# SAFE--MA--RRT: Multi-Agent Motion Planning with Data-Driven Safety Certificates

arXiv: https://arxiv.org/abs/2509.04413 · HTML: https://mlsanity.com/paper/2509.04413/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [From noisy data to feedback controllers: non-conservative design via a matrix S-lemma](https://mlsanity.com/paper/2006.00870/) (2020)
- [Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets](https://mlsanity.com/paper/2002.01023/) (2020)
- [Controller design for robust invariance from noisy data](https://mlsanity.com/paper/2007.13181/) (2020)
- [Data-driven Safe Control of Linear Systems Under Epistemic and Aleatory Uncertainties](https://mlsanity.com/paper/2202.04495/) (2022)
- [Path Planning using Positive Invariant Sets](https://mlsanity.com/paper/1712.01184/) (2017)
- [Data-based guarantees of set invariance properties](https://mlsanity.com/paper/1911.12293/) (2019)
- [Data-Driven Motion Planning for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2508.00154/) (2025)

## Abstract (arXiv)

This paper proposes a fully data-driven motion-planning framework for homogeneous linear multi-agent systems that operate in shared, obstacle-filled workspaces without access to explicit system models. Each agent independently learns its closed-loop behavior from experimental data by solving convex semidefinite programs that generate locally invariant ellipsoids and corresponding state-feedback gains. These ellipsoids, centered along grid-based waypoints, certify the dynamic feasibility of short-range transitions and define safe regions of operation. A sampling-based planner constructs a tree of such waypoints, where transitions are allowed only when adjacent ellipsoids overlap, ensuring invariant-to-invariant transitions and continuous safety. All agents expand their trees simultaneously and are coordinated through a space-time reservation table that guarantees inter-agent safety by preventing simultaneous occupancy and head-on collisions. Each successful edge in the tree is equipped with its own local controller, enabling execution without re-solving optimization problems at runtime. The resulting trajectories are not only dynamically feasible but also provably safe with respect to both environmental constraints and inter-agent collisions. Simulation results demonstrate the effectiveness of the approach in synthesizing synchronized, safe trajectories for multiple agents under shared dynamics and constraints, using only data and convex optimization tools.