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

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 references 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 model used for planning, which likely results in overly conservative references. 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 performance of the model used for planning 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 novel 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.