# Data-Driven Motion Planning for Uncertain Nonlinear Systems

arXiv: https://arxiv.org/abs/2508.00154 · HTML: https://mlsanity.com/paper/2508.00154/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 31 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Funnel Libraries for Real-Time Robust Feedback Motion Planning](https://mlsanity.com/paper/1601.04037/) (2016)
- [Low-complexity Learning of Linear Quadratic Regulators from Noisy Data](https://mlsanity.com/paper/2005.01082/) (2020)
- [Sampling-based Algorithms for Optimal Motion Planning Using Closed-loop Prediction](https://mlsanity.com/paper/1601.06326/) (2016)
- [Hybrid Systems Differential Dynamic Programming for Whole-Body Motion Planning of Legged Robots](https://mlsanity.com/paper/2006.08102/) (2020)
- [Controller design for robust invariance from noisy data](https://mlsanity.com/paper/2007.13181/) (2020)
- [Safe and Robust Motion Planning for Dynamic Robotics via Control Barrier Functions](https://mlsanity.com/paper/2011.06748/) (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)

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

- [SAFE--MA--RRT: Multi-Agent Motion Planning with Data-Driven Safety Certificates](https://mlsanity.com/paper/2509.04413/) (2025)

## Abstract (arXiv)

This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and solves data-driven linear-matrix-inequality problems to learn several ellipsoidal invariant sets together with their local state-feedback gains. The convex hull of these ellipsoids, still invariant under a piece-wise-affine controller obtained by interpolating the gains, is then approximated by a polytope. Safe transitions between nodes are ensured by verifying the intersection of consecutive convex-hull polytopes and introducing an intermediate node for a smooth transition. Control gains are interpolated in real time via simplex-based interpolation, keeping the state inside the invariant polytopes throughout the motion. Unlike traditional approaches that rely on system dynamics models, our method requires only data to compute safe regions and design state-feedback controllers. The approach is validated through simulations, demonstrating the effectiveness of the proposed method in achieving safe, dynamically feasible paths for complex nonlinear systems.