LPV-MPC for Lateral Control in Full-Scale Autonomous Racing

Hassan Jardali; Ihab S. Mohamed; Durgakant Pushp; Lantao Liu

cs.ROMar 14, 2026

LPV-MPC for Lateral Control in Full-Scale Autonomous Racing

Authors: Hassan Jardali, Ihab S. Mohamed, Durgakant Pushp, Lantao Liu

Organizations: Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN 47408 USA

Abstract

Autonomous racing has attracted significant attention recently, presenting challenges in selecting an optimal controller that operates within the onboard system's computational limits and meets operational constraints such as limited track time and high costs. This paper introduces a Linear Parameter-Varying Model Predictive Controller (LPV-MPC) for lateral control. Implemented on an IAC AV-24, the controller achieved stable performance at speeds exceeding 160 mph (71.5 m/s). We detail the controller design, the methodology for extracting model parameters, and key system-level and implementation considerations. Additionally, we report results from our final race run, providing a comprehensive analysis of both vehicle dynamics and controller performance. A Python implementation of the framework is available at: https://tinyurl.com/LPV-MPC-acados

Figures & tables

Fig. 1 : IU-LART IAC AV-24 autonomous racing vehicle [ 3 ] .

Fig. 2 : Overview of the single-track bicycle model, highlighting relevant forces, angles, and lateral errors in their positive directions.

Tires	$B_{p}$	$C_{p}$	$D_{p}$	$E_{p}$	$C_{\text{linear}}$
Front	34.59	1.81	2100	-1.0	$132\text{\,}\mathrm{k}$
Rear	35.04	1.96	3036	-0.26	$209\text{\,}\mathrm{k}$

TABLE I : Initial Pacejka Parameters values using IMS data.

D_{p}

is in Newtons (N), and

C_{\text{linear}}

is in N/rad.

Fig. 3 : Measured cornering forces versus slip angles with the corresponding fitted Pacejka curve, obtained from the final IMS run at a longitudinal velocity of

56\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}

. Note that the vertical offset in the Pacejka model (typically denoted as

s_{hy}

) was not accounted for.

Fig. 4 : High-level software architecture of our autonomous racing system for a single-car format [ 3 ] .

Panel of Figure 6 — Fig. 5 : Experimental results for path tracking during our highest speed lap. The highlighted areas mark the start and finish of the lap.

Fig. 6 : Tracking errors vs. velocity during the complete run.

Fig. 7 : Measured cornering forces

F_{y}

versus slip angles,

\alpha_{f}

and

\alpha_{r}

, with the corresponding fitted Pacejka curve, obtained from the final run at a longitudinal velocity of

72\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}

. The Linear Force curve depicts the estimated force computed using the cornering stiffness parameters that were determined during the practice runs and employed during the final run.

Tires	$B_{p}$	$C_{p}$	$D_{p}$	$E_{p}$	$C_{\text{linear}}$
Front	22.30	2.00	3885.85	-1.00	$173\text{\,}\mathrm{k}$
Rear	26.08	2.00	5342.89	-1.00	$278\text{\,}\mathrm{k}$

TABLE II : Pacejka parameter values obtained via EM optimization using our final run data.

D_{p}

is in Newtons [N], and

C_{\text{linear}}

is in [N/rad]. Note that these parameters have not been tested with the proposed controller.

Fig. 8 : Lateral vs. longitudinal acceleration (g-g diagram) during the complete run. Accelerations were measured using the on-board IMU.

Fig. 9 : Lateral model error vs. velocity during the final run.

Fig. 10 : Computation time

t_{\text{comp.}}

of the control loop during the high-speed lap.

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Nonlinear MPC Autonomous Racing Model Predictive Control Vehicle Dynamics Adaptive Control

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This paper presents Adaptive Differentiable Model Predictive Contouring Control (AD-MPCC), a framework for autonomous racing that integrates differentiable MPCC with online parameter estimation to handle varying road-surface conditions. For online parameter estimation, we leverage a parameterized Pacejka Magic Formula together with a regularized moving-horizon estimation scheme with exponentially decaying weights to capture road interactions and update parameters in real time. Furthermore, we propose a differentiable MPCC (Diff-MPCC) framework that enables optimal adjustment of objective weights based on predefined long-horizon performance costs. To implement Diff-MPCC for online objective weight adaptation, we propose a Pacejka-informed machine learning model that is trained in a supervised manner using data generated by Diff-MPCC to tune the objective weights. Simulation results demonstrate that AD-MPCC reliably ensures safety and achieves faster lap times compared to baseline controllers in both single-surface and multiple-surface scenarios.

Abstract

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