Signal Temporal Logic (STL) is a formal language over continuous-time signals (such as trajectories of a multi-agent system) that allows for the specification of complex spatial and temporal system requirements (such as staying sufficiently close to each other within certain time intervals). To promote robustness in multi-agent motion planning with such complex requirements, we consider motion planning with the goal of maximizing the temporal robustness of their joint STL specification, i.e. maximizing the permissible time shifts of each agent's trajectory while still satisfying the STL specification. Previous methods presented temporally robust motion planning and control in a discrete-time Mixed Integer Linear Programming (MILP) optimization scheme. In contrast, we parameterize the trajectory by continuous B\'ezier curves, where the curvature and the time-traversal of the trajectory are parameterized individually. We show an algorithm generating continuous-time temporally robust trajectories and prove soundness of our approach. Moreover, we empirically show that our parametrization realizes this with a considerable speed-up compared to state-of-the-art methods based on constant interval time discretization.

翻译：信号时序逻辑（STL）是一种基于连续时间信号（如多智能体系统的轨迹）的形式化语言，能够对复杂的时空系统需求（例如在特定时间区间内保持彼此足够接近）进行规范描述。为提升具有此类复杂需求的多智能体运动规划鲁棒性，我们以最大化联合STL规范的时间鲁棒性为目标开展运动规划研究，即在满足STL规范的前提下，最大化每个智能体轨迹的可容许时间偏移量。现有方法在离散时间混合整数线性规划（MILP）优化框架中实现了时间鲁棒性运动规划与控制。与此不同，我们采用连续贝塞尔曲线对轨迹进行参数化，其中曲率与轨迹的时间遍历特性被分别参数化。本文提出了一种生成连续时间鲁棒轨迹的算法，并证明了该方法的正确性。此外，实验表明，与基于恒定时间间隔离散化的现有主流方法相比，本文参数化方法能够实现显著的加速效果。