用时变凸集统一规划控制，确保机器人满足逻辑约束。
STL-GCS: A Planner-Controller Framework for Signal Temporal Logic via Graphs of Time-varying Convex Sets
- 将STL任务转为时变凸集，保证规划轨迹满足逻辑要求
- 结合B样条参数化，实现连续时间下的轨迹平滑与避障
- 实测验证在空间机械臂上有效应对执行误差
我们提出一种统一的轨迹规划与控制框架，用于满足基于凸谓词定义的信号时序逻辑（STL）规范。在规划层，将STL任务编码为配置空间中的时变凸集，设计使得系统对这些集合的前向不变性可保证在指定鲁棒性裕度下满足规范。该表示被提升至时空联合空间，并与凸集图（GCS）框架结合，形成在凸时空集合上的最短路径规划问题。轨迹采用B样条参数化，支持连续时间下对STL满足性、碰撞避免及平滑性的约束。在控制层，复用规划中使用的时变凸集设计反馈控制器，可在存在跟踪误差和模型失配的情况下优先保障执行中STL规范的满足。该方法在仿真及真实空间机器人平台上进行了验证。
原文摘要 · Abstract (English)
We present a unified trajectory planning and control framework for the satisfaction of Signal Temporal Logic (STL) specifications defined over convex predicates. At the planning layer, STL tasks are encoded as time-varying convex sets in configuration space, specifically designed so that forward invariance of the system with respect to these sets implies satisfaction of the specification with a prescribed robustness margin. This representation is then lifted to the joint time--configuration space and combined with the Graphs of Convex Sets (GCS) framework, yielding a shortest-path formulation of the planning problem over convex spatio-temporal sets. Trajectories are parameterized by B-splines, which enable continuous-time enforcement of STL satisfaction, collision avoidance, and smoothness constraints. At the control layer, the same time-varying sets used for planning are exploited to design a feedback controller that tracks the planned trajectory while prioritizing satisfaction of the STL specification during execution in the presence of tracking errors and model mismatch. We validate the proposed approach in simulation and in real-world experiments on space robotic platforms.
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