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

arXiv: https://arxiv.org/abs/2406.01848 · HTML: https://mlsanity.com/paper/2406.01848/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [CoFineLLM: Conformal Finetuning of LLMs for Language-Instructed Robot Planning](https://mlsanity.com/paper/2511.06575/) (2025)

## Abstract (arXiv)

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.