Multi-agent interaction and enhanced safety in autonomous overtaking with backward reachability analysis

Safe and efficient autonomous driving in complex multi-agent traffic scenarios requires proactive decision-making to anticipate human driver behavior while remaining robust against uncertainty in their actions. A key challenge lies in enabling collision-free navigation without relying on overly conservative motion planning strategies. Hamilton-Jacobi Backward Reachability Analysis (BRA) offers a powerful framework for safety verification in autonomous systems by defining a metric that characterizes the set of states from which collisions become inevitable, even under optimal control. In this work, the computational burden of computing the Backward Reachable Tube (BRT) via the Level Set Method is mitigated through a targeted grid selection strategy tailored for realistic driving scenarios, where safety is integrated into the Model Predictive Control (MPC) framework through a dual-layered approach. First, a minimally interventional reachability-based constraint is introduced and activated only in near-unsafe configurations that could lead to unavoidable collisions to preserve planning flexibility. Second, a novel attentive-level module based on reachability analysis is proposed, enabling continuous risk assessment in the presence of multiple human-driven vehicles. To provide a complete evaluation of the algorithm's effectiveness, simulations are conducted both with the safety-preserving constraint enabled and disabled, revealing potential collisions and highlighting the contribution of the proposed algorithm. The combined effect of the attentive layer and the reactive safety-preserving constraint is demonstrated through autonomous multi-agent overtaking scenarios on two-lane roads involving both preceding vehicles and oncoming traffic, highlighting improved safety and performance with respect to baseline methods.