标题： 作为在线运动生成安全手段的 captivity-escape 游戏 显示英文标题

标题： Captivity-Escape Games as a Means for Safety in Online Motion Generation

摘要： 本文提出了一种方法，解决了现有确保在线基于模型的运动生成安全性的框架和方法中存在的保守性、计算开销大以及数值精度有限的问题，这些方法通常被称为快速且安全的跟踪。 计算限制将在线运动规划限制在低保真模型上。 然而，使用低保真模型进行规划会危及安全性，因为无法保证生成的参考轨迹具有动态可行性。 这可能导致不可避免的跟踪误差，从而引发安全关键约束违反的情况。 现有框架通过在运动规划中增加一个安全裕度来缓解这种安全风险，该安全裕度可以防止最坏情况下的跟踪误差导致约束违反。 然而，这些框架所采用的方法根据规划模型的经验选择性能来确定安全裕度，这可能导致过于保守的参考轨迹。 此外，这些方法计算复杂度较高，最先进的方法在数值精度方面也受到限制。 我们采取了不同的视角，并通过一种方法克服了这些限制，该方法通过将规划模型性能适应给定的安全裕度来减轻现有框架中的保守性。 我们的方法通过利用文中提出的特定的零和微分博弈——捕获-逃脱博弈，实现了更高的数值精度，并显著减少了所需的计算时间。 我们通过一个数值实例演示了我们的方法，并将其与最先进的方法进行了比较。 显示英文摘要

摘要： This paper presents a method that addresses the conservatism, computational effort, and limited numerical accuracy of existing frameworks and methods that ensure safety in online model-based motion generation, commonly referred to as fast and safe tracking. Computational limitations restrict online motion planning to low-fidelity models. However, planning with low-fidelity models compromises safety, as the dynamic feasibility of resulting reference trajectories is not ensured. This potentially leads to unavoidable tracking errors that may cause safety-critical constraint violations. Existing frameworks mitigate this safety risk by augmenting safety-critical constraints in motion planning by a safety margin that prevents constraint violations under worst-case tracking errors. However, the methods employed in these frameworks determine the safety margin based on a heuristically selected performance of the planning model, which likely results in overly conservative reference trajectories. Furthermore, these methods are computationally intensive, and the state-of-the-art method is limited in numerical accuracy. We adopt a different perspective and address these limitations with a method that mitigates conservatism in existing frameworks by adapting the planning model performance to a given safety margin. Our method achieves numerical accuracy and requires significantly less computation time than existing methods by leveraging a captivity-escape game, which is a specific zero-sum differential game formulated in this paper. We demonstrate our method using a numerical example and compare it to the state of the art.