A high-performance neural network vehicle dynamics model for trajectory tracking control

Vehicle intelligence is an effective way to improve driving safety and comfort and reduce traffic accidents. The trajectory tracking control of unmanned vehicles is the core module of intelligent vehicles. As a redundant system, the X-by-wire electric vehicle has the advantage that the turning angles and driving torque of the four wheels can be precisely controlled and it has a higher degree of controllability and flexibility. In this paper, a trajectory tracking control algorithm based on a hierarchical control architecture is designed based on x-by-wire vehicles. The hierarchical control algorithm architecture includes the trajectory tracking layer, tire force distribution layer, and actuator control layer. The trajectory tracking layer uses the longitudinal force, lateral force, and yaw moment as the control variables; the model predictive control algorithm controls the vehicle to follow the desired trajectory. The tire force distribution layer is solved by transforming the tire force distribution problem into a quadratic programming problem with constraints. Based on the expected resultant force and resultant moment, the longitudinal force and lateral force of each tire in the vehicle coordinate system are obtained. The actuator control layer converts the coordinate system to obtain the longitudinal force and lateral force in the tire coordinate system, which uses the arctangent function tire model to solve the desired tire slip angle, and then obtains the vehicle steer angle and driving torque. To verify the effectiveness of the trajectory tracking control algorithm of the hierarchical control architecture, the proposed trajectory tracking control algorithm is simulated and verified through the variable speed double line change condition and the low road friction coefficient double line change condition. The simulation results show that the control algorithm proposed in this paper has the accuracy to follow the desired trajectory.Definition:

Trajectory tracking and speed control for intelligent vehicles are put forward higher requirements on accuracy by the high traffic density scenario. A standard Model Predictive Control (MPC) algorithm focuses on the trajectory tracking but ignores the speed control. This paper proposes a simultaneous trajectory tracking and speed control algorithm based on MPC approach to address fine control in both space and time dimensions for intelligent vehicles. A threefold cost function including lateral and longitudinal speed as well as comfort has been proposed to improve the control algorithm. The simulations and comparisons demonstrate that the proposed method has a better tracking and speed control performance than the existing method.

Neural dynamics change over time and with physiologic state. Modeling of neural dynamics can thus be understood at two levels: (i) identifying the latent process that governs how and when states change, and (ii) identifying the generative circuit mechanisms within each state. Here, we develop a data-driven modeling method that tackles these two levels simultaneously. We formulate a parametric network model of neural dynamics that embeds state-dependent modulation. The modulation itself is controlled by a latent switching process, modeled as a Hidden Markov Model (HMM). A key challenge is that the model itself has internal states that must be estimated from observed data. This leads to a triune optimization problem, consisting of model parameterization of the HMM and neural dynamics, alongside state estimation. Our method brings together several optimization frameworks alongside estimation-theoretic constructs to solve this problem efficiently, enabling blind identification of state transitions and neural dynamics. We validate this methodology on ground-truth data with known parameters, and find that it accurately infers the transitions in latent state and the dynamics of each state. We demonstrate its capability of inferring changes in brain dynamics from electrophysiological data by testing it on electroencephalography recordings with labeled state transitions. While similar methods exist to infer switches and dynamics on the level of individual neurons, there is no directly comparable method available for mesoscale modeling of neural circuits. Our methodology enables blind modeling of changing neural dynamics allowing for inference of modulatory circuit mechanisms.

In this paper, the unmanned vehicle trajectory tracking problems were studied. In order to improve the stability of unmanned vehicles, the trajectory tracking control algorithm based on model predictive control (MPC) algorithm was researched by adding the dynamic constraints of centroid, acceleration and tire side angle on the basis of vehicle dynamics model. The trajectory planning layer was established on top of the trajectory tracking control layer, and the Carsim/Simulink simulation platform was built. At different speeds and under different road adhesion conditions, the algorithm was verified and compared. The simulation results showed that the model predictive control algorithm with dynamic constraints was provided with excellent tracking performance under severe conditions and well adaptive to environment interference.

This paper explores lane changing trajectory planning and tracking control for intelligent vehicle on curved road. A novel arcs trajectory is planned for the desired lane changing trajectory. A kinematic controller and a dynamics controller are designed to implement the trajectory tracking control. Firstly, the kinematic model and dynamics model of intelligent vehicle with non-holonomic constraint are established. Secondly, two constraints of lane changing on curved road in practice (LCCP) are proposed. Thirdly, two arcs with same curvature are constructed for the desired lane changing trajectory. According to the geometrical characteristics of arcs trajectory, equations of desired state can be calculated. Finally, the backstepping method is employed to design a kinematic trajectory tracking controller. Then the sliding-mode dynamics controller is designed to ensure that the motion of the intelligent vehicle can follow the desired velocity generated by kinematic controller. The stability of control system is proved by Lyapunov theory. Computer simulation demonstrates that the desired arcs trajectory and state curves with B-spline optimization can meet the requirements of LCCP constraints and the proposed control schemes can make tracking errors to converge uniformly.

