Path tracking of autonomous driving robotic vehicle based on improved model predictive control

This paper presents a two-layer controller for accurate and robust lateral path tracking control of highly automated vehicles. The upper-layer controller, which produces the front wheel steering angle, is implemented with a Linear Time-Varying MPC (LTV-MPC) whose prediction and control horizon are both optimized offline with particle swarm optimization (PSO) under varying working conditions. A constraint on the slip angle is imposed to prevent lateral forces from saturation to guarantee vehicle stability. The lower layer is a radial basis function neural network proportion-integral-derivative (RBFNN-PID) controller that generates electric current control signals executable by the steering motor to rapidly track the target steering angle. The nonlinear characteristics of the steering system are modeled and are identified on-line with the RBFNN so that the PID controller’s control parameters can be adjusted adaptively. The results of CarSim-Matlab/Simulink joint simulations show that the proposed hierarchical controller achieves a good level of path tracking accuracy while maintaining vehicle stability throughout the path tracking process, and is robust to dynamic changes in vehicle velocities and road adhesion coefficients.

In this study, to improve the accuracy of path tracking in intelligent vehicles, we propose an intelligent vehicle path-tracking control method based on improved model predictive control (MPC) combined with hybrid proportional-integral-derivative (PID) control theory. In the lateral control, a constraint on the side deflection of the front wheel is added based on traditional MPC and a relaxation factor is introduced to improve the stability of vehicle control for the driving stability. In longitudinal control, a hybrid PID controller is designed for different road conditions to improve the accuracy of control of vehicle speed. We present the results of a co-simulation using Carim and MATLAB/Simulink and a test with a sample vehicle, which show that the proposed path tracking controller can greatly improve the path tracking accuracy and stability of an intelligent vehicle. The model-based prediction, rolling optimization solution, feedback control, and the addition of a constraint on the side deflection of the front wheel as well as a relaxation factor can ensure the lateral driving stability of an intelligent vehicle. The proposed approach achieved a lateral error of less than 1%, and the yaw angle was controlled within 4°. The longitudinal speed control based on hybrid PID controller can improve the response speed of the system and meet the real-time requirements of vehicle driving.

Design and development of sensor based Automatic steering control system for automobiles

PurposeSea Lion Optimization (SLnO) algorithm involves the ability of exploration and exploitation phases, and it is able to solve combinatorial optimization problems. For these reasons, it is considered a global optimizer. The scheduling operation is completed by imitating the hunting behavior of sea lions.Design/methodology/approachCloud computing (CC) is a type of distributed computing, contributory in a massive number of available resources and demands, and its goal is sharing the resources as services over the internet. Because of the optimal using of these services is everlasting challenge, the issue of task scheduling in CC is significant. In this paper, a task scheduling technique for CC based on SLnO and multiple-objective model are proposed. It enables decreasing in overall completion time, cost and power consumption; and maximizes the resources utilization. The simulation results on the tested data illustrated that the SLnO scheduler performed better performance than other state-of-the-art schedulers in terms of makespan, cost, energy consumption, resources utilization and degree of imbalance.FindingsThe performance of the SLnO, Vocalization of Whale Optimization Algorithm (VWOA), Whale Optimization Algorithm (WOA), Grey Wolf Optimization (GWO) and Round Robin (RR) algorithms for 100, 200, 300, 400 and 500 independent cloud tasks on 8, 16 and 32 VMs was evaluated. The results show that SLnO algorithm has better performance than VWOA, WOA, GWO and RR in terms of makespan and imbalance degree. In addition, SLnO exhausts less power than VWOA, WOA, GWO and RR. More precisely, SLnO conserves 5.6, 21.96, 22.7 and 73.98% energy compared to VWOA, WOA, GWO and RR mechanisms, respectively. On the other hand, SLnO algorithm shows better performance than the VWOA and other algorithms. The SLnO algorithm's overall execution cost of scheduling the cloud tasks is minimized by 20.62, 39.9, 42.44 and 46.9% compared with VWOA, WOA, GWO and RR algorithms, respectively. Finally, the SLnO algorithm's average resource utilization is increased by 6, 10, 11.8 and 31.8% compared with those of VWOA, WOA, GWO and RR mechanisms, respectively.Originality/valueTo the best of the authors’ knowledge, this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.

