Optimal Control Synthesis with Relaxed Global Temporal Logic Specifications for Homogeneous Multi-robot Teams

TL;DR

This paper presents a novel control synthesis method for homogeneous robot teams that integrates automata-based and MILP-based techniques to handle global temporal logic specifications with user-defined relaxation preferences, improving efficiency and feasibility.

Contribution

It introduces a combined automata and MILP approach for control synthesis that accommodates relaxed specifications and reduces computational complexity.

Findings

Efficient control synthesis for multi-robot teams with relaxed specifications.

Automata-based relaxation automaton captures allowable mission relaxations.

MILP formulation avoids state-space explosion, enhancing scalability.

Abstract

In this work, we address the problem of control synthesis for a homogeneous team of robots given a global temporal logic specification and formal user preferences for relaxation in case of infeasibility. The relaxation preferences are represented as a Weighted Finite-state Edit System and are used to compute a relaxed specification automaton that captures all allowable relaxations of the mission specification and their costs. For synthesis, we introduce a Mixed Integer Linear Programming (MILP) formulation that combines the motion of the team of robots with the relaxed specification automaton. Our approach combines automata-based and MILP-based methods and leverages the strengths of both approaches while avoiding their shortcomings. Specifically, the relaxed specification automaton explicitly accounts for the progress towards satisfaction, and the MILP-based optimization approach avoids the state-space explosion associated with explicit product-automata construction, thereby efficiently solving the problem. The case studies highlight the efficiency of the proposed approach.