基于微分平坦的分层轨迹规划算法

doi:10.12382/bgxb.2021.0756

摘要/Abstract

摘要：

为充分考虑横纵向耦合和汽车运动学特性对轨迹规划的影响,提出一种分层优化的轨迹规划算法框架。利用贝塞尔曲线的凸包性设计安全走廊约束,以轨迹平滑性为目标函数得到一个基于贝塞尔曲线节点的下层规划器。在上层规划器中,基于下层规划器求解得到的横纵向贝塞尔曲线和车辆运动学模型的微分平坦输出进行三维耦合,构建满足车辆乘坐舒适性、高效性和安全性的目标函数,利用粒子群优化算法对贝塞尔轨迹初始参数进行二次优化得到综合性能最优的行驶轨迹。仿真结果表明:新算法在保证安全性的同时,具有良好的乘坐舒适性和可跟踪性;由于二次规划与粒子群优化算法的求解效率高,此框架实时性强,具有概率完备性。

关键词: 轨迹规划, 微分平坦, 贝塞尔曲线, 二次规划, 粒子群优化算法

Abstract:

To fully consider the influence of transverse and longitudinal coupling and vehicle kinematics on trajectory planning, a hierarchical optimization-based trajectory planning algorithm framework is proposed. The safe corridor constraint is designed with the convex hull of a Bezier curve. Taking the trajectory smoothness as the objective function, we obtain a lower planner based on Bezier curve nodes. In the upper planner, based on the transverse and longitudinal Bezier curves solved by the lower planner and the differentially flat output of the vehicle kinematics model, the objective function meeting the vehicle ride comfort, efficiency and safety requirements is constructed, and quadratic optimization is applied to the initial parameters of the Bezier trajectory by particle swarm optimization algorithm to obtain the driving trajectory with the best comprehensive performance. The simulation results show that: the algorithm has good ride comfort and traceability while ensuring safety; due to the high efficiency of quadratic programming and particle swarm optimization, this framework has strong real-time and probabilistic completeness.

Key words: trajectory planning, differential flatness, bezier curve, quadratic programming, particle swarm optimization algorithm

中图分类号:

TJ810.2

周孝添, 任宏斌, 苏波, 齐志权, 汪洋. 基于微分平坦的分层轨迹规划算法[J]. 兵工学报, 2023, 44(2): 394-405.

ZHOU Xiaotian, REN Hongbin, SU Bo, QI Zhiquan, WANG Yang. Hierarchical Trajectory Planning Algorithm based on Differential Flatness[J]. Acta Armamentarii, 2023, 44(2): 394-405.

图/表 15

图1 避障轨迹规划

Fig.1 Obstacle avoidance trajectory planning

图2 状态空间与平坦空间的映射关系

Fig.2 Mapping between state space and flat space

图3 车辆运动学模型

Fig.3 Vehicle kinematics model

图4 算法流程

Fig.4 Flow chart of the algorithm

图5 变道避障示意图

Fig.5 Schematic diagram of obstacle avoidance by lane changing

表1 仿真实验参数

Table 1 Simulation experiment parameters

参数	数值
汽车质量m/kg	1217
转动惯量I_z/(kg·m²)	1020
质心到前轴距离L_f/m	1.165
质心到后轴距离L_r/m	1.265
前轮转向刚度C_f/(N·rad^-1)	40000
后轮转向刚度C_r/(N·rad^-1)	40000
车道有效宽度D/m	3.6

图6 5次多项式采样过程

Fig.6 Quintic polynomial sampling process

图7 基于微分平坦分层轨迹规划仿真过程

Fig.7 Simulation process of hierarchical trajectory planning based on differential flatness