Abstract. This paper focuses on the 4-PUU parallel mechanism with Schönflies motion, investigating its kinematic analysis and utilizing intelligent algorithms to solve its forward kinematics equations. Using screw theory as the mathematical framework, the number and nature of the degrees of freedom of the 4-PUU parallel mechanism are analyzed, proving that the mechanism can achieve 3T1R motion. The forward and inverse position kinematics equations are established with link lengths as constraints, and the velocity and acceleration equations of the mechanism are derived using the vector method. The forward kinematics equations of the mechanism are transformed into an unconstrained optimization problem, which is solved using an improved beluga whale optimization (BWO). To enhance the uniformity of the initial population distribution, a chaotic-opposition-based learning initialization strategy is introduced. Additionally, an elite strategy and a golden-sine-based position update mechanism are incorporated to improve the optimization capability of BWO. The integration of these strategies results in an enhanced optimization algorithm with superior global search ability. Given the mechanism's dimensional parameters, theoretical and motion simulations are conducted using MATLAB and Adams. The results indicate that the motion simulation curves from Adams closely match the numerical simulation curves from MATLAB, validating the theoretical derivation. Building on this, the improved beluga whale optimization (IBWO) algorithm, along with comparison algorithms (DEb1, ABC, PSO), is applied to solve the forward kinematics equations for interpolation points along the simulated trajectory. Numerical experiments demonstrate that IBWO outperforms the other comparison algorithms in solving the problem efficiently and accurately.

IntroductionAccurate path tracking is essential for achieving intelligent operation in unmanned agricultural machinery. To address the limitations of traditional agricultural machine path tracking methods, which are susceptible to high frequency oscillations and external disturbances, this study proposes a fixed time super-twisting sliding mode adaptive path-tracking control for unmanned agricultural vehicles.MethodsThe approach utilizes a Regularized Least Squares Extreme Learning Machine (RLS-ELM) to improve robustness and adaptability under certain operating conditions. A generalized terminal sliding mode surface is first designed by incorporating both lateral and heading deviations of the vehicle. Next, a Super-Twisting Sliding Mode control law is developed to perform path tracking, while the RLS-ELM is used to estimate and compensate for unknown disturbances. The stability of the proposed control system is verified through the construction of a new Lyapunov function.ResultsThe control algorithm is validated via field experiments on an agricultural platform. Results show that, compared to the Fixed-Time Generalized Terminal Super Twisting control method (FGST) and the Fixed-Time Sliding Mode Controller (FTSMC), the Extreme Learning Machine-Adaptive Fixed-Time Generalized Super-Twisting (ELM-AFGST) method reduces lateral mean absolute errors by 24.5% and 27.4%, respectively, and decreases heading mean absolute errors by 5.4% and 30.8%, respectively. These findings demonstrate that the proposed path tracking method provides a solid theoretical framework for high-precision path tracking of unmanned agricultural machines.

At present, the lane changing technology for a single driving environment has been relatively mature, but the actual situations are much more complicated, such as the changing curvature and the changes in road conditions. In this paper, a new lane changing obstacle avoidance control strategy for the variable curvature road was proposed. It has two stages including path planning for variable curvature lane changing and inverse system decoupling (ISD) control for path tracking. The first stage established the lane changing path models for the variable curvature road. A longitudinal-lateral safe distance model was proposed to constrain the safe boundary of the lane changing path. The second stage proposed a dynamic decoupling method for longitudinal and lateral motion based on the inverse system decoupling, a direct yaw moment and active front wheel steering coordinated control method was designed. The inverse system decoupling algorithm can correct the single point preview (SPP) method to improve the stability and the path tracking accuracy in the lane changing obstacle avoidance process. The strategy was simulated by CarSim/Simulink co-simulation, and the experiments were carried out on the hardware-in-the-loop platform. The results show that the proposed control strategy can effectively avoid obstacles when the vehicle is driving on the variable curvature road. Besides, for the different road conditions and the strong non-linearity generated during the lane changing process, the control strategy can reduce the tracking error by a maximum of 32.7%, both the yaw rate and side slip angle can be controlled in a smaller range.

