基于四阶贝塞尔曲线的应急救援车辆轨迹规划方法

doi:10.3901/JME.2025.02.198

摘要/Abstract

摘要： 为确保应急救援车辆的行驶安全性、舒适性、稳定性以及高机动性，同时针对应急救援车辆所具有的车宽大、重心高、转弯半径大等实际特征，提出一种基于三维-分段式四阶贝塞尔曲线的应急救援车辆轨迹规划方法。将车速信息视为对应轨迹坐标的垂向坐标，采用三维贝塞尔曲线进行车辆轨迹规划，从而同时实现轨迹规划和车速规划且将车速信息与车辆轨迹坐标一一对应。同时，为实现轨迹规划中多个优化目标与车辆智能驾驶实际需求的有效贴合，采用分段式贝塞尔曲线设计车辆轨迹，将车辆轨迹分为避撞过程和回正过程，从而实现车辆轨迹设计目标的动态优化。结果表明，所提出的基于三维-分段式四阶贝塞尔曲线的轨迹规划方法可在确保车辆安全、舒适、稳定性设计目标的同时，有效提高轨迹规划机动性，提升换道效率，降低换道时间。

关键词: 智能车辆, 轨迹规划, 贝塞尔曲线, 目标优化

Abstract: In order to ensure the driving safety, comfort, stability and high mobility of emergency rescue vehicles, at the same time, according to the actual characteristics of emergency rescue vehicles like large vehicle width, high center of gravity, large turning radius, a trajectory planning method of emergency rescue vehicle based on three-dimensional segmented fourth-order Bezier curve is proposed. The vehicle speed information is regarded as the vertical coordinates of the corresponding trajectory coordinates, and the three-dimensional Bezier curve is used for vehicle trajectory planning, so as to realize trajectory planning and vehicle speed planning at the same time, and the vehicle speed information is corresponding to the vehicle trajectory coordinates one by one. In addition, in order to realize the effective fit between multiple optimization objectives in trajectory planning and the actual needs of vehicle intelligent driving, the segmented Bezier curve is used to design the vehicle trajectory, and the vehicle trajectory is divided into collision avoidance process and correction process, so as to realize the dynamic optimization of vehicle trajectory design objectives. The results show that the proposed trajectory planning method based on three-dimensional segmented fourth-order Bezier curve can effectively improve the mobility of trajectory planning, improve lane changing efficiency and reduce lane changing time while ensuring the design objectives of vehicle safety, comfort and stability.

Key words: intelligent vehicle, trajectory planning, Bezier curves, objective optimization

中图分类号:

陈特, 蔡英凤, 陈龙, 徐兴. 基于四阶贝塞尔曲线的应急救援车辆轨迹规划方法[J]. 机械工程学报, 2025, 61(2): 198-209.

CHEN Te, CAI Yingfeng, CHEN Long, XU Xing. Trajectory Planning Method of Emergency Rescue Vehicle Based on Fourth-order Bezier Curve[J]. Journal of Mechanical Engineering, 2025, 61(2): 198-209.

