We propose a novel symbolic control framework for enforcing temporal logic specifications in Euler-Lagrange systems that addresses the key limitations of traditional abstraction-based approaches. Unlike existing methods that require exact system models and provide guarantees only at discrete sampling instants, our approach relies only on bounds on system parameters and input constraints, and ensures correctness for the full continuous-time trajectory. The framework combines scalable abstraction of a simplified virtual system with a closed-form, model-free controller that guarantees trajectories satisfy the original specification while respecting input bounds and remaining robust to unknown but bounded disturbances. We provide feasibility conditions for the construction of confinement regions and analyze the trade-off between efficiency and conservatism. Case studies on pendulum dynamics, a two-link manipulator, and multi-agent systems, including hardware experiments, demonstrate that the proposed approach ensures both correctness and safety while significantly reducing computational time and memory requirements. These results highlight its scalability and practicality for real-world robotic systems where precise models are unavailable and continuous-time guarantees are essential.

翻译：本文提出一种新颖的符号控制框架，用于在欧拉-拉格朗日系统中强制执行时序逻辑规约，该框架解决了传统基于抽象方法的关键局限性。与需要精确系统模型且仅在离散采样时刻提供保证的现有方法不同，我们的方法仅依赖系统参数边界和输入约束，并确保完整连续时间轨迹的正确性。该框架将简化虚拟系统的可扩展抽象与封闭形式的无模型控制器相结合，该控制器在满足输入边界并对未知但有界扰动保持鲁棒性的同时，保证轨迹满足原始规约。我们给出了构建约束区域的可行性条件，并分析了效率与保守性之间的权衡。通过摆动力学、双连杆机械臂和多智能体系统的案例研究（包括硬件实验）表明，所提方法在显著降低计算时间和内存需求的同时，确保了正确性与安全性。这些结果凸显了该方法在精确模型不可用且连续时间保证至关重要的实际机器人系统中的可扩展性与实用性。