In this paper, two distinct strategies were used to enhance problem-solving abilities. The first strategy involved developing a conjugate gradient algorithm such that a new parameter was extracted and proposed. The second strategy included Improving the Whale Algorithm (WOA) in two ways, the first using the community by taking advantage of the developed conjugate gradient algorithm that was extracted from the first strategy and obtaining the proposed algorithm (CG-WOA) that gives better results than the results from the original algorithm. The second method is to combine the sand cat swarm optimization algorithm (SCSO) with the whale optimization algorithm (WOA), and the proposed algorithm (SCSO-WOA) is obtained. The proposed algorithms (CG-WOA) and (SCSO-WOA) have many characteristics, including their ability to deal with complex optimization problems and their speed efficiency compared to the original algorithm. The diversity of exploration and exploitation operations in the proposed algorithm (SCSO-WOA) gives it the advantage of fast convergence, obtaining the global optimal solution, and avoiding falling into local solutions. The efficiency of the two algorithms (CG-WOA) and (SCSO-WOA) was tested on five standard test functions, so that better numerical results were obtained than the results of the original

Whale optimization algorithm (WOA) is a swarm intelligence optimization algorithm inspired by humpback whale hunting behavior. WOA has many similarities with other swarm intelligence algorithms (PSO, GWO, etc.). WOA’s unique search mechanism enables it to have a strong global search capability while taking into account the strong global search capabilities. In this work, considering the the deficiency of WOA in local search mechanism, combined with the optimization methods of other group intelligent algorithms, perceptual perturbation mechanism is introduced, which makes the agent perform more detailed searches near the local extreme point. At the same time, since the WOA uses a logarithmic spiral curve, the agent cannot fully search all the spaces within its search range, even though the introduction of the perturbation mechanism may still lead to the algorithm falling into a local optimum. Therefore, the equal pitch Archimedes spiral curve is chosen to replace the classic logarithmic spiral curve. In order to fully verify the effect of the search path on the performance of the algorithm, several other spiral curves have been chosen for experimental comparison. By utilizing the 23 benchmark test functions, the simulation results show that WOA (PDWOA) with perceptual perturbation significantly outperforms the standard WOA. Then, based on the PDWOA, the effect of the search path on the performance of the algorithm has been verified. The simulation results show that the equal pitch of the Archimedean spiral curve is best.

To address the shortcomings of the whale optimization algorithm (WOA) in terms of insufficient global search ability and slow convergence speed, a differential evolution chaotic whale optimization algorithm (DECWOA) is proposed in this paper. Firstly, the initial population is generated by introducing the Sine chaos theory at the beginning of the algorithm to increase the population diversity. Secondly, new adaptive inertia weights are introduced into the individual whale position update formula to lay the foundation for the global search and improve the optimization performance of the algorithm. Finally, the differential variance algorithm is fused to improve the global search speed and accuracy of the whale optimization algorithm. The impact of various improvement strategies on the performance of the algorithm is analyzed using different kinds of test functions that are randomly selected. The particle swarm optimization algorithm (PSO), butterfly optimization algorithm (BOA), WOA, chaotic feedback adaptive whale optimization algorithm (CFAWOA), and DECWOA algorithm are compared for the optimal search performance. Experimental simulations are performed using MATLAB software, and the results show that the improved whale optimization algorithm has a better global optimization-seeking capability. The improved whale optimization algorithm is applied to the distribution network fault location of IEEE-33 nodes, and the effectiveness and accuracy of the distribution network fault zone location based on the multistrategy improved whale optimization algorithm is verified.

