AUTONOMOUS CAR MOTION PLANNING USING PATH APPROXIMATION AND GEOMETRIC CONTROL ALGORITHMS

Connected and automated vehicles (CAVs) have the potential to improve many aspects of the current transportation systems such as safety, mobility, and energy efficiency. In order to evaluate the benefits and impacts of a CAV, the CAV control algorithm is typically implemented on vehicles simulated in a traffic microsimulation environment. However, traffic microsimulation usually lacks detailed vehicle and powertrain dynamics, making it challenging to fully understand how a CAV control algorithm will perform and respond on an actual vehicle. Whether the same benefits measured in the simulation will also be observed in real-world remains an open question. One potential approach to fill in this gap is to conduct a co-simulation of traffic microsimulation with detailed vehicle and powertrain dynamics models, often developed in MATLAB Simulink. However, current microsimulation tools such as VISSIM and SUMO do not have a ready-to-use interface for co-simulation with vehicle dynamics and Simulink. Also, even if such an interface exists, it will be tool-specific, making it challenging to shift from one tool to another or test CAV controls in different tools. There are needs for tool-agnostic co-simulation as different microsimulation tools have their pros and cons, and researchers often need to use different tools based on the purposes of the simulation, project needs, and applications. In this work, Flexible Interface for X-in-the-loop Simulation (FIXS) is developed that can support the co-simulation of microsimulation, CAV control algorithm, and vehicle dynamics model in Simulink. Enabled by the FIXS, the benefit and performance of a CAV control algorithm can be better understood with the consideration of vehicle responses and dynamics. The connection to VISSIM and SUMO is handled internally by the interface, and users can easily switch tools by changing a configuration file. The co-simulation capability is demonstrated for a VISSIM eco-approach and departure CAV scenario and a SUMO cooperative merging scenario for both a passenger CAV and a class 8 heavy-duty connected and automated trucks.

This paper uses different physical scenarios to analyze the cyber dynamic continuous time vehicle model with a networked PID controller. First, we model the problem of stateful continuous-time components for the dynamic physical vehicle motion on a graded and flat road without using a PID controller. Second, we model the problem of stateful continuous-time components for the dynamic physical vehicle motion on a graded road using a PID controller in different specification scenarios. Third, we model the problem of stateful continuous-time components for the cyber-physical dynamic vehicle model motion using a networked PID controller at different specification scenarios. The simulation results indicated the superiority and efficacy of the cyber-physical dynamic vehicle model providing high stability and controllability in the vehicle motion using a PID controller and Transceiver (network node).

Vehicle dynamics has been an active field of research for many decades. The well-known single-track model already introduced in 1940 by Riekert and Schunck is still used to explain fundamental effects in vehicle dynamics such as under- and oversteering. However, meanwhile also very complex multibody dynamics models exist, which allow very detailed simulations. On the other hand, real-time computations necessary for active safety and driver assistance systems are demanded for models of lower complexity. As important effects at the handling limits are not covered by the linear single-track model, but complex multibody models cannot be integrated fast enough by electronic control units of safety systems, models with an adjustable degree of complexity are desired. As an example, model-predictive control is an upcoming field of application and relies on models that are integrated over the prediction horizon. Therefore, the selection of an appropriate model is an important task. The crux of the matter is to make a compromise between computation time and accuracy of the model having only a rough guess of the accuracy of the model. In this contribution a systematic approach is proposed. Instead of selecting an existing model, which is supposed to match requirements in computation time and level of detail, a complex model is reduced to match the requirements using symbolic model reduction techniques. This approach has two major advantages: First, the accuracy can be set by the user. Second, the model is continuously adjustable in its complexity or propagation precision.

Coupling aerodynamics to vehicle dynamics in transient crosswinds including a driver model

