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Risk-Aware Optimal Control for Automated Overtaking With Safety Guarantees

This article proposes a solution to the overtaking control problem where an automated vehicle tries to overtake another vehicle with uncertain motion. Our solution allows the automated vehicle to robustly overtake a human-driven vehicle under certain assumptions. Uncertainty in the predicted motion makes the automated overtaking problem hard to solve due to feasibility issues that arise from the fact that the overtaken vehicle (e.g., a vehicle driven by an aggressive driver) may accelerate to prevent the overtaking maneuver. To counteract them, we introduce the weak assumption that the predicted velocity of the overtaken vehicle respects a supermartingale, meaning that its velocity is not increasing in expectation during the maneuver. We show that this formulation presents a natural notion of risk. Based on the martingale assumption, we perform a risk-aware reachability analysis by analytically characterizing the predicted collision probability. Then, we design a risk-aware optimal overtaking algorithm with guaranteed levels of collision avoidance. Finally, we illustrate the effectiveness of the proposed algorithm with a simulated example.