In this paper, a trajectory tracking control algorithm is proposed based on the fractional-order PD (FOPD) controller for a Wheeled Mobile Robot (WMR). Firstly, an improved flat phase property is put forward as a robust controller tuning specification. This specification is capable of guaranteeing the flatness of the phase curve in a frequency interval, so the controlled system robustness can be improved. Then, the stabilization process is discussed with respect to the parameters of the FOPD controller through a visualized 3-dimensional surface, so both the stability and robustness of the controlled system can be guaranteed under the proposed controller. Furthermore, the implementation of the proposed robust FOPD controller is presented, which makes the control algorithm easy to be realized. At last, the effectiveness of the proposed trajectory tracking control algorithm is verified by the simulation and experiment results.

With the intention of delivering an intuitive and simple platform to plan, generate, and track trajectories with a WMR, this paper presents a technological integration of hardware and software. This technological integration consists of a mobile computing device with an app developed by authors for the trajectory planning and a differential drive WMR that possesses an embedded system, in which a trajectory generation algorithm and a trajectory tracking control algorithm -both proposed by authors - are programmed. The mobile computing device wirelessly drives the WMR through the embedded system. The app is developed on the basis of the sketch approach, since it allows drawing sketches of the trajectory intuitively on the mobile device. Also, the app geometrically scales the sketch coordinates to match them with the real WMR workspace. For the trajectory generation, these scaled coordinates are wirelessly sent to the embedded system, where the trajectory generation algorithm joins them by using Bézier polynomials and concatenation of straight-lines. Hence, the tracking task is carried out with the control algorithm, which is proposed departing from the dynamic model of the WMR and whose asymptotic stability proof is performed with the Lyapunov method. Experimental results verify that the technological integration successfully plans, generates, and tracks trajectories, even when the WMR is far from the initial coordinate of the desired trajectory. These results, corroborate the good performance and robustness of the proposed control algorithm. Thus, the introduced technological integration is intuitive and simple since users only have to draw a sketch on the mobile device to carry out the trajectory tracking task.

<div class="section abstract"><div class="htmlview paragraph">Trajectory tracking control is a critical component of the autopilot system, essential for achieving high-performance autonomous driving. This paper presents the design of a stable, reliable, accurate, fast, and robust trajectory tracking controller. Specifically, a lateral and longitudinal trajectory tracking controller based on a linear parameter time-varying model predictive control (LPV-MPC) framework is designed. Firstly, a three-degree-of-freedom vehicle dynamics model and a tracking error model are established. Secondly, a multi-objective function and constraints considering tracking accuracy and lateral stability are formulated, and the quadratic programming (QP) method is employed to solve the optimization problem. Finally, PID speed tracking control is introduced in the longitudinal control scheme for comparison with the proposed MPC longitudinal speed control. A step velocity tracking test validates the effectiveness of the MPC speed tracking controller. In the lateral control scheme, double lane change and circumferential tests are designed to assess the comprehensive performance of the controller under medium-low adhesion road conditions. Additionally, the trajectory tracking performance of the proposed MPC controller is evaluated by comparing it with traditional Sliding Mode Control (SMC) and Linear Quadratic Regulator (LQR) trajectory tracking controllers. The simulation results indicate that the maximum heading error of the MPC controller is less than 0.09 rad, the heading error remains within 0.05 rad, and the front wheel angle stabilizes within 7.5 degrees under both operating conditions. Furthermore, the MPC controller ensures tracking accuracy and smoothness without any obvious jitter while minimizing control inputs to achieve optimal control, thereby significantly enhancing the accuracy and stability of the vehicle's trajectory tracking.</div></div>

Trajectory tracking control algorithm in terms of quasi-velocities for a class of vehicles

<div>Intelligent vehicles can utilize a variety of sensors, computing, and control technologies to autonomously perceive the environment and make decisions to achieve safe, efficient, and automated driving. If the speed planning of intelligent vehicles ignores the vehicle dynamics state, it leads to unreasonable planning speed and is not conducive to improving the accuracy of trajectory tracking control. Meanwhile, trajectory tracking usually does not consider the road and speed information beyond the prediction horizon, resulting in poor tracking precision that is not conducive to improving driving comfort. To solve these problems, this study proposes a new longitudinal speed planning method based on variable universe fuzzy rules and designs the piecewise preview model predictive control (PPMPC) to realize the vehicle trajectory tracking. First, the three-degrees-of-freedom vehicle dynamics model and trajectory tracking model are established and verified. Then, the variable universe fuzzy rules are introduced to design the longitudinal speed planning method, in which the road friction coefficient and road curvature are defined as the input of the speed planning method, and the vehicle lateral deviation is defined as the scaling factor input of the speed variable universe. Based on the dynamics model and trajectory tracking model, the PPMPC method is proposed to improve the accuracy and stability of trajectory tracking. During the PPMPC method design, the reference value of state quantity in the prediction horizon can be updated by using further road information and planning longitudinal speed information. Finally, the results show that the proposed planning algorithm can provide a reasonable longitudinal speed to reduce the tracking lateral error in the tracking control, and the proposed PPMPC can significantly improve the vehicle speed-tracking accuracy and control stability compared with the traditional model predictive control (MPC) method.</div>