Analyzing the performance characteristics and applicable environments of intelligent vehicle lateral control algorithms, this paper establishes the Model Predictive Control (MPC), Pure Pursuit (PP), and Linear Quadratic Regulator (LQR) algorithms and uses 2022b MATLAB software to simulate the lateral error, heading error, and algorithm execution time at speeds of 3 m/s, 7 m/s, and 10 m/s. Urban low-speed scenarios (3 m/s) require high-precision control (such as obstacle avoidance), while high-speed scenarios (10 m/s) require strong stability. Existing research mostly focuses on a single speed and lacks a quantitative comparison across multiple operating conditions. Although MPC has high accuracy, its time consumption fluctuates greatly. LQR has strong real-time performance but a wide range of heading errors. PP has poor low-speed performance but controllable high-speed time consumption growth. It is necessary to define the applicable scenarios of each algorithm through quantitative data. In response to the lack of multi-speed domain quantitative comparison in existing research, this paper conducts multi-condition simulations using MPC, PP, and LQR algorithms and finds that at a low speed of 3 m/s, the peak lateral error of PP (0.45 m) is 55% and 156% higher than MPC (0.29 m) and LQR (0.176 m), respectively. At a speed of 10 m/s, the lateral error standard deviation of MPC (0.08 m) is reduced by 68% compared to PP (0.25 m). In terms of algorithm time consumption, LQR maintains full-speed domain stability (0.11–0.44 ms), while PP time increases by 95% with speed from 3 m/s to 10 m/s. The results show that in terms of lateral error, the MPC and LQR algorithms perform more stably, while the PP algorithm has a larger error at low speeds. Regarding heading error, all algorithms have a relatively large error range, but the MPC and LQR algorithms perform slightly better than the PP algorithm at high speeds. In terms of algorithm execution time, the LQR algorithm has the shortest and most stable execution time, the MPC algorithm has a relatively longer execution time, and the PP algorithm’s execution time varies at different speeds. Through this simulation, if high control accuracy and stability are pursued, the MPC or LQR algorithm can be considered; if real-time performance and computational efficiency are more important, the PP algorithm can be considered.

<div class="section abstract"><div class="htmlview paragraph">Autonomous driving technology is more and more important nowadays, it has been changing the living style of our society. As for autonomous driving planning and control, vehicle dynamics has strong nonlinearity and uncertainty, so vehicle dynamics and control is one of the most challenging parts. At present, many kinds of specific vehicle dynamics models have been proposed, this review attempts to give an overview of the state of the art of vehicle dynamics models for autonomous driving. Firstly, this review starts from the simple geometric model, vehicle kinematics model, dynamic bicycle model, double-track vehicle model and multi degree of freedom (DOF) dynamics model, and discusses the specific use of these classical models for autonomous driving state estimation, trajectory prediction, motion planning, motion control and so on. Secondly, data driven or AI based vehicle models have been reviewed, and their specific applications in automatic driving and their modeling and training processes are introduced. At the end of this review, the advantages and disadvantages of these vehicle models are summarized, and the future research directions and possible explorations are discussed to guide readers.</div></div>

Trajectory-following control is the basis for the practical application of an articulated virtual rail train transportation system. In this paper, a planar nonlinear dynamics model of an articulated vehicle is derived using the Euler-Lagrange method. A trajectory-following control strategy based on the first following point is proposed, and a feedback linearization control algorithm is designed based on the vehicle dynamics model to achieve the trajectory following of the rear vehicle. Based on the target trajectory formed by the first following point and measured by virtual sensors, a vector analysis method grounded in geometric relationships is proposed to solve in real time for the desired position, velocity, and acceleration of the vehicle. Finally, a MATLAB/SIMPACK dynamics virtual prototype is established to test the vehicle's trajectory-following effectiveness and dynamics performance under lane change and circular curve routes. The results indicate that the control algorithm can achieve trajectory following while maintaining good vehicle dynamics performance. It is robust to variations in vehicle mass, vehicle speed, tire cornering stiffness, and road friction coefficient.

Autonomous driving technology has advanced significantly in the past decade. In the case of autonomous racing, the crucial challenge lies in guiding the vehicle along the desired path while ensuring safety and efficiency. Several control systems have been developed for fast and accurate path tracking, offering their own unique advantages and limitations. Here we present an investigation into three prominent control strategies in a critical comparative analysis. These control algorithms include Pure Pursuit (PP), Model Predictive Control (MPC) and Model Predictive Contouring Control (MPCC). These control algorithms were chosen due to their difference in complexities starting from a simple PP to a much more complex MPCC. These algorithms are then experimentally validated on a physical F1Tenth vehicle. The simulation results show that PP exhibited the fastest computation time, its performance in the presence of noise and delay was inferior to MPC and MPCC. While MPC demonstrated strong performance in its robustness and resilience to noise and delay compared to PP and MPCC. MPCC, despite producing the fastest lap time, faced challenges in handling noise and delay although not as severe as PP, making MPC the best overall controller for unwanted disturbances. In contrast to the simulated findings, PP demonstrated superior performance in physical implementations compared to MPC and MPCC. The computational demands of optimization-based algorithms result in a computation delay where the algorithm calculates for the vehicle's position one iteration behind its actual movement. This shows that shortening computational delay is critical in a physical system.