图8 硬件在环(HIL)实验平台

Fig.8 Hardware-in-the-loop (HIL) experimental platform

图9 变道仿真过程

Fig.9 Lane changing simulation process

图10 换道轨迹跟踪仿真结果

Fig.10 Simulation results of lane changingtrajectory tracking

图11 车辆换道性能参数

Fig.11 Lane changing performance parameters of the vehicle

图12 无人驾驶平台

Fig.12 Self-driving platform

图13 换道交通场景

Fig.13 Lane changing traffic scene

图14 换道轨迹跟踪结果

Fig.14 Tracking result for lane changing trajectory

参考文献 25

[1]	SHARMA O, SAHOO N C, PUHAN N B. Recent advances in motion and behavior planning techniques for software architecture of autonomous vehicles:a state-of-the-art survey[J]. Engineering Applications of Artificial Intelligence, 2021, 101(3):104211. doi: 10.1016/j.engappai.2021.104211 URL
[2]	LIN X K, LIN J N, SU Z Y, et al. Research on key technologies of power internet of things based on artificial intelligence technology[J]. IOP Conference Series:Earth and Environmental Science, 2021, 714(4):042067. doi: 10.1088/1755-1315/714/4/042067
[3]	CHEN Y, CHEN S Z, REN H B, et al. Path tracking and handling stability control strategy with collision avoidance for the autonomous vehicle under extreme conditions[J]. IEEE Transactions on Vehicular Technology, 2020, 69(12):14602-14617. doi: 10.1109/TVT.25 URL
[4]	ZHANG S S, WEI L, LI B C, et al. Trajectory planning of overtaking for intelligent vehicle based on X-Sin function[C]// Proceedings of IEEE International Conference on Mechatronics & Automation.Tianjin,China:IEEE, 2014:618-622.
[5]	聂枝根, 王万琼, 赵伟强, 等. 基于轨迹预瞄的智能汽车变道动态轨迹规划与跟踪控制[J]. 交通运输工程学报, 2020, 104(2):151-164.
	NIE Z G, WANG W Q, ZHAO W Q, et al. Dynamic trajectory planning and tracking control for lane change of intelligent vehicle based on trajectory preview[J]. Journal of Traffic and Transportation Engineering, 2020, 104(2):151-164. (in Chinese)
[6]	KANARIS A, KOSMATOPOULOS E B, LOANNOU P A. Strategies and spacing requirements for lane changing and merging in automated highway systems[J]. IEEE Transactions on Vehicular Technology, 2001, 50(6):1568-1581. doi: 10.1109/25.966586 URL
[7]	牛国臣, 李文帅, 魏洪旭. 基于双五次多项式的智能汽车换道轨迹规划[J]. 汽车工程, 2021, 43(7):978-986,1004.
	NIU G C, LI W S, WEI H X. Intelligent vehicle lane changing trajectory planing based on double quintic polynomials[J]. Automotive Engineering, 2021, 43(7):978-986,1004. (in Chinese)
[8]	LI H L, LUO Y T, WU J. Collision-Free path planning for intelligent vehicles based on bizier curve[J]. IEEE Access, 2019, 99:1-1.
[9]	SHIM T, ADIREDDY G, YUAN H L. Autonomous vehicle collision avoidance system using path planning and model-predictive-control-based active front steering and wheel torque control[J]. Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering, 2012, 226(6):767-778. doi: 10.1177/0954407011430275 URL
[10]	CONG Y F, SAWODNY O, CHEN H, et al. Motion planning for an autonomous vehicle driving on motorways by using flatness properties[C]//Proceedings of IEEE International Conference on Control Applications.Yokohama, Japan:IEEE, 2010:908-913.
[11]	WANG Z J, ZHA J Q, WANG J M. Flatness-based model predictive control for autonomous vehicle trajectory tracking[C]// Proceedings of the 2019 22nd Intelligent Transportation Systems Conference (ITSC). Auckland, New Zealand: IEEE, 2019:4146-4151.
