A Tricycle Model to Accurately Control an Autonomous Racecar with Locked Differential

TL;DR

This work introduces a locked-differential tricycle model for autonomous racing and embeds it in an MPC framework with micro-step discretization to enable real-time prediction near tire limits. It combines a high-fidelity multi-body model for calibration with a tractable tricycle representation that captures rear-wheel yaw moment contributions and load transfer, validated on Monza and in high-fidelity simulations. The planning stack includes offline trajectory generation, online longitudinal preview via friction-ellipse constraints, and a low-level longitudinal controller transitioning MPC outputs to throttle/brake commands. Results show improved lateral tracking and stability over traditional single-track models, particularly in tight-radius and high-curvature sections, while maintaining computational feasibility for real-time control. The work highlights a practical trade-off between model fidelity and tractable implementation, and points toward extending the approach to other differential configurations such as limited-slip designs.

Abstract

In this paper, we present a novel formulation to model the effects of a locked differential on the lateral dynamics of an autonomous open-wheel racecar. The model is used in a Model Predictive Controller in which we included a micro-steps discretization approach to accurately linearize the dynamics and produce a prediction suitable for real-time implementation. The stability analysis of the model is presented, as well as a brief description of the overall planning and control scheme which includes an offline trajectory generation pipeline, an online local speed profile planner, and a low-level longitudinal controller. An improvement of the lateral path tracking is demonstrated in preliminary experimental results that have been produced on a Dallara AV-21 during the first Indy Autonomous Challenge event on the Monza F1 racetrack. Final adjustments and tuning have been performed in a high-fidelity simulator demonstrating the effectiveness of the solution when performing close to the tire limits.

Figures (11)

• Figure 1: Dallara AV-21 - TII UNIMORE Racing during the Indy Autonomous Challenge at MIMO 2023 in the Monza F1 circuit. © Autodromo Nazionale Monza
• Figure 2: A comparison between experimental data and the multibody model is presented. The slip angle is plotted on the x-axis, and the estimated wheel force is shown on the y-axis. It can be observed that the inner wheels (right side), where there is less vertical load acting, are working in the non-linear region of the tire.
• Figure 3: Comparison between the experimental measurement of the yaw moment due to the locked differential (through slip ratio calculations), used as a reference (in blue), and the estimation from the multi-body model (in orange). The noisy reference is related to the accuracy of the estimation and the highly nonlinear nature of the measurement. The higher the curvature, the greater the resisting yaw moment to turn in. Here, the central section of the Monza track is shown, including Variante 2 and the Lesmo turns.
• Figure 4: Scheme of the three-wheels model, in curvilinear coordinates, included in the MPC.
• Figure 5: Poles for the three-wheels model at $v_x = 8 m/s$. The proposed step size for the integration allows the system poles to lay within the stability region of the explicit Euler method.