  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.