[12]	GUO H, FEI W, HONG C, et al. Stability control of vehicle with tire blowout using differential flatness based MPC method[C]// Proceedings of the 2012 10th World Congress on Intelligent Control and Automation. Beijing,China: IEEE, 2012:2066-2071.
[13]	MCNAUGHTON M, URMSON C, DOLAN J, et al. Motion planning for autonomous driving with a conformal spatiotemporal lattice[C]//Proceedings of IEEE International Conference on Robotics & Automation. Shanghai:IEEE, 2011.
[14]	GONZALEZ D, PEREZ J, LATTARULO R, et al. Continuous curvature planning with obstacle avoidance capabilities in urban scenarios[C]// Proceedings of IEEE International Conference on Intelligent Transportation Systems.Qingdao, China: IEEE, 2014:1430-1435.
[15]	ROSS I M, FAHROO F. Pseudospectral methods for optimal motion planning of differentially flat systems[C]// Proceedings of IEEE Conference on Decision & Control. Las Vegas,NV, US: IEEE, 2002: 1135-1140.
[16]	赵新, 纪永祥, 罗熙斌, 等. 基于改进粒子群优化算法的近炸引信最佳炸高计算方法[J]. 兵工学报, 2021, 42(5):924-929.
	ZHAO X, JI Y X, LUO X B, et al. Computation method for the optimal burst height of proximity fuze based on improved particle swarm optimization algorithm[J]. Acta Armamentarii, 2021, 42(5):924-929. (in Chinese) doi: 10.3969/j.issn.1000-1093.2021.05.004
[17]	杜广泽, 张旭东, 邹渊, 等. 非结构道路场景下轮式无人车辆避障算法[J]. 兵工学报, 2020, 41(10):2096-2105. doi: 10.3969/j.issn.1000-1093.2020.10.020
	DU G Z, ZHANG X D, ZOU Y, et al. Obstacle avoidance agorithm for autonomous wheeled vehicle in unstructured environments[J]. Acta Armamentarii, 2020, 41(10): 2096-2105. (in Chinese)
[18]	BODY S, VANDENBERGHE L. Convex optimization[M]. Cambridge, UK: Cambridge University Press, 2004:76-84.
[19]	KIENCKE U, NIELSEN L. Automotive control systems: for engine,driveline and vehicle[J]. Measurement ence and Technology, 2000, 11(12):1828.
[20]	RAJAMANI R. Vehicle dynamics and control[M]. Beijing: China Machine Press, 2011.
[21]	TAUBMAN B A O, MIKULINCER M, GILLATH O. The multidimensional driving style inventory—scale construct and validation[J]. Accident Analysis & Prevention, 2004, 36(3):323-332. doi: 10.1016/S0001-4575(03)00010-1 URL
[22]	LIANG Y, LI Y N, KHAJEPOUR A, et al. Holistic adaptive multi-model predictive control for the path following of 4WID autonomous vehicles[J]. IEEE Transactions on Vehicular Technology, 2020, 99:1-1.
[23]	王沙晶. 基于Frenet坐标系采样的自动驾驶轨迹规划算法研究[D]. 兰州: 兰州理工大学, 2019.
	WANG S J. Research of trajectory planning for autonomous driving based frenet coordinate and sampling[D]. Lanzhou: Lanzhou University of Technology, 2019. (in Chinese)
[24]	陈龙, 邹凯, 蔡英凤, 等. 基于NMPC的智能汽车纵横向综合轨迹跟踪控制[J]. 汽车工程, 2021, 43(2):153-161.
	CHEN L, ZOU K, CAI Y F, et al. Integrated longitudinal and transverse trajectory tracking control of intelligent vehicle based on NMPC[J]. Automotive Engineering, 2021, 43(2):153-161. (in Chinese)
[25]	李睿, 项昌乐, 王超, 等. 自动驾驶履带车辆鲁棒自适应轨迹跟踪控制方法[J]. 兵工学报, 2021, 13(16):1128-1137.
	LI R, XIANG C L, WANG C, et al. Robust adaptive trajectory tracking control method for autonomous tracked vehicle[J]. Acta Armamentarii, 2021, 13(16):1128-1137. (in Chinese)