# Temporal Logic Motion Planning with Convex Optimization via Graphs of Convex Sets

arXiv: https://arxiv.org/abs/2301.07773 · HTML: https://mlsanity.com/paper/2301.07773/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2023.

## Built on by (most cited first, 9 of 9)

- [LTLDoG: Satisfying Temporally-Extended Symbolic Constraints for Safe Diffusion-based Planning](https://mlsanity.com/paper/2405.04235/) (2024)
- [Simultaneous Task Allocation and Planning for Multi-Robots under Hierarchical Temporal Logic Specifications](https://mlsanity.com/paper/2401.04003/) (2024)
- [Space-Time Graphs of Convex Sets for Multi-Robot Motion Planning](https://mlsanity.com/paper/2503.00583/) (2025)
- [Integrating Disambiguation and User Preferences into Large Language Models for Robot Motion Planning](https://mlsanity.com/paper/2404.14547/) (2024)
- [Search-Based Spatiotemporal and Multi-Robot Motion Planning on Graphs of Space-Time Convex Sets](https://mlsanity.com/paper/2607.00444/) (2026)
- [Nl2Hltl2Plan: Scaling Up Natural Language Understanding for Multi-Robots Through Hierarchical Temporal Logic Task Representation](https://mlsanity.com/paper/2408.08188/) (2024)
- [LLM-Grounded Dynamic Task Planning with Hierarchical Temporal Logic for Human-Aware Multi-Robot Handover](https://mlsanity.com/paper/2602.09472/) (2026)
- [Unified Branch-and-Bound Search for the Steiner Traveling Salesman Problem on Graphs of Convex Sets](https://mlsanity.com/paper/2608.21319/) (2026)
- [LTLDiff: Finite Linear Temporal Logic-Guided Data Generation and Diffusion Policies for Multi-agent Robotic Manipulation](https://mlsanity.com/paper/2609.11043/) (2026)

## Abstract (arXiv)

Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics. In this paper, we cast Linear Temporal Logic (LTL) motion planning as a shortest path problem in a Graph of Convex Sets (GCS) and solve it with convex optimization. This approach brings together the best of modern optimization-based temporal logic planners and older automata-theoretic methods, addressing the limitations of each: we avoid clipping and passthrough by representing paths with continuous Bezier curves; computational complexity is polynomial (not exponential) in the number of sample points; global optimality can be certified (though it is not guaranteed); soundness and probabilistic completeness are guaranteed under mild assumptions; and most importantly, the method scales to complex specifications and high-dimensional systems, including a 30-DoF humanoid. Open-source code is available at https://github.com/vincekurtz/ltl_gcs.