Receding Horizon Control With Online Barrier Function Design Under Signal Temporal Logic Specifications

Signal temporal logic (STL) has been found to be an expressive language for describing complex, time-constrained tasks in several robotic applications. Existing methods encode such specifications by either using integer constraints or by employing set invariance techniques. While in the first case this results in a mixed integer linear program (MILP), control problems, in the latter case, designer-specific choices may induce conservatism in the robot's performance and the satisfaction of the task. In this article, a continuous-time receding horizon control scheme (RHS) is proposed that exploits the tradeoff between task satisfaction and performance costs such as actuation and state costs, traditionally considered in RHS schemes. The satisfaction of the STL tasks is encoded using time-varying control barrier functions that are designed online, thus avoiding the integer expressions that are often used in literature. The recursive feasibility of the proposed scheme is guaranteed by the satisfaction of a time-varying terminal constraint that ensures the satisfaction of the task with predetermined robustness. The effectiveness of the method is illustrated in a multirobot simulation scenario.