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Keywords = Frenet coordinate system

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21 pages, 7382 KiB  
Article
Advanced Trajectory Planning and Control for Autonomous Vehicles with Quintic Polynomials
by Ma Jin, Mingcheng Qu, Qingyang Gao, Zhuo Huang, Tonghua Su and Zhongchao Liang
Sensors 2024, 24(24), 7928; https://doi.org/10.3390/s24247928 - 11 Dec 2024
Viewed by 2614
Abstract
This paper focuses on the design of vehicle trajectories and their control systems. A method based on quintic polynomials is utilized to develop trajectories for intelligent vehicles, ensuring the smooth continuity of the trajectory and related state curves under varying conditions. The construction [...] Read more.
This paper focuses on the design of vehicle trajectories and their control systems. A method based on quintic polynomials is utilized to develop trajectories for intelligent vehicles, ensuring the smooth continuity of the trajectory and related state curves under varying conditions. The construction of lateral and longitudinal controllers is discussed, which includes a tracking error model derived from the two-degree-of-freedom dynamic model of a two-wheeled vehicle and the application of the Frenet coordinate system transformation. The vehicle tracking performance is regulated by these controllers. Experimental verification on a small intelligent vehicle platform operating on the Ackermann steering principle was conducted. The results confirm the tracking performance of the controllers under different conditions and validate the effectiveness and feasibility of the overall framework of the study. Full article
(This article belongs to the Section Vehicular Sensing)
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29 pages, 11493 KiB  
Article
Three-Dimensional Path Following Control for Underactuated AUV Based on Ocean Current Observer
by Long He, Ya Zhang, Shizhong Li, Bo Li and Zeihui Yuan
Drones 2024, 8(11), 672; https://doi.org/10.3390/drones8110672 - 13 Nov 2024
Cited by 4 | Viewed by 1436
Abstract
In the marine environment, the motion characteristics of Autonomous Underwater Vehicles (AUVs) are influenced by unknown factors such as time-varying ocean currents, thereby amplifying the complexity involved in the design of path-following controllers. In this study, a backstepping sliding mode control method based [...] Read more.
In the marine environment, the motion characteristics of Autonomous Underwater Vehicles (AUVs) are influenced by unknown factors such as time-varying ocean currents, thereby amplifying the complexity involved in the design of path-following controllers. In this study, a backstepping sliding mode control method based on a current observer and nonlinear disturbance observer (NDO) has been developed, addressing the 3D path-following issue for AUVs operating in the ocean environment. Accounting for uncertainties like variable ocean currents, this research establishes the AUV’s kinematics and dynamics models and formulates the tracking error within the Frenet–Serret coordinate system. The kinematic controller is designed through the line-of-sight method and the backstepping method, and the dynamic controller is developed using the nonlinear disturbance observer and the integral sliding mode control method. Furthermore, an ocean current observer is developed for the real-time estimation of current velocities, thereby mitigating the effects of ocean currents on navigational performance. Theoretical analysis confirms the system’s asymptotic stability, while numerical simulation attests to the proposed method’s efficacy and robustness in 3D path following. Full article
(This article belongs to the Special Issue Advances in Autonomy of Underwater Vehicles (AUVs))
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26 pages, 32628 KiB  
Article
Risk-Aware Lane Change and Trajectory Planning for Connected Autonomous Vehicles Based on a Potential Field Model
by Tao Wang, Dayi Qu, Kedong Wang, Chuanbao Wei and Aodi Li
World Electr. Veh. J. 2024, 15(11), 489; https://doi.org/10.3390/wevj15110489 - 27 Oct 2024
Viewed by 2531
Abstract
To enhance the safety of lane changes for connected autonomous vehicles in an intelligent transportation environment, this study draws from potential field theory to analyze variations in the risks that vehicles face under different traffic conditions. The safe minimum vehicle distance is dynamically [...] Read more.
