# Funnel Libraries for Real-Time Robust Feedback Motion Planning

arXiv: https://arxiv.org/abs/1601.04037 · HTML: https://mlsanity.com/paper/1601.04037/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2016.

## Built on by (most cited first, 29 of 29)

- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)
- [Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Prediction](https://mlsanity.com/paper/2312.08604/) (2023)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates](https://mlsanity.com/paper/2405.14058/) (2024)
- [CIMRL: Combining IMitation and Reinforcement Learning for Safe Autonomous Driving](https://mlsanity.com/paper/2406.08878/) (2024)
- [Neural Koopman Lyapunov Control](https://mlsanity.com/paper/2201.05098/) (2022)
- [Generating Formal Safety Assurances for High-Dimensional Reachability](https://mlsanity.com/paper/2209.12336/) (2022)
- [Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty](https://mlsanity.com/paper/2210.05989/) (2022)
- [Robotic Table Wiping via Reinforcement Learning and Whole-body Trajectory Optimization](https://mlsanity.com/paper/2210.10865/) (2022)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [ForceSight: Text-Guided Mobile Manipulation with Visual-Force Goals](https://mlsanity.com/paper/2309.12312/) (2023)
- [Robust Imitation of a Few Demonstrations with a Backwards Model](https://mlsanity.com/paper/2210.09337/) (2022)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Towards Disturbance-Free Visual Mobile Manipulation](https://mlsanity.com/paper/2112.12612/) (2021)
- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)
- [Learning to Efficiently Plan Robust Frictional Multi-Object Grasps](https://mlsanity.com/paper/2210.07420/) (2022)
- [A Mathematical Characterization of Minimally Sufficient Robot Brains](https://mlsanity.com/paper/2308.09041/) (2023)
- [Learning Contraction Policies from Offline Data](https://mlsanity.com/paper/2112.05911/) (2021)
- [Federated reinforcement learning for robot motion planning with zero-shot generalization](https://mlsanity.com/paper/2403.13245/) (2024)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)
- [Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers](https://mlsanity.com/paper/2605.25346/) (2026)
- [Learning Provably Robust Motion Planners Using Funnel Libraries](https://mlsanity.com/paper/2111.08733/) (2021)
- [An introduction to optimization under uncertainty -- A short survey](https://mlsanity.com/paper/2212.00862/) (2022)
- [Data-Driven Motion Planning for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2508.00154/) (2025)
- [From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs](https://mlsanity.com/paper/2607.19306/) (2026)
- [Efficient Dynamic Shielding for Parametric Safety Specifications](https://mlsanity.com/paper/2505.22104/) (2025)
- [RENEW: Risk- and Energy-Aware Navigation in Dynamic Waterways](https://mlsanity.com/paper/2601.16424/) (2026)
- [GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics](https://mlsanity.com/paper/2607.01203/) (2026)
- [RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments](https://mlsanity.com/paper/2609.39854/) (2026)

## Abstract (arXiv)

We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we consider scenarios where these plans must be generated in real-time, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our approach is to pre-compute a library of "funnels" along different maneuvers of the system that the state is guaranteed to remain within (despite bounded disturbances) when the feedback controller corresponding to the maneuver is executed. We leverage powerful computational machinery from convex optimization (sums-of-squares programming in particular) to compute these funnels. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate and validate our method using extensive hardware experiments on a small fixed-wing airplane avoiding obstacles at high speed (~12 mph), along with thorough simulation experiments of ground vehicle and quadrotor models navigating through cluttered environments. To our knowledge, these demonstrations constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in real-time in environments with complex geometric constraints.