Autonomous systems like aircraft and assistive robots often operate in scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi reachability can provide guaranteed safe sets and controllers for such systems. However, often these same scenarios have unknown or uncertain environments, system dynamics, or predictions of other agents. As the system is operating, it may learn new knowledge about these uncertainties and should therefore update its safety analysis accordingly. However, work to learn and update safety analysis is limited to small systems of about two dimensions due to the computational complexity of the analysis. In this paper we synthesize several techniques to speed up computation: decomposition, warm-starting, and adaptive grids. Using this new framework we can update safe sets by one or more orders of magnitude faster than prior work, making this technique practical for many realistic systems. We demonstrate our results on simulated 2D and 10D near-hover quadcopters operating in a windy environment.

中文翻译：

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使用Hamilton-Jacobi可达性的自治系统安全性的可扩展学习

诸如飞机和辅助机器人之类的自主系统通常在保证安全至关重要的情况下运行。诸如Hamilton-Jacobi可达性之类的方法可以为此类系统提供有保证的安全设置和控制器。但是，通常这些相同的方案具有未知或不确定的环境，系统动态或其他代理的预测。当系统运行时，它可能会学习有关这些不确定性的新知识，因此应相应地更新其安全性分析。但是，由于分析的计算复杂性，学习和更新安全性分析的工作仅限于约二维的小型系统。在本文中，我们综合了几种可加快计算速度的技术：分解，热启动和自适应网格。使用此新框架，我们可以比以前的工作快一个或多个数量级来更新安全集，从而使该技术可用于许多实际系统。我们在有风的环境中运行的模拟2D和10D近悬四轴飞行器上演示了我们的结果。