (GMPC)

摘要：

针对轮式移动机器人（WMR）在轨迹跟踪过程中因定位失准和未知干扰等因素导致的位姿偏移问题，提出一种基于几何模型预测控制（GMPC）的增强型粒子群优化混合器（EPSO-Mixer）算法，旨在提升WMR的轨迹跟踪性能。首先，以粒子群优化（PSO）为基础，提出一种增强型粒子群优化（EPSO）算法，以加快收敛并提升优化能力；其次，利用EPSO对GMPC进行改进，根据当前偏移程度筛选出最优跟踪参数，以有效地减小轨迹跟踪误差；最后，结合混合多层感知器（MLP-Mixer）架构，提出EPSO-Mixer算法，从而进一步增强对全局最优解的搜索能力，同时生成更具适应性的控制策略。仿真实验结果表明，与非线性模型预测控制和经典GMPC算法相比，EPSO-Mixer GMPC有效提升了WMR在位姿偏移条件下的轨迹跟踪性能，误差减小8.0%~82.3%，并显著改善了运动中的振动问题。可见，EPSO-Mixer算法能够提供更有效的控制策略，不仅降低了参数调整的难度与时间成本，而且显著增强了轨迹跟踪控制的自适应能力。

关键词: 轮式移动机器人, 轨迹跟踪, 粒子群优化, 混合多层感知器, 几何模型预测控制

CLC Number:

TP242.6

Songjian GU, Fuxiang WU, Xiangyang GAO, Mengjie YANG, Yibing ZHAN, Jun CHENG. Trajectory tracking algorithm for mobile robots based on geometric model predictive control[J]. Journal of Computer Applications, 2025, 45(9): 3026-3035.

古松健, 吴福祥, 高向阳, 杨梦杰, 詹忆冰, 程俊. 基于几何模型预测控制的移动机器人轨迹跟踪算法[J]. 《计算机应用》唯一官方网站, 2025, 45(9): 3026-3035.

Figures/Tables 16

Fig. 1 Kinematics model of FWDMR

Tab. 1 Symbols used in GMPC framework and their meanings

符号	意义
$R n$	n维向量空间
$S E (2)$	二维空间中的特殊欧几里得群
$s e (2)$	与 $S E (2)$ 相关的李代数
$X ∈ S E (2)$	刚体在平面中移动的状态向量
$X d ∈ S E (2)$	刚体在平面中移动的参考状态向量
$ζ ∈ R 3$	刚体在平面中移动的速度向量
$ζ Λ ∈ s e (2)$	李代数中的速度元素
$u ∈ R 2$	控制输入
$Ψ ∈ S E (2)$	$X d$ 和 $X$ 之间的差值
$ψ Λ ∈ s e (2)$	与 $Ψ$ 相关的李代数
$X ˙ = d d t X$	$X$ 的一阶时间导数

Tab. 1 Symbols used in GMPC framework and their meanings

符号	意义
$R n$	n维向量空间
$S E (2)$	二维空间中的特殊欧几里得群
$s e (2)$	与 $S E (2)$ 相关的李代数
$X ∈ S E (2)$	刚体在平面中移动的状态向量
$X d ∈ S E (2)$	刚体在平面中移动的参考状态向量
$ζ ∈ R 3$	刚体在平面中移动的速度向量
$ζ Λ ∈ s e (2)$	李代数中的速度元素
$u ∈ R 2$	控制输入
$Ψ ∈ S E (2)$	$X d$ 和 $X$ 之间的差值
$ψ Λ ∈ s e (2)$	与 $Ψ$ 相关的李代数
$X ˙ = d d t X$	$X$ 的一阶时间导数

Tab. 2 Rules for updating acceleration factors

调整时段	$c 1$	$c 2$
探索阶段	大幅增加	大幅减小
开发阶段	小幅增加	小幅减小
收敛阶段	小幅增加	小幅减小
结束阶段	大幅减小	大幅增加

Tab. 2 Rules for updating acceleration factors

调整时段	$c 1$	$c 2$
探索阶段	大幅增加	大幅减小
开发阶段	小幅增加	小幅减小
收敛阶段	小幅增加	小幅减小
结束阶段	大幅减小	大幅增加

Fig. 2 Principle of EPSO-GMPC algorithm

Fig. 3 Mixer algorithm structure

Fig. 4 Framework of EPSO-Mixer trajectory tracking algorithm

Tab. 3 PSO parameter setting

参数	含义	数值
$n V a r$	未知（决策）变量的数量	5
$n P o p$	粒子数	50
$c 1 i n t$	认知加速因子初始值	2
$c 2 i n t$	社会加速因子初始值	2
$G$	最大迭代次数	50或100
$ω m a x$	惯性权重最大值	0.99
$ω m i n$	惯性权重最小值	0.1
$ω d$	阻尼因子	0.99

Tab. 3 PSO parameter setting

参数	含义	数值
$n V a r$	未知（决策）变量的数量	5
$n P o p$	粒子数	50
$c 1 i n t$	认知加速因子初始值	2
$c 2 i n t$	社会加速因子初始值	2
$G$	最大迭代次数	50或100
$ω m a x$	惯性权重最大值	0.99
$ω m i n$	惯性权重最小值	0.1
$ω d$	阻尼因子	0.99

Tab. 4 Comparison of maximum iteration numbers and best fitness values of different algorithms

算法	最大迭代次数	最佳适应度
经典PSO	50	4.65×10^-3
经典PSO	100	1.70×10^-4
文献［22］算法	50	3.80×10^-2
文献［22］算法	100	4.04×10^-3
文献［23］算法	50	7.69×10^-2
文献［23］算法	100	3.39×10^-4
文献［26］算法	50	1.11×10^-5
文献［26］算法	100	7.11×10^-8
EPSO	50	1.89×10^-11
EPSO	100	1.32×10^-20

Fig. 5 Optimization results of PSO algorithms for spherical functions

Fig. 6 Simulation object and simulation platform interface

Fig. 7 Tracking performance of various control schemes under conventional condition for circular trajectory

Fig. 8 Tracking performance of various control schemes under 30 ° course shift for circular trajectory

Fig. 9 Tracking performance of various control schemes under 60 ° course shift for circular trajectory

Fig. 10 Tracking performance of various control schemes under 90 ° course shift for circular trajectory

Fig. 11 Tracking performance of various control schemes under 60° course shift for S-shaped trajectory

Tab. 5 Comparison of optimization results of different algorithms

算法	Q₁	Q₂	Q₃	R	N	SSE	提升/%
BPNN	19 256	15 593	1 901	0.4	17	3.464	29.7
GA	22 438	19 848	2 298	0.3	15	3.275	33.6
EPSO	22 611	15 597	2 462	0.2	18	3.134	36.4
XGBoost^［27］	24 445	20 438	2 410	0.5	15	3.785	23.2
gMLP^［28］	19 807	17 758	2 470	0.9	14	3.332	30.0
TabNet^［29］	22 916	14 652	2 417	0.1	14	3.389	31.3
EPSO-Mixer	23 606	15 325	2 446	0.6	18	2.894	41.3

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Trajectory tracking algorithm for mobile robots based on geometric model predictive control

基于几何模型预测控制的移动机器人轨迹跟踪算法

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