<div class="htmlview paragraph">In racetrack conditions, brake systems are subjected to extreme energy loads and energy load distributions. This can lead to very high friction surface temperatures, especially on the brake corner that operates, for a given track, with the most available traction and the highest energy loading. Individual brake corners can be stressed to the point of extreme fade and lining wear, and the resultant degradation in brake corner performance can affect the performance of the entire brake system, causing significant changes in pedal feel, brake balance, and brake lining life. It is therefore important in high performance brake system design to ensure favorable operating conditions for the selected brake corner components under the full range of conditions that the intended vehicle application will place them under.</div> <div class="htmlview paragraph">To address this task in an early design stage, it is helpful to use brake system modeling tools to analyze system performance. Traditional modeling approaches have relied upon simple mathematical representation of measured brake corner output and fluid displacement (data which often result from inertia dyno testing) to predict system level performance. Many brake system analysis tools also include only a quasi-static two-dimensional vehicle dynamics model and do not fully capture cornering influences on braking energy load distribution. This paper will present a method of measuring brake corner output and compliance behavior during high energy usage conditions on a brake dynamometer and representing this behavior with neural network models. The resulting models are integrated with a fully 3-dimensional vehicle dynamics and 1-dimensional brake thermal model to result in significantly more accurate brake system performance predictions that include the vehicle dynamics influences on brake corner energy loading, brake corner responses such as in-stop fade and recovery, and in-stop lining wear and its influence on compliance.</div> <div class="htmlview paragraph">The resultant integrated neural-network brake corner and vehicle dynamics model is demonstrated in both straight-line braking events and simple race track simulations.</div>

HighlightsWhat are the main findings?In response to the limited existing research on high-speed autonomous driving under low-adhesion, slippery road conditions, a novel MPC-PID fused trajectory tracking control algorithm is proposed. This approach significantly enhances tracking accuracy and vehicle stability under such complex scenarios.Joint simulation results demonstrate that the proposed method improves trajectory tracking accuracy by at least 22.2%, while comfort, fuel economy, and safety are improved by 9.4%, 19.8%, and 5.3%, respectively.What is the implication of the main finding?This work provides theoretical support and simulation validation for high-speed trajectory tracking control under low-adhesion conditions, offering high engineering applicability and practical significance.The proposed approach facilitates real-time, precise, and robust autonomous driving in dynamically complex environments, promoting the deployment of high-performance control strategies in real-world applications.Autonomous vehicle trajectory tracking control is one of the hot topics in the autonomous driving field. One of the most widely used control methods is MPC (Model Predictive Control). As the control system generally becomes more nonlinear and complex, more nonlinear system factors are added to the MPC method. However, tracking accuracy and the amount of calculation needed are both dependent on a lot of contradictions for NMPC (Nonlinear Model Predictive Control). This research proposes a control algorithm for MPC-fused PID (Proportional-Integral-Derivative) control that ensures tracking accuracy under different high-speed driving conditions on wet and slippery road surfaces. The objective of the algorithm is twofold: first, to enhance trajectory tracking accuracy, and second, to ensure real-time control and optimize the vehicle’s comfort, economy, and safety indexes. The results of the joint simulation in Carsim/MATLAB Simulink show that trajectory tracking accuracy is improved by at least 22.2% under high-speed driving conditions of a vehicle on a wet and slippery road. At the same time, the comfort, economy, and safety of the vehicle are improved by at least 9.4%, 19.8%, and 5.3%, respectively.

Quadrotor unmanned aerial vehicles are utilized in basically every sector of society, including the business, civil, and military industries. Popular applications include delivery, agriculture, target-acquisition, surveying, surveillance, and rescue. They are widely used due to their exceptional features such as accuracy, capability to perform swift inspections, simplicity in deploying perilous and uncertain missions, and additional praiseworthy attributes. This article presents a comprehensive analysis of the theoretical frameworks that have been proposed for the purpose of quadrotor modelling and control. Detailed examinations are conducted on every methodology that underpins the control algorithms, spanning from traditional linear to modern. The analysis looks at hybrid control technique models, which incorporate adaptive components across multiple controllers to improve overall performance and resilience by addressing individual algorithm shortcomings. This analysis also delves deeper into potential future research avenues. These include the development of learning-based or hybrid methodologies that employ machine learning and artificial intelligence to optimize performance and adaptability. For instance, model reference adaptive control systems can learn adaptation laws through machine learning techniques, as opposed to depending on predefined adaptation laws. By training neural networks or fuzzy logic controllers to forecast optimal adaptation parameters based on sensor data, the quadrotor can adjust to fluctuating conditions more effectively. A comparison table is provided to elaborate on the advantages, disadvantages, and hybrid versions of each control algorithm. This will serve as a concise guide that will promote innovation, facilitate the selection and integration of appropriate control algorithms, and enhance the functionality of quadrotor control systems.

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.

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