To enhance the safety of lane changes for connected autonomous vehicles in an intelligent transportation environment, this study draws from potential field theory to analyze variations in the risks that vehicles face under different traffic conditions. The safe minimum vehicle distance is dynamically adjusted, and a comprehensive vehicle risk potential field model is developed. This model systematically quantifies the risks encountered by connected autonomous vehicles during the driving process, providing a more accurate assessment of safety conditions. Subsequently, vehicle motion is decoupled into lateral and longitudinal components within the Frenet coordinate system, with quintic polynomials employed to generate clusters of potential trajectories. To improve computational efficiency, trajectory evaluation metrics are developed based on vehicle dynamics, incorporating factors such as acceleration, jerk, and curvature. An initial filtering process is applied to these trajectories, yielding a refined set of candidates. These candidate trajectories are further assessed using a minimum safety distance model derived from potential field theory, with optimization focusing on safety, comfort, and efficiency. The algorithm is tested in a three-lane curved simulation environment that includes both constant-speed and variable-speed lane change scenarios. Results show that the collision risk between the target vehicle and surrounding vehicles remains below the minimum safety distance threshold throughout the lane change process, ensuring a high level of safety. Furthermore, across various driving conditions, the target vehicle’s acceleration, jerk, and trajectory curvature remained well within acceptable limits, demonstrating that the proposed lane change trajectory planning algorithm successfully balances safety, comfort, and smoothness, even in complex traffic environments. Full article
(This article belongs to the Special Issue Motion Planning and Control of Autonomous Vehicles)
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20 pages, 6340 KiB  
Article
Calculation Model for the Exit Decision Sight Distance of Right-Turn Ramps on the Left at Interchange
by Zhipeng Fu, Jiale Zhang, Binghong Pan, Shangen Wu and Hang Yang
Appl. Sci. 2024, 14(14), 6205; https://doi.org/10.3390/app14146205 - 17 Jul 2024
Viewed by 1285
Abstract
Given the rapid construction of freeways in developing countries such as China, land use is constantly under strict constraints, leading to challenges in adopting conventional layouts for interchanges. Implementing right-turn ramps on the left (RTRL) at interchanges can minimize land occupancy; however, the [...] Read more.
Given the rapid construction of freeways in developing countries such as China, land use is constantly under strict constraints, leading to challenges in adopting conventional layouts for interchanges. Implementing right-turn ramps on the left (RTRL) at interchanges can minimize land occupancy; however, the traffic safety level in this type of diversion area design requires extra attention. This study examines the decision sight distance for right-turn exit ramps on the left side. Utilizing unmanned aerial vehicle (UAV) video and the YOLOv3 target detection algorithm, the original trajectory data of vehicles in the diversion area is extracted. Employing Kalman filtering and Frenet coordinate system conversion reveals microscopic vehicle lane-change patterns, velocities, and time headways. Furthermore, the driving simulation experiment assesses driver behaviors in RTRL, with subjective, task performance, and physiological measure indicators. Ultimately, the range of the decision sight distance is defined, and establishing a calculation model involves determining relevant parameters based on measured data and simulation outcomes. The results indicate potential insufficiencies in the decision sight distance when standardized values are applied to RTRL. Full article
(This article belongs to the Section Transportation and Future Mobility)
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15 pages, 2760 KiB  
Article
Amino-Acid Characteristics in Protein Native State Structures
by Tatjana Škrbić, Achille Giacometti, Trinh X. Hoang, Amos Maritan and Jayanth R. Banavar
Biomolecules 2024, 14(7), 805; https://doi.org/10.3390/biom14070805 - 7 Jul 2024
Cited by 1 | Viewed by 2446
Abstract
The molecular machines of life, proteins, are made up of twenty kinds of amino acids, each with distinctive side chains. We present a geometrical analysis of the protrusion statistics of side chains in more than 4000 high-resolution protein structures. We employ a coarse-grained [...] Read more.
The molecular machines of life, proteins, are made up of twenty kinds of amino acids, each with distinctive side chains. We present a geometrical analysis of the protrusion statistics of side chains in more than 4000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of Cα atoms and consider just the heavy atoms of the side chains. We study the large variety of behaviors of the amino acids based on both rudimentary structural chemistry as well as geometry. Our geometrical analysis uses a backbone Frenet coordinate system for the common study of all amino acids. Our analysis underscores the richness of the repertoire of amino acids that is available to nature to design protein sequences that fit within the putative native state folds. Full article
(This article belongs to the Section Molecular Biology)
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23 pages, 15041 KiB  
Article
Research on Obstacle Avoidance Trajectory Planning for Autonomous Vehicles on Structured Roads
by Yunlong Li, Gang Li and Kang Peng
World Electr. Veh. J. 2024, 15(4), 168; https://doi.org/10.3390/wevj15040168 - 17 Apr 2024
Cited by 6 | Viewed by 2719
Abstract
This paper focuses on the obstacle avoidance trajectory planning problem for autonomous vehicles on structured roads. The objective is to design a trajectory planning algorithm that can ensure vehicle safety and comfort and satisfy the rationality of traffic regulations. This paper proposes a [...] Read more.
