Many modern autonomous systems, particularly multi-agent systems, are time-critical and need to be robust against timing uncertainties. Previous works have studied left and right time robustness of signal temporal logic specifications by considering time shifts in the predicates that are either only to the left or only to the right. We propose a combined notion of temporal robustness which simultaneously considers left and right time shifts. For instance, in a scenario where a robot plans a trajectory around a pedestrian, this combined notion can now capture uncertainty of the pedestrian arriving earlier or later than anticipated. We first derive desirable properties of this new notion with respect to left and right time shifts and then design control laws for linear systems that maximize temporal robustness using mixed-integer linear programming. Finally, we present two case studies to illustrate how the proposed temporal robustness accounts for timing uncertainties.

翻译：许多现代自主系统，特别是多智能体系统，具有时间敏感性且需应对时序不确定性。已有研究通过仅考虑谓词向左或向右的时间偏移，探讨了信号时序逻辑规范的左右时间鲁棒性。本文提出一种联合的时间鲁棒性概念，可同时考虑左右时间偏移。例如在机器人规划绕行行人的轨迹场景中，该联合概念能捕捉行人比预期提前或延迟到达的不确定性。我们首先推导了这一新概念相对于左右时间偏移的优良性质，随后利用混合整数线性规划设计了可最大化时间鲁棒性的线性系统控制律。最后通过两个案例研究，展示了所提时间鲁棒性如何应对时序不确定性。