# An Abstraction-Free Method for Multi-Robot Temporal Logic Optimal Control Synthesis

arXiv: https://arxiv.org/abs/1909.00526 · HTML: https://mlsanity.com/paper/1909.00526/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2019.

## Built on by (most cited first, 11 of 11)

- [Conformal Temporal Logic Planning using Large Language Models](https://mlsanity.com/paper/2309.10092/) (2023)
- [Overcoming Exploration: Deep Reinforcement Learning for Continuous Control in Cluttered Environments from Temporal Logic Specifications](https://mlsanity.com/paper/2201.12231/) (2022)
- [ConformalNL2LTL: Translating Natural Language Instructions into Temporal Logic Formulas with Conformal Correctness Guarantees](https://mlsanity.com/paper/2504.21022/) (2025)
- [Learning Minimally-Violating Continuous Control for Infeasible Linear Temporal Logic Specifications](https://mlsanity.com/paper/2210.01162/) (2022)
- [Decomposition-based Hierarchical Task Allocation and Planning for Multi-Robots under Hierarchical Temporal Logic Specifications](https://mlsanity.com/paper/2308.10393/) (2023)
- [Simultaneous Task Allocation and Planning for Multi-Robots under Hierarchical Temporal Logic Specifications](https://mlsanity.com/paper/2401.04003/) (2024)
- [Safety-Critical Learning of Robot Control with Temporal Logic Specifications](https://mlsanity.com/paper/2109.02791/) (2021)
- [CatlNet: Learning Communication and Coordination Policies from CaTL+ Specifications](https://mlsanity.com/paper/2212.11792/) (2022)
- [Nl2Hltl2Plan: Scaling Up Natural Language Understanding for Multi-Robots Through Hierarchical Temporal Logic Task Representation](https://mlsanity.com/paper/2408.08188/) (2024)
- [RRT*former: Environment-Aware Sampling-Based Motion Planning using Transformer](https://mlsanity.com/paper/2511.15414/) (2025)
- [Legislating World-Model-Based Planning with Legal Reasoning](https://mlsanity.com/paper/2609.15113/) (2026)

## Abstract (arXiv)

The majority of existing Linear Temporal Logic (LTL) planning methods rely on the construction of a discrete product automaton, that combines a discrete abstraction of robot mobility and a Bddotuchi automaton that captures the LTL specification. Representing this product automaton as a graph and using graph search techniques, optimal plans that satisfy the LTL task can be synthesized. However, constructing expressive discrete abstractions makes the synthesis problem computationally intractable. In this paper, we propose a new sampling-based LTL planning algorithm that does not require any discrete abstraction of robot mobility. Instead, it incrementally builds trees that explore the product state-space, until a maximum number of iterations is reached or a feasible plan is found. The use of trees makes data storage and graph search tractable, which significantly increases the scalability of our algorithm. To accelerate the construction of feasible plans, we introduce bias in the sampling process which is guided by transitions in the Bddotuchi automaton that belong to the shortest path to the accepting states. We show that our planning algorithm, with and without bias, is probabilistically complete and asymptotically optimal. Finally, we present numerical experiments showing that our method outperforms relevant temporal logic planning methods.