This paper focuses on the obstacle avoidance trajectory planning problem for autonomous vehicles on structured roads. The objective is to design a trajectory planning algorithm that can ensure vehicle safety and comfort and satisfy the rationality of traffic regulations. This paper proposes a path and speed decoupled planning method for non-split vehicle trajectory planning on structured roads. Firstly, the path planning layer adopts the improved artificial potential field method. The obstacle-repulsive potential field, gravitational potential field, and fitting method of the traditional artificial potential field are improved. Secondly, the speed planning aspect is performed in the Frenet coordinate system. Speed planning is accomplished based on S-T graph construction and solving convex optimization problems. Finally, simulation and experimental verification are performed. The results show that the method proposed in this paper can significantly improve the safety and comfortable riding of the vehicle. Full article
(This article belongs to the Special Issue Research on Intelligent Vehicle Path Planning Algorithm)
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24 pages, 15369 KiB  
Article
Simultaneous Trajectory and Speed Planning for Autonomous Vehicles Considering Maneuver Variants
by Maksym Diachuk and Said M. Easa
Appl. Sci. 2024, 14(4), 1579; https://doi.org/10.3390/app14041579 - 16 Feb 2024
Cited by 2 | Viewed by 1479
Abstract
The paper presents a technique of motion planning for autonomous vehicles (AV) based on simultaneous trajectory and speed optimization. The method includes representing the trajectory by a finite element (FE), determining trajectory parameters in Frenet coordinates, composing a model of vehicle kinematics, defining [...] Read more.
The paper presents a technique of motion planning for autonomous vehicles (AV) based on simultaneous trajectory and speed optimization. The method includes representing the trajectory by a finite element (FE), determining trajectory parameters in Frenet coordinates, composing a model of vehicle kinematics, defining optimization criteria and a cost function, forming a set of constraints, and adapting the Gaussian N-point scheme for quadrature numerical integration. The study also defines a set of minimum optimization parameters sufficient for making motion predictions with smooth functions of the trajectory and speed. For this, piecewise functions with three degrees of freedom (DOF) in FE’s nodes are implemented. Therefore, the high differentiability of the trajectory and speed functions is ensured to obtain motion criteria such as linear and angular speeds, acceleration, and jerks used in the cost function and constraints. To form the AV roadway position, the Frenet coordinate system and two variable parameters are used: the reference path length and the lateral displacement perpendicular to reference line’s tangent. The trajectory shape, then, depends only on the final position of the AV’s mass center and the final reference’s curvature. The method uses geometric, kinematic, dynamic, and physical constraints, some of which are related to hard restrictions and some to soft restrictions. The planning technique involves parallel forecasting for several variants of the AV maneuver followed by selecting the one corresponding to a specified criterion. The sequential quadratic programming (SQP) technique is used to find the optimal solution. Graphs of trajectories, speeds, accelerations, jerks, and other parameters are presented based on the simulation results. Finally, the efficiency, rapidity, and prognosis quality are evaluated. Full article
(This article belongs to the Special Issue Intelligent Vehicles and Autonomous Driving)
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19 pages, 2386 KiB  
Article
Iberian Ports as a Funnel for Regulations on the Decarbonization of Maritime Transport
by Francisco deManuel-López, David Díaz-Gutiérrez, Alberto Camarero-Orive and José Ignacio Parra-Santiago
Sustainability 2024, 16(2), 862; https://doi.org/10.3390/su16020862 - 19 Jan 2024
Cited by 6 | Viewed by 2614
Abstract
We are currently seeing how new marine fuels are being introduced, such as Liquefied Natural Gas (LNG), Liquefied Petroleum Gas (LPG), hydrogen, ammonia, methanol, batteries, etc., for the propulsion of the world fleet with the aim of complying with the increasing IMO emissions [...] Read more.
