Receding horizon robot control in partially unknown environments with temporal logic constraints

Abstract

This paper addresses the control of a mobile robot that has to accomplish a finite task in a partially unknown static environment in minimum time. The task is expressed as a syntactically co-safe Linear Temporal Logic (scLTL) formula over a set of properties that can be satisfied at the regions of a partitioned environment. The robot discovers a-priori unknown properties upon covering the corresponding region by its limited sensing range. Instead of resorting to an abstraction of the hybrid system modeling the robot's motion in the environment, we propose an approach based on parameterizing the continuous motion of the vehicle and introduce a measure of violation that is used to enforce the satisfaction of the specification. Then, we formulate a parametric Optimal Control Problem (OCP), where the objective is a convex combination of the overall time and the measure of violation function. The OCP is solved in a receding horizon manner only upon detecting previously unknown properties of the environment. The approach is illustrated with a numerical case study.