<div class="htmlview paragraph">To evaluate the handling behaviour of the vehicle in the normal-driving and limit manoeuvres, under a variety of road conditions (dry, wet, μ-split, etc.), a dynamic model that can be effectively integrated with chassis control systems' algorithms like anti-skid devices, vehicle dynamic control, active suspensions, servo-assisted steering and braking, would be very useful.</div> <div class="htmlview paragraph">A modular, flexible, 15 degrees of freedom (DOF) model of the vehicle dynamics, implemented in Simulink, is presented here. It can be used “stand-alone” for vehicle handling performance prediction; integrated with control system algorithms, for their synthesis and offline pre-calibration; in “Hardware-in-the-loop” configurations, for testing control and diagnosis algorithms functionality.</div> <div class="htmlview paragraph">The model uses the Pacejka Magic Formulae for tyre modelisation and a Lagrangian approach for chassis, corners and powertrain dynamics. Suspensions' kinematics and compliance effects are reproduced through a functional approach, so that either experimental data can be imported directly from a full-vehicle test bench, or look-up tables can be derived from suspension requirements.</div> <div class="htmlview paragraph">The model has been used for simulating several “open-loop” handling manoeuvres, including roll-over tests, with wind and road gradient influences. A good correlation with experimental data has been observed.</div>

<div class="section abstract"><div class="htmlview paragraph">With the load of urban traffic system becomes more serious, the Automatic Parking System (APS) plays an important role in alleviating the burden of drivers and improving vehicle safety. The APS is consisted of environmental perception, path planning and path following. The path following controls the lateral movement of vehicle during the parking process, and requires the trajectory tracking error to be as small as possible. At present, some control algorithms are used including PID control, pure pursuit control, etc. However, these algorithms relying heavily on parameters and environment, have some problems such as slow response and low precision. To solve this problem, a path following control method based on Model Predictive Control (MPC) algorithm is proposed in this paper. Firstly, Kinematic vehicle model and path tracker based on MPC algorithm are built. Secondly, a test bench that composed of CANoe hardware in the loop (HIL) system and steering wheel system is built. According to the result of path planning, the HIL system based on MPC algorithm generates a real-time target steering angle, and sends it to the steering wheel. The steering wheel system is a column electric power steering system, which completes the steering wheel angle control and sends the steering wheel actual angle to the vehicle dynamic model of HIL system, forming the vehicle real-time motion trajectory. Thirdly, a comparison experiment with pure pursuit tracking control algorithm is carried out, and the results indicate that the designed MPC algorithms has excellent robustness and can minimize the tracking error.</div></div>

Controller design for autonomous 4-wheeled ground vehicles is performed with differential flatness theory. Using a 3-DOF nonlinear model of the vehicle's dynamics and through the application of differential flatness theory an equivalent model in linear canonical (Brunovksy) form is obtained. The processing of velocity measurements (provided by a small number of on-board sensors) through a Kalman Filter which has been redesigned in the form of a disturbance observer results in accurate identification of external disturbances affecting the vehicle's dynamic model. By including in the vehicle's controller an additional term that compensates for the estimated disturbance forces, the vehicle's motion characteristics remain unchanged.

The problem of pursuit and evasion is a classic problem that has intrigued mathematicians for many generations. Suppose a target or evader is moving along a given curve in the plane. A pursuer or chaser is moving such that its line of sight is always pointing towards the target. The classic problem is to determine the trajectory of the pursuer such that it eventually captures the target. There is extensive literature on this problem, see for example the recent book by Nahin (Nahin, 2007). A special case of the pursuit problem is the case where the curve of the target is a circle. This is a classic problem which was first treated by Hathaway (Hathaway, 1921), see also the book by Davis (Davis, 1962). In the classic problems, the line of sight is always pointing towards the target. This method of pursuit is also known as 'pure pursuit' or 'dog pursuit' or 'courbe de chien' in French. Although there have been some modern works on extensions of the classic problem of pursuit, see for example (Marshall, 2005), here we completely abandon the 'pure pursuit' restriction and we treat the problem where the pursuer is required to capture or intercept the target in a given prescribed time or in minimum time. Also, in the classic problem, the velocities of the target and pursuer are assumed constant and there is no consideration of the physics of the motion, such as thrust forces, hydrodynamic or aerodynamic drag and other forces that might be acting on the target and pursuer. In an active-passive rendezvous problem between two vehicles, the passive or target vehicle moves passively along its trajectory. The active or chaser vehicle is controlled or guided such as to meet the passive vehicle at a later time, matching both the location and the velocity of the target vehicle. An interception problem is similar to the rendezvous problem, except that there is no need to match the final velocities of the two vehicles. On the other hand, in a cooperative rendezvous problem, the two vehicles are active and maneuver such as to meet at a later time, at the same location with the same velocity. The two vehicles start the motion from different initial locations and might have different initial velocities. An optimal control problem consists of finding the control histories, i.e., the controls as a function of time, and the state variables of the dynamical system such as to minimize a performance index. The differential equations of motion of the vehicles are treated as dynamical constraints. One possible approach to the solution of the rendezvous problem is to formulate it as an optimal control problem in which one is seeking the controls such as to