We are currently seeing how new marine fuels are being introduced, such as Liquefied Natural Gas (LNG), Liquefied Petroleum Gas (LPG), hydrogen, ammonia, methanol, batteries, etc., for the propulsion of the world fleet with the aim of complying with the increasing IMO emissions regulations. The frenetic effort made by shipping companies to decarbonize maritime transport must be followed by an unstoppable adaptation of ports from the historical supply of only fuel and diesel to covering the demands of new fuels, ensuring their renewable origin; onshore power supply (OPS); or even the storage of captured CO2. This article compiles the current environmental regulations applied to maritime transport to provide an analysis of the current situation and a link between vessels’ requirements to comply with such regulations and port environmental infrastructure. This work demonstrates that technological development is growing faster onboard vessels than at ports. It is demonstrated that except for the case of LNG, the theoretical shipping fuel world demand of each type of alternative fuel cannot be absorbed by current world production, where we found big gaps between supply and demand of up to 96.9%. This work concludes that to speed up this process, ports will need European aid as well as private investment. It is proposed that for the next steps, the port system needs to provide the required infrastructure to vessels on time, which inevitably means improvements in competitiveness and governance to promote the blue economy and the concept of smart ports, attracting main international shipping lines with a complete decarbonization hub on their routes by taking advantage of the geostrategic role of the Iberian ports. At the same time, the port governance model must be more flexible in the decision-making process, anticipating changes in maritime regulations with the challenge of coordinating public and private interests, serving as a link, once again, between ship and society. Full article
(This article belongs to the Section Sustainable Oceans)
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18 pages, 3678 KiB  
Article
Intelligent Vehicle Decision-Making and Trajectory Planning Method Based on Deep Reinforcement Learning in the Frenet Space
by Jiawei Wang, Liang Chu, Yao Zhang, Yabin Mao and Chong Guo
Sensors 2023, 23(24), 9819; https://doi.org/10.3390/s23249819 - 14 Dec 2023
Cited by 7 | Viewed by 3187
Abstract
The complexity inherent in navigating intricate traffic environments poses substantial hurdles for intelligent driving technology. The continual progress in mapping and sensor technologies has equipped vehicles with the capability to intricately perceive their exact position and the intricate interplay among surrounding traffic elements. [...] Read more.
The complexity inherent in navigating intricate traffic environments poses substantial hurdles for intelligent driving technology. The continual progress in mapping and sensor technologies has equipped vehicles with the capability to intricately perceive their exact position and the intricate interplay among surrounding traffic elements. Building upon this foundation, this paper introduces a deep reinforcement learning method to solve the decision-making and trajectory planning problem of intelligent vehicles. The method employs a deep learning framework for feature extraction, utilizing a grid map generated from a blend of static environmental markers such as road centerlines and lane demarcations, in addition to dynamic environmental cues including vehicle positions across varied lanes, all harmonized within the Frenet coordinate system. The grid map serves as the input for the state space, and the input for the action space comprises a vector encompassing lane change timing, velocity, and vertical displacement at the lane change endpoint. To optimize the action strategy, a reinforcement learning approach is employed. The feasibility, stability, and efficiency of the proposed method are substantiated via experiments conducted in the CARLA simulator across diverse driving scenarios, and the proposed method can increase the average success rate of lane change by 6.8% and 13.1% compared with the traditional planning control algorithm and the simple reinforcement learning method. Full article
(This article belongs to the Special Issue Integrated Control and Sensing Technology for Electric Vehicles)
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18 pages, 3385 KiB  
Article
Model Predictive Control Based on State Space and Risk Augmentation for Unmanned Surface Vessel Trajectory Tracking
by Wei Li, Jun Zhang, Fang Wang and Hanyun Zhou
J. Mar. Sci. Eng. 2023, 11(12), 2283; https://doi.org/10.3390/jmse11122283 - 30 Nov 2023
Cited by 8 | Viewed by 2097
Abstract
The underactuated unmanned surface vessel (USV) has been identified as a promising solution for future maritime transport. However, the challenges of precise trajectory tracking and obstacle avoidance remain unresolved for USVs. To this end, this paper models the problem of path tracking through [...] Read more.
