Generating receding-horizon motion trajectories for autonomous vehicles in real-time while also providing safety guarantees is challenging. This is because a future trajectory needs to be planned before the previously computed trajectory is completely executed. This becomes even more difficult if the trajectory is required to satisfy continuous-time collision-avoidance constraints while accounting for a large number of obstacles. To address these challenges, this paper proposes a novel real-time, receding-horizon motion planning algorithm named REachability-based trajectory Design via Exact Formulation of Implicit NEural signed Distance functions (REDEFINED). REDEFINED first applies offline reachability analysis to compute zonotope-based reachable sets that overapproximate the motion of the ego vehicle. During online planning, REDEFINED leverages zonotope arithmetic to construct a neural implicit representation that computes the exact signed distance between a parameterized swept volume of the ego vehicle and obstacle vehicles. REDEFINED then implements a novel, real-time optimization framework that utilizes the neural network to construct a collision avoidance constraint. REDEFINED is compared to a variety of state-of-the-art techniques and is demonstrated to successfully enable the vehicle to safely navigate through complex environments. Code, data, and video demonstrations can be found at https://roahmlab.github.io/redefined/.

翻译：在实时生成自动驾驶车辆滚动时域运动轨迹的同时提供安全保证是一项挑战。这是因为需要在完全执行先前计算的轨迹之前规划未来轨迹。若要求轨迹在考虑大量障碍物的同时满足连续时间避碰约束，则该问题将变得更为困难。为应对这些挑战，本文提出一种名为REDEFINED（基于隐式神经符号距离函数精确建模的可达性轨迹设计）的新型实时滚动时域运动规划算法。该算法首先应用离线可达性分析计算基于超椭球体的可达集，以过估计自车运动范围。在线规划阶段，REDEFINED利用超椭球体算术构建神经隐式表示，可精确计算参数化自车扫掠体与障碍车辆之间的符号距离。进而实现一种新颖的实时优化框架，通过神经网络构建避碰约束。将REDEFINED与多种先进技术进行对比，证明其能成功引导车辆安全穿越复杂环境。相关代码、数据及视频演示详见https://roahmlab.github.io/redefined/。