Automated driving is poised to transform the transportation landscape of the future, but several challenges remain before full automation is achieved. One of these challenges lies in managing perception uncertainties, such as those arising from radar and sensor measurements, while maintaining control in low tire-road friction conditions. These challenges often occur simultaneously in adverse weather conditions, but are typically researched separately. Their combined effect on safety and performance remains underexplored, even though addressing them together is critical for robust and reliable automated driving systems.

Lower tire-road friction limits the available tire force required for obstacle avoidance. Properly modeling these tire friction limits is particularly important in dynamic and uncertain environments to adequately account for the changing environment responsively. Moreover, addressing perception uncertainties and modeling low-friction conditions individually can significantly increase computational demands which poses challenges to achieve real-time performance required for real-world implementation. Therefore, this thesis jointly considers perception uncertainties and low tire-road friction conditions, accounting for their interacting effects. This is accomplished by addressing the following research question: "How can perception uncertainties be effectively integrated into motion-planning models for obstacle avoidance to improve performance and safety of automated vehicles in various road conditions?"

To address this question, a grid-based stochastic model predictive control framework is extended, implementing a non-linear bicycle model and a Fiala tire model (brush model) to consider realistic vehicle capabilities in low-friction conditions. Grid-based stochastic model predictive control reduces the uncertain obstacle environment into a set of linear constraints, utilizing an occupancy probability grid to effectively consider perception uncertainties. While the developed framework is presented as a proof-of-concept with a focus on safety and feasibility over real-time implementation, computational efficiency is not overlooked. By reformulating the constraints, the uncertainties are effectively accounted for while also reducing the optimization time by simplifying the probabilistic obstacle space to a deterministic convex region. If the nominal reformulation fails, a novel back-up method generates a conservative back-up set of constraints improving the safety and feasibility of the method. Two different back-up strategies are proposed, providing a trade-off between accuracy and computational effort.

To evaluate the contributions, three simulations were conducted. The first comparing the non-linear bicycle model and Fiala tire model to more simplistic models at various tire-road friction coefficients, highlighting the improvement in control of the proposed model in low-friction conditions. The second simulation evaluated the performance of the proposed back-up methods and environment representation by simulating tight scenarios that would fail using only the nominal approach. Feasibility rates increased compared to the baseline back-up method (43.8%) with feasibility rates of 62.5% for the precomputed back-up method and 75.0% for the current-state back-up method. These simulation results demonstrate that the capability of the proposed framework to compute feasible solutions and that the framework is able to compute valid hulls that are safe when the nominal approach fails to reformulate the constraints. The final simulation evaluated the performance of the complete proposed method by simulating both tight scenarios requiring a back-up method as well as various friction levels. These simulations demonstrated that the proposed framework is effective at lower friction levels, achieving high feasibility rates of 87.5% for the current-state back-up method, and 91.6% for the precomputed back-up method. This high accuracy is particularly promising for real-time applications using the precomputed back-up strategy, since this method leverages parallel computation of the back-up constraints.

This thesis demonstrated the effectiveness of the proposed extended grid-based stochastic model predictive control framework in considering perception uncertainties in low-friction road conditions. While presented as a proof-of-concept with an emphasis on feasibility and safety rather than real-time implementation, the proposed framework lays the groundwork for real-time applications, marking a step in solving all edge cases required to reach fully automated vehicles.