# Control of Mobile Robots Using Barrier Functions Under Temporal Logic Specifications

## TL;DR

This paper introduces a fully automatic control framework for mobile robots that translates temporal logic specifications into barrier function-based quadratic programs, ensuring safe and feasible task execution.

## Contribution

It presents a novel method to encode temporal logic specifications into barrier function-based quadratic programs with strategies to handle infeasibility.

## Key findings

- Successfully synthesized robot trajectories satisfying temporal logic specifications.
- Demonstrated the approach's effectiveness through simulations and real experiments.
- Proposed methods improve control feasibility under complex task constraints.

## Abstract

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. In particular, we consider a fragment of linear temporal logic which encompasses a large class of motion planning specifications for a robotic system. Control barrier functions 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. In this paper, a fully automatic framework which translates a user defined specification in temporal logic to a sequence of barrier function based quadratic programs is presented. In addition, with the aim of alleviating infeasibility scenarios, we propose methods for composition of barrier functions as well as a prioritization based control method to guarantee feasibility of the controller. 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.