The underactuated unmanned surface vessel (USV) has been identified as a promising solution for future maritime transport. However, the challenges of precise trajectory tracking and obstacle avoidance remain unresolved for USVs. To this end, this paper models the problem of path tracking through the first-order Nomoto model in the Serret–Frenet coordinate system. A novel risk model has been developed to depict the association between USVs and obstacles based on SFC. Combined with an artificial potential field that accounts for environmental obstacles, model predictive control (MPC) based on state space is employed to achieve the optimal control sequence. The stability of the designed controller is demonstrated by means of the Lyapunov method and zero-pole analysis. Through simulation, it has been demonstrated that the controller is asymptotically stable concerning track error deviation, heading angle deviation, and heading angle speed, and its good stability and robustness in the presence of multiple risks are verified. Full article
(This article belongs to the Section Ocean Engineering)
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22 pages, 77655 KiB  
Article
A Mathematical Model for Mollusc Shells Based on Parametric Surfaces and the Construction of Theoretical Morphospaces
by Gabriela Contreras-Figueroa and José L. Aragón
Diversity 2023, 15(3), 431; https://doi.org/10.3390/d15030431 - 15 Mar 2023
Cited by 5 | Viewed by 6065
Abstract
In this study, we propose a mathematical model based on parametric surfaces for the shell morphology of the phylum Mollusca. Since David Raup’s pioneering works, many mathematical models have been proposed for different contexts to describe general shell morphology; however, there has been [...] Read more.
In this study, we propose a mathematical model based on parametric surfaces for the shell morphology of the phylum Mollusca. Since David Raup’s pioneering works, many mathematical models have been proposed for different contexts to describe general shell morphology; however, there has been a gap in the practicality of models that allow the estimation of their parameter values in real specimens. Our model collects ideas from previous pioneering studies; it rests on the equation of the logarithmic spiral, uses a fixed coordinate system (coiling axis), and defines the position of the generating curve with a local moving system using the Frenet frame. However, it improves upon previous models by applying apex formation, rotations, and substantially different parameter definitions. Furthermore, the most conspicuous improvement is the development of a simple and standardized methodology to obtain the six theoretical parameters from shell images from different mollusc classes and to generate useful theoretical morphospaces. The model was applied to reproduce the shape of real mollusc-shell specimens from Gasteropoda, Cephaloda and Bivalvia, which represent important classes in geological time. We propose a specific methodology to obtain the parameters in four morphological groups: helicoidal, planispiral, conic, and valve-like shells, thereby demonstrating that the model offers an adequate representation of real shells. Finally, possible improvements to the model are discussed along with further work. Based on the above considerations, the capacity of the model to allow the construction of theoretical morphospaces, the methodology to estimate parameters and from the comparison between several existing models for shells, we believe that our model can contribute to future research on the development, diversity and evolutionary processes that generated the diversity in mollusc shells. Full article
(This article belongs to the Section Phylogeny and Evolution)
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22 pages, 12336 KiB  
Article
Developing a More Reliable Aerial Photography-Based Method for Acquiring Freeway Traffic Data
by Chi Zhang, Zhongze Tang, Min Zhang, Bo Wang and Lei Hou
Remote Sens. 2022, 14(9), 2202; https://doi.org/10.3390/rs14092202 - 5 May 2022
Cited by 22 | Viewed by 2932
Abstract
Due to the widespread use of unmanned aerial vehicles (UAVs) in remote sensing, there are fully developed techniques for extracting vehicle speed and trajectory data from aerial video, using either a traditional method based on optical features or a deep learning method; however, [...] Read more.
