Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of the state-space, deal only with a convex fragment of temporal logic, or are not provably complete. We propose a scalable, provably complete algorithm that synthesizes continuous trajectories to satisfy non-convex \gls*{rtl} specifications. We separate discrete task planning and continuous motion planning on-the-fly and harness highly efficient boolean satisfiability (SAT) and \gls*{lp} solvers to find dynamically feasible trajectories that satisfy non-convex \gls*{rtl} specifications for high dimensional systems. The proposed design algorithms are proven sound and complete, and simulation results demonstrate our approach's scalability.

中文翻译：

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实时时序逻辑的自动轨迹合成

许多安全关键系统必须在保证安全性和正确性的情况下达到高级任务规范。通过从时序逻辑规范中合成控制器，最近朝着这个目标取得了很大进展。然而，现有方法仅限于相对较短和简单的规范。此外，现有方法要么考虑状态空间的一些先验离散化，要么仅处理时间逻辑的凸片段，要么无法证明是完整的。我们提出了一种可扩展的、可证明的完整算法，该算法合成连续轨迹以满足非凸 \gls*{rtl} 规范。我们在运行中分离离散任务规划和连续运动规划，并利用高效的布尔可满足性 (SAT) 和 \gls*{lp} 求解器来找到满足非凸 \gls*{rtl} 规范的动态可行轨迹维系统。所提出的设计算法被证明是合理和完整的，仿真结果证明了我们方法的可扩展性。