参考文献

[1] WANG Y，HU J，WANG F，et al. Tire road friction coefficient estimation：Review and research perspectives[J]. Chin. J. Mech. Eng.，2022，35(2)：1-11.
[2] CHEN T，CHEN L，XU X，et al. Simultaneous path following and lateral stability control of 4WD-4WS autonomous electric vehicles with actuator saturation[J]. Advances in Engineering Software，2019，128：46-54.
[3] CHEN T，CHEN L，CAI Y F，et al. Robust sideslip angle observer with regional stability constraint for an uncertain singular intelligent vehicle system[J]. IET Control Theory & Applications，2018，12(13)：1802-1811.
[4] WANG Y，XU L，ZHANG F，et al. An adaptive fault-tolerant EKF for vehicle states estimation with multiple partial missing measurements[J]. IEEE/ASME Transactions on Mechatronics，2021，26(3)：1318-1327.
[5] LI Y，YIN G，ZHUANG W，et al. Compensating delays and noises in motion control of autonomous electric vehicles by using deep learning and unscented Kalman predictor[J]. IEEE Transactions on Systems，Man，and Cybernetics：Systems，2020，50(11)：4326-4338.
[6] 董昊轩，殷国栋，庄伟超，等. 基于迭代动态规划的网联电动汽车经济性巡航车速优化[J]. 机械工程学报，2021，57(6)：121-130. DONG Haoxuan，YIN Guodong，ZHUANG Weichao，et al. Economic cruising velocity optimization using iterative dynamic programming of connected electric vehicle[J]. Journal of Mechanical Engineering，2021，57(6)：121-130.
[7] 薛培林，吴愿，殷国栋，等. 基于信息融合的城市自主车辆实时目标识别[J]. 机械工程学报，2020，56(12)：165-173. XUE Peilin，WU Yuan，YIN Guodong，et al. Real-time target recognition for urban autonomous vehicles based on information fusion[J]. Journal of Mechanical Engineering，2020，56(12)：165-173.
[8] 王明强，王震坡，张雷. 基于碰撞风险评估的智能汽车局部路径规划方法研究[J]. 机械工程学报，2021，57(10)：28-41. WANG Mingqiang，WANG Zhenpo，ZHANG Lei. Local path planning for intelligent vehicles based on collision risk evaluation[J]. Journal of Mechanical Engineering，2021，57(10)：28-41.
[9] 彭海军，施博洋，王昕炜，等. 考虑区间不确定性的双摆吊车运动轨迹规划[J]. 机械工程学报，2019，55(2)：204-213. PENG Haijun，SHI Boyang，WANG Xinwei，et al. Trajectory planning of double pendulum crane considering interval uncertainty[J]. Journal of Mechanical Engineering，2019，55(2)：204-213.
[10] LIU Y，ZHOU B，WANG X，et al. Dynamic lane- changing trajectory planning for autonomous vehicles based on discrete global trajectory[J]. IEEE Trans Intell Transp Syst.，2022，23(7)：8513-8527.
[11] LIM M，LEE S，SUNWOO M，et al. Hybrid trajectory planning for autonomous driving in on-road dynamic scenarios[J]. IEEE Trans. Intell. Transp. Syst.，2019，22(1)：341-355.
[12] CHEN T，XU X，CHEN L，et al. Estimation of longitudinal force，lateral vehicle speed and yaw rate for four-wheel independent driven electric vehicles[J]. Mech. Syst. Signal Process，2018，101：377-388.
[13] 卢山峰，徐兴，陈龙，等. 轮毂电机驱动汽车电子差速与差动助力转向的协调控制[J]. 机械工程学报，2017，53(16)：78-85. LU Shanfeng，XU Xing，CHEN Long，et al. Coordinated control of electronic differential and differential assist steering for electric vehicle driven by in-wheel motors[J]. Journal of Mechanical Engineering，2017，53(16)：78-85.
[14] 钱立军，吴冰，仇多洋，等. 基于hp自适应伪谱法的自主泊车路径规划[J]. 机械工程学报，2020，56(4)：125-134. QIAN Lijun，WU Bing，QIU Duoyang，et al. Path planning of autonomous parking based on hp-adaptive pseudospectral method[J]. Journal of Mechanical Engineering，2020，56(4)：125-134.
[15] 刘梓林，黎予生，郑玲. 基于非结构化环境点云稀疏表示的无人驾驶汽车局部路径规划方法[J]. 机械工程学报，2020，56(2)：163-173. LIU Zilin，LI Yusheng，ZHENG Ling. Local path planning for autonomous vehicles based on sparse representation of point cloud in unstructured environments[J]. Journal of Mechanical Engineering，2020，56(2)：163-173.
[16] 李爱娟，李舜酩，沈峘，等. 智能车大角度弯道转向曲率连续的轨迹规划方法[J]. 中国机械工程，2014，25(2)：273-278. LI Aijuan，LI Shunming，SHEN Huan，et al. Continuous curvature trajectory planning method of large angle steering for intelligent vehicle[J]. China Mechanical Engineering，2014，25(2)：273-278.
[17] 张利鹏，苏泰，严勇. 基于采样区域优化的智能车辆轨迹规划方法[J]. 机械工程学报，2021，57：1-12. ZHANG Lipeng，SU Tai，YAN Yong. Trajectory planning method of intelligent vehicle based on sampling area optimization[J]. Journal of Mechanical Engineering，2021，57：1-12.
[18] 赵树恩，王金祥，李玉玲. 基于多目标优化的智能车辆换道轨迹规划[J]. 交通运输工程学报，2021，21(2)：232-242. ZHAO Shuen，LI Jinxiang，LI Yuling. Lane changing trajectory planning of intelligent vehicle based on multiple objective optimization[J]. Journal of Traffic and Transportation Engineering，2021，21(2)：232-242.
[19] 采国顺，刘昊吉，冯吉伟，等. 智能汽车的运动规划与控制研究综述[J]. 汽车安全与节能学报，2021，12(3)：279-297. CAI Guoshun，LIU Haoji，FENG Jiwei，et al. Review on the research of motion planning and control for intelligent vehicles[J]. Journal of Automotive Safety and Energy，2021，12(3)：279-297.
[20] 王慧然，王其东，陈无畏，等. 基于车辆行驶安全边界的换道控制[J]. 机械工程学报，2020，56(18)：143-153. WANG Huiran，WANG Qidong，CHEN Wuwei，et al. Lane change control based on vehicle driving safe boundary[J]. Journal of Mechanical Engineering，2020，56(18)：143-153.
[21] 余伶俐，邵玄雅，龙子威，等. 智能车辆深度强化学习的模型迁移轨迹规划方法[J]. 控制理论与应用，2019，36(9)：1409-1422. YU Lingli，SHAO Xuanya，LONG Ziwei，et al. Intelligent land vehicle model transfer trajectory planning method of deep reinforcement learning[J]. Control Theory and Applications，2019，36(9)：1409-1422.
[22] 孙秦豫，付锐，王畅，等. 人机协作系统中车辆轨迹规划与轨迹跟踪控制研究[J]. 中国公路学报，2021，34(9)：146-160. SUN Qinyu，FU Rui，WANG Chang，et al. Vehicle trajectory-planning and trajectory-tracking control in human-autonomous collaboration system[J]. China Journal of Highway and Transport，2021，34(9)：146-160.
[23] 王莹，卫翀，马路. 基于二次规划的智能车辆动态换道轨迹规划研究[J]. 中国公路学报，2021，34(7)：79-94. WANG Ying，WEI Chong，MA Lu. Dynamic lane- changing trajectory planning model for intelligent vehicle based on quadratic programming[J]. China Journal of Highway and Transport，2021，34(7)：79-94.