In this paper, we propose a framework for the control of mobile robots subject to temporal logic specifications using barrier functions. Complex task specifications can be conveniently encoded using linear temporal logic (LTL). In particular, we consider a fragment of LTL which encompasses a large class of motion planning specifications for a robotic system. Control barrier functions (CBFs) have recently emerged as a convenient tool to guarantee reachability and safety for a system. In addition, they can be encoded as affine constraints in a quadratic program (QP). In the case of complex system specifications, we show that following QP based methods in existing literature can lead to infeasibility and hence we provide a method of composition of multiple barrier functions in order to mitigate infeasibility. A scheme to prioritize different barrier functions which allows the user to encode the notion of priority based control, is also introduced. We prove that the resulting system trajectory synthesized by the proposed controller satisfies the given specification. Robotic simulation and experimental results are provided in addition to the theoretical framework.

中文翻译：

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在时序逻辑规范下使用障碍函数控制移动机器人

在本文中，我们提出了一个使用屏障函数控制受时间逻辑规范约束的移动机器人的框架。复杂的任务规范可以使用线性时序逻辑 (LTL) 方便地进行编码。特别是，我们考虑了 LTL 的一个片段，它包含了机器人系统的一大类运动规划规范。控制屏障功能 (CBF) 最近已成为保证系统可达性和安全性的便捷工具。此外，它们可以被编码为二次规划 (QP) 中的仿射约束。在复杂系统规范的情况下，我们表明遵循现有文献中基于 QP 的方法会导致不可行，因此我们提供了一种组合多个屏障函数的方法以减轻不可行。还介绍了一种优先考虑不同屏障功能的方案，该方案允许用户对基于优先级的控制概念进行编码。我们证明了由所提出的控制器合成的最终系统轨迹满足给定的规范。除了理论框架外，还提供了机器人模拟和实验结果。