Path planning and tracking control for differential-drive robots based on A<sup>*</sup> and multi-reference point MPC

doi:10.3785/j.issn.1008-973X.2026.08.002

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (8): 1627-1637 DOI: 10.3785/j.issn.1008-973X.2026.08.002

Path planning and tracking control for differential-drive robots based on A^* and multi-reference point MPC

Mengbin DUAN1(

),Guoxing BAI1,2,Yu MENG1,*(

),Qing GU1,Zhen WANG3,Elxat ELHAM1,Shaochong LIU1

1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2. Postdoctoral Research Station of Jidong Development Group Co Ltd, Tangshan 063200, China
3. Shenzhen Yinwang Intelligent Technology Co. Ltd, Shenzhen 518100, China

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Abstract

An integrated system for path planning and tracking control was developed to address the structural mismatch between the discrete path generated by the A^* algorithm and the continuous inputs required by multi-reference point model predictive control (M-MPC), and to improve the tracking accuracy and smoothness of path tracking control. The A^* reference path was smoothed and discretized at equal arc-length intervals, and the generated reference point sequence was introduced into the prediction horizon of the M-MPC controller. A heading alignment mechanism was designed to mitigate the problem of large initial heading deviations between the reference path and the differential-drive robot, thereby ensuring a seamless transition from path planning to tracking control. Experimental results demonstrated that the proposed system achieved high accuracy and smoothness. Compared with the direct combination system of the A^* algorithm and M-MPC, the peak and average values of the displacement error were reduced by 51.85% and 20.40%, respectively, while the cumulative control increment was decreased by 28.86%. Compared with the systems combining the smoothed A^* algorithm and a pure pursuit controller or a single reference point MPC, the peak and average values of the displacement error was decreased by at least 52.80% and 41.58%, respectively. The proposed system improved the tracking accuracy and smoothness, and enhanced the motion control performance of differential-drive robots in complex environments.

Key words： differential-drive robot path planning path tracking control A^* algorithm nonlinear model predictive control equal arc-length interval discretization

Received: 14 July 2025 Published: 16 July 2026

CLC:

TP 393

Fund: 金属矿山安全技术国家重点实验室资助项目（2025GZKJ05）；国家重点研发计划资助项目（2023YFC3806603）；中国博士后科学基金资助项目（2022M710354）；国家自然科学基金资助项目（52202505）；唐山市人才资助项目（C202503022）.

Corresponding Authors: Yu MENG E-mail: M202420748@xs.ustb.edu.cn;myu@ustb.edu.cn

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	Mengbin DUAN
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	Elxat ELHAM
	Shaochong LIU

Cite this article:

Mengbin DUAN,Guoxing BAI,Yu MENG,Qing GU,Zhen WANG,Elxat ELHAM,Shaochong LIU. Path planning and tracking control for differential-drive robots based on A^* and multi-reference point MPC. Journal of ZheJiang University (Engineering Science), 2026, 60(8): 1627-1637.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.08.002 OR https://www.zjujournals.com/eng/Y2026/V60/I8/1627

基于A^*与多参考点MPC的差动机器人路径规划与跟踪控制

为了解决A^*算法生成的离散路径与多参考点模型预测控制（M-MPC）所需的连续输入之间的结构失配问题，提升路径跟踪控制的精确性和平顺性，提出面向路径规划与跟踪控制的集成系统. 对A^*参考路径进行平滑和等弧长间距离散化处理，将生成的参考点序列引入M-MPC控制器的预测时域，并设计航向对齐机制，以缓解A^*参考路径与差动机器人之间存在较大初始航向偏差的问题，实现路径规划与跟踪控制的平稳衔接. 实验结果表明，提出的系统具有较高的精度和平顺性；与A^*算法和M-MPC直接结合的系统相比，位移误差峰值和均值分别降低了51.85%和20.40%，控制增量累加值降低了28.86%；与平滑后的A^*算法和纯跟踪或单参考点MPC结合的系统相比，位移误差峰值和均值分别降低了至少52.80%和41.58%. 所提系统提升了跟踪精度与平顺性，改善了差动机器人在复杂环境中的运动控制性能.

关键词： 差动机器人, 路径规划, 路径跟踪控制, A^*算法, 非线性模型预测控制, 等弧长间距离散化

Fig.1 Hierarchical planning and control architecture for differential-drive robots

Fig.2 Comparison of smoothing effects of B-spline curves with various degrees

Fig.3 Schematic diagram of initial heading and planned path of differential-drive robots

Fig.4 Kinematic model for differential-drive robots

Tab.1 Parameters configuration for M-MPC controller

Fig.5 Path tracking results under different path preprocessing strategies

Fig.6 Displacement errors under different path preprocessing strategies

Fig.7 Heading errors under different path preprocessing strategies

Fig.8 Angular velocity curves under different path preprocessing strategies

Tab.2 Experimental results under different path preprocessing strategies

Fig.9 Path tracking results with or without heading alignment mechanism

Fig.10 Displacement error with or without heading alignment mechanism

Fig.11 Path tracking results of different control systems

Fig.12 Displacement errors of different control systems

Fig.13 Heading errors of different control systems

Fig.14 Angular velocity curves of different control systems

Tab.3 Displacement and heading errors of different control systems


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