Real-time trajectory planning in highly dynamic poses high challenges for the safe performance of highly automated vehicles, especially when considering the limited computational resources. In this paper, we propose a novel optimization-free trajectory planning approach for highly automated vehicles that integrates Bézier curve-based path planning with constrained backstepping-control-based velocity planning. Firstly, by leveraging the geometric properties of Bézier curves, we ensure several smooth and static-obstacle-collision-free paths. Subsequently, we implement backstepping control to plan the velocity considering states and control input constraints for selected paths. Finally, the planned trajectories are evaluated, and the optimal one is chosen based on predefined rules. This optimization-free property makes the proposed method update the trajectory at high frequencies, improving the ability to deal with highly dynamic environments. Simulation results based on Carsim demonstrate the effectiveness of the proposed method.
GuoJKurupUShahM.Is it safe to drive? An overview of factors, metrics, and datasets for driveability assessment in autonomous driving. IEEE Trans Intell Transp Syst2019; 21(8): 3135–3151.
2.
LiMCaoHLiG, et al. A two-layer potential-field-driven model predictive shared control towards driver-automation cooperation. IEEE Trans Intell Transp Syst2020; 23(5): 4415–4431.
3.
GonzálezDPérezJMilanésV, et al. A review of motion planning techniques for automated vehicles. IEEE Trans Intell Transp Syst2015; 17(4): 1135–1145.
4.
GordonTJLidbergM.Automated driving and autonomous functions on road vehicles. Veh Syst Dyn2015; 53(7): 958–994.
5.
LiXSunZCaoD, et al. Development of a new integrated local trajectory planning and tracking control framework for autonomous ground vehicles. Mech Syst Signal Process2017; 87: 118–137.
6.
GasparettoABoscariolPLanzuttiA, et al. Path planning and trajectory planning algorithms: a general overview. In: CarboneGGomez-BravoF (eds) Motion and operation planning of robotic systems: background and practical approaches. Springer, 2015, pp.3–27.
7.
GarciaMAPMontielOCastilloO, et al. Path planning for autonomous mobile robot navigation with ant colony optimization and fuzzy cost function evaluation. Appl Soft Comput2009; 9(3): 1102–1110.
8.
DevaursDSiméonTCortésJ.Optimal path planning in complex cost spaces with sampling-based algorithms. IEEE Trans Autom Sci Eng2015; 13(2): 415–424.
9.
JailletLCortésJSiméonT.Sampling-based path planning on configuration-space costmaps. IEEE Trans Robot2010; 26(4): 635–646.
10.
GuoYYaoDLiB, et al. Trajectory planning for an autonomous vehicle in spatially constrained environments. IEEE Trans Intell Transp Syst2022; 23(10): 18326–18336.
11.
NiuTWangLXuY, et al. Quintic Bézier curve and numerical optimal solution based path planning approach in seismic exploration. Control Eng Pract2024; 145: 105855.
12.
SongBWangZZouL.An improved PSO algorithm for smooth path planning of mobile robots using continuous high-degree Bezier curve. Appl Soft Comput2021; 100: 106960.
13.
SchäferLManzingerSAlthoffM.Computation of solution spaces for optimization-based trajectory planning. IEEE Trans Intell Veh2021; 8(1): 216–231.
14.
FergusonDStentzA.Using interpolation to improve path planning: the Field D* algorithm. J Field Robot2006; 23(2): 79–101.
15.
JonesMDjahelSWelshK.Path-planning for unmanned aerial vehicles with environment complexity considerations: a survey. ACM Comput Surv2023; 55(11): 1–39.
16.
NaderiKRajamäkiJHämäläinenP. RT-RRT*: a real-time path planning algorithm based on RRT. In: Proceedings of the 8th ACM SIGGRAPH conference on motion in games, Paris, France, 16–18 November 2015, pp.113–118. New York: ACM.
17.
SudAAndersenECurtisS, et al. Real-time path planning in dynamic virtual environments using multiagent navigation graphs. IEEE Trans Vis Comput Graph2008; 14(3): 526–538.
18.
WangMShanHLuR, et al. Real-time path planning based on hybrid-VANET-enhanced transportation system. IEEE Trans Veh Technol2014; 64(5): 1664–1678.
19.
RoutADeepakBBiswalBB.Advances in weld seam tracking techniques for robotic welding: a review. Robot Comput Integr Manuf2019; 56: 12–37.
20.
FaridGCocuzzaSYounasT, et al. Modified A-star (A*) approach to plan the motion of a quadrotor UAV in three-dimensional obstacle-cluttered environment. Appl Sci2022; 12(12): 5791.
21.
ZhuDDSunJQ.A new algorithm based on Dijkstra for vehicle path planning considering intersection attribute. IEEE Access2021; 9: 19761–19775.
22.
KaramanSFrazzoliE.Sampling-based algorithms for optimal motion planning. Int J Rob Res2011; 30(7): 846–894.
23.
TangLWangHLiuZ, et al. A real-time quadrotor trajectory planning framework based on B-spline and nonuniform kinodynamic search. J Field Robot2021; 38(3): 452–475.
24.
ArtunedoAVillagraJGodoyJ, et al. Motion planning approach considering localization uncertainty. IEEE Trans Veh Technol2020; 69(6): 5983–5994.
25.
ScheffePPedrosaMVAFlaßkampK, et al. Receding horizon control using graph search for multi-agent trajectory planning. IEEE Trans Control Syst Technol2022; 31(3): 1092–1105.
26.
KingstonZMollMKavrakiLE.Sampling-based methods for motion planning with constraints. Annu Rev Control Robot Auton Syst2018; 1(1): 159–185.
27.
LinFShenLYYuanCM, et al. Certified space curve fitting and trajectory planning for CNC machining with cubic B-splines. Comput Aided Des2019; 106: 13–29.
28.
LeiYZChengYYangXT.An optimization-free approximation framework for connected and automated vehicles eco-trajectory planning under limited computing capacity. Transp Res Part C Emerg Technol2025; 171: 104949.
29.
SuoHWeiBWuJ, et al. Threat cost based multi-level prediction D-star algorithm. 2023.
30.
WangPYangJZhangY, et al. Obstacle-avoidance path-planning algorithm for autonomous vehicles based on B-spline algorithm. World Electr Veh J2022; 13(12): 233.
31.
DaXGrizzleJ.Combining trajectory optimization, supervised machine learning, and model structure for mitigating the curse of dimensionality in the control of bipedal robots. Int J Rob Res2019; 38(9): 1063–1097.
32.
GuoXGXuWDWangJL, et al. BLF-based neuroadaptive fault-tolerant control for nonlinear vehicular platoon with time-varying fault directions and distance restrictions. IEEE Trans Intell Transp Syst2021; 23(8): 12388–12398.
33.
SamieeSAzadiSKazemiR, et al. Performance evaluation of a novel vehicle collision avoidance lane change algorithm. In: SchulzeTMüllerBMeyerG (eds) Advanced microsystems for automotive applications 2015: smart systems for green and automated driving. Springer International Publishing, 2016, pp.103–116.
34.
TangXYangKWangH, et al. Driving environment uncertainty-aware motion planning for autonomous vehicles. Chin J Mech Eng2022; 35(1): 120.
35.
FanHZhuFLiuC, et al. Baidu apollo em motion planner. arXiv preprint arXiv:1807.08048, 2018.