Path tracking is a crucial part of agricultural machinery automatic navigation system (ANS) and has been extensively investigated in prior research. Although existing ANS designs perform satisfactorily under mild soil condition, path-tracking algorithms are often challenged by unknown disturbances arising from complicated field environment and machine conditions. The current literature lacks a detailed analysis of the influence of the sideslip angle under specific operating speeds and path scenarios for agricultural machinery, which serves as the primary motivation for this study. In this paper, simulations are conducted for sprayers and harvesters across various paths, curvatures, and speeds to analyze the impact of sideslip on path-tracking performance. The results indicate that under the typical low-speed and large-curvature conditions of agricultural machinery, neglecting sideslip effects leads to a mismatch between the theoretical model and the actual vehicle motion. Compared to an MPC based on a kinematic model that disregards the sideslip angle, explicitly incorporating the sideslip angle into the kinematic model reduces the maximum lateral tracking error from 0.234 m to 0.174 m for a U-shaped path, and from 0.263 m to 0.194 m for a rectangular-shaped path. Simulation at different travel speeds further demonstrates that proposed algorithm achieves smaller sideslip amplitudes and faster attenuation after completing turns compared to conventional MPC. These findings offer valuable insights for the design of path-tracking algorithms in agricultural machinery autonomous driving systems.

This paper presents an innovative path tracking method of model predictive control based on multi-point preview (MPP-MPC) that the original equation of state is augmented by considering a dynamics model of the multiple preview points. The path tracking issue is formulated as an optimal control problem with dynamic disturbance, i.e., the future road curvature. Hence, an ameliorative Kalman filter is adopted to fuse the information about camera and vehicle dynamics to accurately estimate the road curvature. To ensure lateral control performance, dynamic constraints are defined by the estimated road curvature to guarantee comfort and safety. In the control domain of model predictive control (MPC), the model can be approximated as a linear time-invariant model (LTIM) to reduce the computational complexity. The MPC problem can be transformed into a standard quadratic programming (QP) problem with dynamic constraints of guaranteed comfort and safety. Finally, the complex path tracking problem can be solved by the QP problem. Through lane keeping experiments, it is shown that the tracking accuracy and steering smoothness can be significantly improved by the proposed method.

Irrelevant features in data collected from oil refineries affect system performance due to conflicts between normal data and detected faults. Selecting the relevant features from the data leads to better classification results. Optimization algorithms are successfully applied in the feature selection task in many systems. One of the powerful optimization algorithms that is used for feature selection is the Whale Optimization Algorithm (WOA), which is a nature-inspired metaheuristic optimization algorithm that mimics the social behavior of humpback whales. This study presents an improvement to WOA using a tent chaotic map to select the most relevant features and enhance performance. The Tent map mainly applies randomness to generate diversification into the search process and escape from local optima in WOA. The tent map is used for generating the initial population, producing values in control parameters, and updating the position of search agents. The proposed approach combines the tent map with WOA, called TWOA, to enrich population diversity, prevent premature convergence, and speed up convergence. TWOA is applied in a soft sensor with actual data collected from the Salahuddin oil refinery in Iraq. The soft sensor was designed using several stages, including data collection, preprocessing, clustering, feature selection, and classification. The proposed TWOA achieved a higher fault classification result of 99.98% compared to other algorithms.

Integrated path planning and control through proximal policy optimization for a marine current turbine

This paper describes theoretical estimation of domains mean using double sampling with a non-linear cost function in the presence of non-response. The estimation of domain mean is proposed using auxiliary information in which the study and auxiliary variable suffers from non-response in the second phase sampling. The expression of the biases and mean square errors of the proposed estimators are obtained. The optimal stratum sample sizes for given set of non-linear cost function are developed.