Captivity-Escape Games as a Means for Safety in Online Motion Generation
This addresses safety-critical constraint violations in online motion planning for robotics or autonomous systems, though it appears to be an incremental improvement over existing frameworks.
The paper tackles the problem of overly conservative, computationally intensive, and numerically inaccurate safety margins in online motion generation by proposing a method that adapts model performance to given safety margins using a novel captivity-escape game formulation, achieving improved numerical accuracy and significantly reduced computation time compared to state-of-the-art methods.
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.