Modares Mechanical Engineering

Modares Mechanical Engineering

Integrated Longitudinal and Lateral Control for Path Tracking of Autonomous Vehicles Based on NMPC and MHE Under Network Delay and Uncertainty

Document Type : Original Article

Authors
Shahram Azadi
Seyed Shamir Shojaee
Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
10.48311/mme.2026.118574.82920
Abstract
Autonomous vehicles require a precise control system capable of handling nonlinear vehicle dynamics safely perform agile maneuvers, such as lane changes. However, in real-world operating conditions, factors such as sensor measurement noise, process noise, time delays, and data packet loss can compromise the stability of the control system. In this research, an integrated control framework based on Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) is proposed. In the proposed method, the MHE filters out noise effects and reconstructs the system states during periods of data loss and time delays by incorporating physical constraints and the dynamic model. Subsequently, the NMPC receives the corrected states and calculates optimal commands aimed at minimizing the tracking error and maintaining passenger comfort. Simulation results of a double lane change maneuver at a speed of 108 km/h demonstrate that in a critical scenario (comprising a 100 ms network delay, 20% data packet loss, sensor noise, and uncertainties arising from employing a twin-track model with the Pacejka tire formula in the simulation plant), the proposed approach exhibits superior performance compared to the Extended Kalman Filter (EKF) algorithm. This structure fully maintains the vehicle's stability while preventing undesirable oscillations in the steering angle and traction force. Recording a maximum lateral error of 0.1 m and a Root Mean Square Error (RMSE) of 0.044 m demonstrates the outstanding performance of this system in ensuring safety and stability.
Keywords
Autonomous Vehicle
Nonlinear Model Predictive Control (NMPC)
Moving Horizon Estimation (MHE)
Sensor Uncertainty
Path Tracking
Subjects
[1] S. Thrun et al., “Stanley: The robot that won the DARPA Grand Challenge,” J. Field Robot., vol. 23, no. 9, pp. 661–692, 2006,DOI: 10.1002/rob.20147.
[2] D. S. Lal, A. Vivek, and G. Selvaraj, “Lateral control of an autonomous vehicle based on Pure Pursuit algorithm,” in 2017 International Conference on Technological Advancements in Power and Energy (TAP Energy), Dec. 2017, pp. 1–8. DOI: 10.1109/TAPENERGY.2017.8397361.
[3] K. M. Junaid and S. Wang, “Autonomous Vehicle Following-Performance Comparison and Proposition of a Quasi-Linear Controller,” Inf. Technol. Control, vol. 36, no. 4, Dec. 2007, Accessed: Dec. 19, 2025. [Online]. Available: https://itc.ktu.lt/index.php/ITC/article/view/11891
[4] H. Sazgar, Sh. Azadi, and R. Kazemi, " Trajectory planning and integrated control with the Nonlinear Bicycle Model for high-speed autonomous lane change," Modares Mechanical Engineering Journal, vol. 18, no. 2, pp. 103–114, Mar. 2018. (in persian)
[5] H. Sazgar and A. K. Khalaji, " Motion Planning in Critical Lane Change Maneuvers Considering the Stability Margins of the Vehicle," Modares Mechanical Engineering Journal, vol. 24, no. 4, pp. 225–238, Aug. 2024. (in persian)
[6] P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat, “Predictive Active Steering Control for Autonomous Vehicle Systems,” IEEE Trans. Control Syst. Technol., vol. 15, no. 3, pp. 566–580, May 2007, DOI: 10.1109/TCST.2007.894653.
[7] J. P. Allamaa, P. Listov, H. V. der Auweraer, C. Jones, and T. D. Son, “Real-time Nonlinear MPC Strategy with Full Vehicle Validation for Autonomous Driving,” May 27, 2022, arXiv: arXiv:2110.03349. DOI: 10.48550/arXiv.2110.03349.
[8] M. A. Ghomashi and R. Kazemi, " Motion Path Following Coordinated Control for In-Wheel Motor Electric Vehicle via Implementation Robust Control and Optimal Control," Journal of Modeling in Engineering, vol. 23, no. 80, pp. 131–145, Mar. 2025, DOI: 10.22075/jme.2024.31752.2531. (in persian)
[9] M. Fazel and M. Yazdanpanah, " Using Integrated Predictive Model Control in the Simulation of Stability and Traction Control of an Electric Vehicle," Amirkabir Journal of Mechanical Engineering, vol. 57, no. 5, pp. 611–632, Jul. 2025, DOI: 10.22060/mej.2025.24465.7872. (in persian)
[10] T. Kim, T.-H. Park, T. Kim, and T.-H. Park, “Extended Kalman Filter (EKF) Design for Vehicle Position Tracking Using Reliability Function of Radar and Lidar,” Sensors, vol. 20, no. 15, July 2020, DOI: 10.3390/s20154126.
[11] E. Kayacan, W. Saeys, H. Ramon, C. Belta, and J. M. Peschel, “Experimental Validation of Linear and Nonlinear MPC on an Articulated Unmanned Ground Vehicle,” IEEEASME Trans. Mechatron., vol. 23, no. 5, pp. 2023–2030, Oct. 2018, DOI: 10.1109/TMECH.2018.2854877.
[12] Y. Kebbati, A. Rauh, N. Ait-Oufroukh, D. Ichalal, and V. Vigneron, “Learning-based model predictive control with moving horizon state estimation for autonomous racing,” Int. J. Control, vol. 98, no. 7, pp. 1542–1552, July 2025, DOI: 10.1080/00207179.2024.2409305.
[13] S. Niu, R. Zhang, B. Ren, B. Gao, Y. Ge, and L. Xiong, “Integrated AISGP Model for Real-Time Autonomous Vehicle State Estimation and Path Tracking Control,” IEEE Trans. Veh. Technol., pp. 1–15, 2025, DOI: 10.1109/TVT.2025.3606541.
[14] A. E. S. Morando et al., “Optimizing Unmanned Air–Ground Vehicle Maneuvers Using Nonlinear Model Predictive Control and Moving Horizon Estimation,” Automation, vol. 5, no. 3, pp. 324–342, July 2024, DOI: 10.3390/automation5030020.
[15] R. Rajamani, Vehicle dynamics and control. in Mechanical engineering series. New York: Springer Science + Business Media, 2005.
[16] R. N. Jazar, Vehicle Dynamics. Cham: Springer International Publishing, 2017. DOI: 10.1007/978-3-319-53441-1.
[17] H. B. Pacejka, Tire and Vehicle Dynamics, 3rd ed. Oxford, UK: Elsevier, 2012. DOI: 10.1016/C2010-0-66481-2.
[18] A. Alessandri, M. Baglietto, and G. Battistelli, “Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes,” Automatica, vol. 44, no. 7, pp. 1753-1765,Jul.2008. DOI:10.1016/j.automatica.2007.11.020.
[19] L. Grüne and J. Pannek, Nonlinear Model Predictive Control. in Communications and Control Engineering. Cham: Springer International Publishing, 2017. DOI: 10.1007/978-3-319-46024-6.
[20] D. Simon, Optimal State Estimation: Kalman, H-Infinity and Nonlinear Approaches. Hoboken, NJ: John Wiley & Sons, 2006.DOI: 10.1002/0470045345.
Modares Mechanical Engineering
Volume 26, Issue 7
July 2026
Pages 583-597