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

2025-06-02

AI Summary

Existing online motion planning methods rely on low-fidelity dynamical models, leading to overly conservative safety margins, high computational overhead, and insufficient numerical precision—thus failing to strictly guarantee dynamic feasibility and safety constraints. This paper proposes the first safety-aware motion generation framework grounded in a captivity-escape differential game, wherein safety margins are treated as tunable inputs that inversely adapt the planner’s model fidelity to balance safety and agility. By formulating the problem as a zero-sum differential game, robustifying safety constraints, and jointly analyzing planning–tracking error coupling, the method significantly reduces computation time while improving numerical accuracy. Experiments demonstrate that, while ensuring trajectory dynamic feasibility, the proposed approach substantially enhances both safety assurance and real-time performance over state-of-the-art methods.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Intelligent Robots: Motion and Path Planning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Reduces conservatism in online motion planning safety margins
• Improves computational efficiency of safety-critical motion generation
• Enhances numerical accuracy in dynamic feasibility tracking

Innovation

• Adapts planning model to safety margin
• Uses captivity-escape game for efficiency
• Improves numerical accuracy and speed