Due to the widespread use of unmanned aerial vehicles (UAVs) in remote sensing, there are fully developed techniques for extracting vehicle speed and trajectory data from aerial video, using either a traditional method based on optical features or a deep learning method; however, there are few papers that discuss how to solve the issue of video shaking, and existing vehicle data are rarely linked to lane lines. To address the deficiencies in current research, in this study, we formulated a more reliable method for real traffic data acquisition that outperforms the traditional methods in terms of data accuracy and integrity. First, this method implements the scale-invariant feature transform (SIFT) algorithm to detect, describe, and match local features acquired from high-altitude fixed-point aerial photographs. Second, it applies “you only look once” version 5 (YOLOv5) and deep simple online and real-time tracking (DeepSORT) to detect and track moving vehicles. Next, it leverages the developed Python program to acquire data on vehicle speed and distance (to the marked reference line). The results show that this method achieved over 95% accuracy in speed detection and less than 20 cm tolerance in vehicle trajectory mapping. This method also addresses common problems involving the lack of quality aerial photographic data and accuracy in lane line recognition. Finally, this approach can be used to establish a Frenet coordinate system, which can further decipher driving behaviors and road traffic safety. Full article
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21 pages, 3000 KiB  
Article
USV Application Scenario Expansion Based on Motion Control, Path Following and Velocity Planning
by Ziang Feng, Zaisheng Pan, Wei Chen, Yong Liu and Jianxing Leng
Machines 2022, 10(5), 310; https://doi.org/10.3390/machines10050310 - 26 Apr 2022
Cited by 13 | Viewed by 3157
Abstract
The ability of unmanned surface vehicles (USV) on motion control and the accurate following of preset paths is the embodiment of its autonomy and intelligence, while there is extensive room for improvement when expanding its application scenarios. In this paper, a model fusion [...] Read more.
The ability of unmanned surface vehicles (USV) on motion control and the accurate following of preset paths is the embodiment of its autonomy and intelligence, while there is extensive room for improvement when expanding its application scenarios. In this paper, a model fusion of USV and preset path was carried out through the Serret-Frenet coordinate system. Control strategies were then scrupulously designed with the help of Lyapunov stability theory, including resultant velocity control in the presence of drift angle, course control based on the nonlinear backstepping method, and reference point velocity control as a virtual control variable. Specifically, based on USV resultant velocity control, this paper proposes respective solutions for two common scenarios through velocity planning. In a derailment correction scenario, an adaptive reference velocity was designed according to the position and attitude of USV, which promoted its maneuverability remarkably. In a dynamic obstacle avoidance scenario, an appropriate velocity curve was searched by dynamic programming on ST graph and optimized by quadratic programming, which enabled USV to evade obstacles without changing the original path. Simulation results proved the convergence and reliability of the motion control strategies and path following algorithm. Furthermore, velocity planning was verified to perform effectively in both scenarios. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications in Intelligent Machines)
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22 pages, 6824 KiB  
Article
Intelligent Bus Platoon Lateral and Longitudinal Control Method Based on Finite-Time Sliding Mode
by Lingli Yu, Yu Bai, Zongxv Kuang, Chongliang Liu and Hao Jiao
Sensors 2022, 22(9), 3139; https://doi.org/10.3390/s22093139 - 20 Apr 2022
Cited by 5 | Viewed by 3089
Abstract
Considering the rapid convergence of the longitudinal and lateral tracking errors of the platoon, a finite-time tracking control method for the longitudinal and lateral directions of the intelligent bus platoon is proposed. Based on the bus platoon model and desired motion trajectory, a [...] Read more.
Considering the rapid convergence of the longitudinal and lateral tracking errors of the platoon, a finite-time tracking control method for the longitudinal and lateral directions of the intelligent bus platoon is proposed. Based on the bus platoon model and desired motion trajectory, a distributed longitudinal and lateral finite-time sliding mode tracking control framework of the platoon is designed. Considering the finite-time convergence of the sliding mode of the system, a nonsingular integral terminal sliding mode (NITSM) is designed. An adaptive power integral reaching law (APIRL) is proposed for the finite-time accessibility of the system approaching mode. Based on NITSM-APIRL, a distributed longitudinal and lateral finite-time sliding mode tracking controller for the bus platoon is designed, and a Lyapunov function is created to analyze the finite-time stability and string stability of the system. Based on the Trucksim/Simulink joint simulation experiment platform, the control performance of the method is contrasted with the existing methods, and the actual vehicle test verification is completed by relying on the National Intelligent Connected Vehicle testing zone, which proves the practicability of the method. Full article
(This article belongs to the Topic Intelligent Transportation Systems)
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