Optimized adaptive MPC for lateral control of autonomous vehicles (2509.17215v1)

Abstract: Autonomous vehicles are the upcoming solution to most transportation problems such as safety, comfort and efficiency. The steering control is one of the main important tasks in achieving autonomous driving. Model predictive control (MPC) is among the fittest controllers for this task due to its optimal performance and ability to handle constraints. This paper proposes an adaptive MPC controller (AMPC) for the path tracking task, and an improved PSO algorithm for optimising the AMPC parameters. Parameter adaption is realised online using a lookup table approach. The propose AMPC performance is assessed and compared with the classic MPC and the Pure Pursuit controller through simulations. Code can be found here: https://github.com/yassinekebbati/Optimized_adaptive_MPC

• The paper presents an adaptive MPC framework that integrates an improved PSO algorithm for online tuning of controller parameters.
• It leverages a Laguerre function-based approach to reduce computational load while ensuring constraint-aware, accurate lateral control in dynamic scenarios.
• Simulation results demonstrate significantly lower mean squared errors compared to classic MPC and Pure Pursuit, confirming enhanced stability and robustness.

Optimized Adaptive Model Predictive Control for Lateral Control of Autonomous Vehicles

Introduction

The paper presents an adaptive Model Predictive Control (AMPC) framework for lateral control in autonomous vehicles, integrating an improved Particle Swarm Optimization (PSO) algorithm for online parameter tuning. The motivation stems from the need for robust, constraint-aware controllers capable of handling dynamic environments and actuator limitations, which are inadequately addressed by traditional controllers such as Pure Pursuit and classic MPC. The proposed approach leverages Laguerre function-based MPC for computational efficiency and introduces a lookup table-based online adaptation mechanism for controller parameters, including prediction and control horizons, weighting matrices, and Laguerre terms.

Vehicle Dynamics Modeling and MPC Formulation

The lateral dynamics are modeled using a linearized 2-DOF bicycle model, capturing essential lateral and yaw motions. The model incorporates tire-road interactions via linearized cornering stiffness and slip angle approximations, resulting in a continuous-time state-space representation. Discretization yields a prediction model suitable for MPC, with the state matrix $A_k$ adaptively updated based on real-time longitudinal velocity, enabling the controller to handle varying speed profiles.

The MPC controller is augmented with an integrator to ensure zero steady-state error and is formulated as a constrained quadratic programming (QP) problem. The cost function penalizes both tracking error and control effort, subject to actuator and output constraints. Laguerre function approximation is employed to reduce the dimensionality of the control sequence, allowing for long control horizons with fewer parameters and thus lower computational overhead. The QP is solved using Hildreth's method, with active set identification for inequality constraints.

Improved Particle Swarm Optimization for Controller Tuning

The PSO algorithm is enhanced with dynamic inertia weight and acceleration coefficients, transitioning through exploration, exploitation, convergence, and jumping-out phases. The inertia weight $\omega$ is updated exponentially rather than linearly, promoting faster convergence and improved global search capability. The cognitive ($c_1$) and social ($c_2$) acceleration coefficients are adaptively adjusted based on the optimization phase, as per a predefined logic, to balance exploration and exploitation.

The improved PSO is tasked with optimizing the MPC parameters: prediction horizon ($N_p$), control horizon ($N_c$), weighting matrices ($Q$, $R$), and the number of Laguerre terms ($N$). The mean squared error (MSE) of the tracking performance serves as the fitness function. The optimization is performed over a range of longitudinal velocities and reference trajectories, with the resulting optimal parameters stored in a lookup table for online adaptation.

Simulation Results and Comparative Analysis

The proposed AMPC is evaluated using a high-fidelity vehicle model (MATLAB Vehicle Dynamics Blockset, 3-DOF dual track, nonlinear Pacejka tire model) across three scenarios:

1. Double Lane Change at Constant Velocity ($v_x=9$ m/s): AMPC achieves an MSE of 0.097, outperforming classic MPC (0.422) and Pure Pursuit (0.482). The AMPC demonstrates superior tracking, smoother steering commands, and more stable heading rates.
2. Double Lane Change with Varying Velocity: Pure Pursuit fails to complete the maneuver. AMPC maintains robust tracking (MSE 0.124) compared to classic MPC (0.489), with adaptive parameter updates ensuring stability across speed changes.
3. General Trajectory with Varying Velocity and Wind Disturbance: Under constant velocity, AMPC yields an MSE of 10.79, outperforming MPC (21.234) and Pure Pursuit (76.639). With varying velocity, AMPC further reduces MSE to 7.219 versus MPC's 25.079. When subjected to lateral wind disturbances, classic MPC diverges, while AMPC maintains trajectory tracking due to its adaptive parameterization.

The improved PSO demonstrates faster convergence and superior fitness values compared to classic and previously improved PSO variants, reaching $10^{-3}$ fitness in 41 generations versus 2.1 and 3.11 for other methods.

Practical and Theoretical Implications

The integration of adaptive MPC with online PSO-based parameter tuning addresses key challenges in autonomous vehicle control: constraint handling, adaptation to dynamic environments, and computational efficiency. The use of Laguerre functions enables real-time implementation on embedded platforms by reducing the computational load. The lookup table-based adaptation mechanism allows for rapid parameter updates in response to changing vehicle states and external disturbances.

The demonstrated robustness to wind disturbances and varying speed profiles highlights the practical viability of the approach for real-world deployment in urban and highway scenarios. The methodology is extensible to other MIMO control tasks in autonomous systems, such as combined lateral-longitudinal control and multi-agent coordination.

Future Directions

The paper suggests further research into leveraging neural networks and adaptive neuro-fuzzy inference systems for learning and generalizing the optimal parameters identified by PSO, potentially enabling end-to-end adaptive control without explicit lookup tables. Additionally, extending the framework to nonlinear MPC formulations and integrating perception-driven reference generation could further enhance autonomy and safety.

Conclusion

The proposed AMPC framework, optimized via an improved PSO algorithm and augmented with Laguerre function approximation, demonstrates significant improvements in lateral control accuracy, adaptability, and robustness for autonomous vehicles. The approach effectively handles dynamic scenarios and external disturbances, outperforming classic MPC and Pure Pursuit controllers. The results support the adoption of adaptive, optimization-driven control architectures in autonomous vehicle systems, with promising avenues for further enhancement through machine learning-based adaptation mechanisms.