提出精确平滑的轨迹优化方法，实现时序逻辑约束下的高效运动规划。
Exact Smooth Reformulations for Trajectory Optimization Under Signal Temporal Logic Specifications
- 通过精确重构max/min运算符，实现无近似误差的可微优化
- 在仿真中验证了方法的准确性和实际性能表现
- 适合需要严格满足时空逻辑约束的机器人路径规划场景
我们研究基于信号时序逻辑（STL）的运动规划，该形式化语言可用于描述空间-时间需求。将STL合成问题建模为利用STL鲁棒性语义的轨迹优化问题。为获得无近似误差的可微问题，引入对max和min算子的精确重表述。所提方法具有精确性、平滑性与正确性。通过数值仿真验证其有效性，展示了良好的实际性能。
原文摘要 · Abstract (English)
We study motion planning under Signal Temporal Logic (STL), a useful formalism for specifying spatial-temporal requirements. We pose STL synthesis as a trajectory optimization problem leveraging the STL robustness semantics. To obtain a differentiable problem without approximation error, we introduce an exact reformulation of the max and min operators. The resulting method is exact, smooth, and sound. We validate it in numerical simulations, demonstrating its practical performance.
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