The present study brings out the influence of a non-linear dynamics model of military vehicle with trailing arm suspension, on the weapon dynamics responses. A 20 degrees of freedom integrated ride and cornering dynamics model has sequentially been coupled with the 7 degrees of freedom weapon dynamics model. The 20 degrees of freedom integrated model includes the bounce, pitch, roll, longitudinal, lateral and yaw motions of the sprung mass and rotational dynamics of the 14 unsprung masses. The 7 degrees of freedom weapon model comprises the coupled elevation and azimuth dynamics. The coupled weapon model includes angular rotation of the elevation drive, breech and muzzle in elevation direction, as well as, angular rotation of the azimuth drive, turret, breech and muzzle in azimuth direction. The actual physical behaviour of each of the hydro-gas trailing arm suspension units is implemented in the governing differential equations. The non-linear governing equations also incorporate the dynamic coupling between each of the axle arms and sprung mass, which is an inherent behaviour of the trailing arm suspension, unlike their equivalent vertical representation. The integrated model has been simulated for different cornering manoeuvres at specified speeds. It is observed that the sprung mass dynamics, emanating from different manoeuvres, significantly affects the coupled elevation and azimuth dynamics responses of the weapon. The weapon dynamics model coupled with the integrated ride and cornering dynamics model of the military vehicle, would be useful for implementation of a suitable robust gun control system in military vehicles.

Traditional models of vehicle dynamics engineered from physical principles are usually simplified and assumed, resulting in the model cannot accurately reflect the actual dynamic characteristics of the vehicle under some working conditions, affecting the control accuracy and even safety. In view of this, inspired by the single-track model, this paper uses the data-driven methods to establish a new high-performance time-delay feedback neural network vehicle dynamics model. The feedback connection of a network can describe complex dynamics. The multi-time-step input of the state and control can include highly nonlinear and strong coupling characteristics of a vehicle. The test results of modeling accuracy show that the proposed model can achieve higher vehicle dynamics prediction accuracy than nonlinear vehicle model. Different from the traditional vehicle dynamics model, the proposed model has long-term memory cells, which can implicitly predict coefficient of friction and can be applied to different road conditions. Then, the trajectory tracking control algorithm is designed based on the proposed vehicle model. According to the steady-state steering assumption, the feedforward front wheel steering angle is calculated, and the steady-state sideslip angle is integrated into the steering feedback according to the reference path to realize the reference trajectory tracking control. Finally, Simulink/CarSim is used to conduct the simulation analysis under the double lane change conditions to evaluate the proposed control algorithm. The analysis results show that the control algorithm based on the proposed model can achieve an accurate tracking control effect of a vehicle at medium and high speeds, providing high-accuracy track tracking and good lateral stability of intelligent vehicles.

Aiming at the problem of large trajectory tracking control errors for multi-axle vehicles on soft terrain, this study comprehensively considers complex wheel-terrain interaction relationships on soft terrain and develops a time-varying parameter-based trajectory tracking control algorithm for soft terrain using MPC (Model Predictive Control). Specifically, it establishes calculation methods for tire longitudinal/lateral forces on soft terrain and fits corresponding force curves. A vehicle dynamics model and trajectory tracking error model adapted to soft terrain conditions are constructed to enhance model accuracy. Considering load transfer during vehicle movement on soft terrain and the correlation between tire lateral forces and wheel loads, time-varying parameter matrices are established to accurately characterize vehicle dynamic characteristics under such conditions. By incorporating time-varying lateral force proportionality coefficients for wheel-terrain interaction, an MPC-based control algorithm is designed. Simulation tests of multi-axle vehicle trajectory tracking demonstrate the effectiveness of the proposed algorithm, showing significant improvement in control accuracy compared with conventional control methods that neglect parameter time-variation characteristics.