Multiple tasks control of nonlinear systems under signal temporal logic and its application to mobile robots

Abstract

This paper addresses the control problem of complex temporal logic tasks for nonlinear systems. A new control barrier function (CBF) called time‐varying extent‐compatible control barrier function (TV‐ECCBF) is proposed, which extends the traditional CBF by considering time‐varying extent or volumes. The main aim of TV‐ECCBF is to tackle the issue of avoiding obstacles in real‐world situations that have irregular or dynamically changing shapes, which cannot be efficiently resolved through traditional CBF methods. To encode complex task specifications, a control framework is presented based on signal temporal logic (STL). Additionally, we introduce robust semantics to discuss the satisfaction of target formulas. Moreover, the control framework generates controllers automatically based on different types of tasks, exhibiting global performance in achieving complex tasks. Finally, two examples of mobile robot systems are presented to demonstrate the effectiveness of the TV‐ECCBF and the proposed design framework.