# Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments

arXiv: https://arxiv.org/abs/2410.20267 · HTML: https://mlsanity.com/paper/2410.20267/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 26 Oct 2024.

## Builds on (most cited first, 21 of 21)

- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach](https://mlsanity.com/paper/2003.04950/) (2020)
- [Optimization-Based Collision Avoidance](https://mlsanity.com/paper/1711.03449/) (2017)
- [Learning Barrier Functions with Memory for Robust Safe Navigation](https://mlsanity.com/paper/2011.01899/) (2020)
- [Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systems](https://mlsanity.com/paper/1611.00122/) (2016)
- [An Efficient Reachability-Based Framework for Provably Safe Autonomous Navigation in Unknown Environments](https://mlsanity.com/paper/1905.00532/) (2019)
- [Online Update of Safety Assurances Using Confidence-Based Predictions](https://mlsanity.com/paper/2210.01199/) (2022)
- [Parameter-Conditioned Reachable Sets for Updating Safety Assurances Online](https://mlsanity.com/paper/2209.14976/) (2022)
- [Generating Formal Safety Assurances for High-Dimensional Reachability](https://mlsanity.com/paper/2209.12336/) (2022)
- [Reachability-Based Safety Guarantees using Efficient Initializations](https://mlsanity.com/paper/1903.07715/) (2019)
- [Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions](https://mlsanity.com/paper/2109.12313/) (2021)
- [N-MPC for Deep Neural Network-Based Collision Avoidance exploiting Depth Images](https://mlsanity.com/paper/2402.13038/) (2024)
- [Fast, Smooth, and Safe: Implicit Control Barrier Functions through Reach-Avoid Differential Dynamic Programming](https://mlsanity.com/paper/2307.00193/) (2023)
- [NMPC-LBF: Nonlinear MPC with Learned Barrier Function for Decentralized Safe Navigation of Multiple Robots in Unknown Environments](https://mlsanity.com/paper/2208.07974/) (2022)
- [Parameterized Fast and Safe Tracking (FaSTrack) using Deepreach](https://mlsanity.com/paper/2404.07431/) (2024)

## Built on by (most cited first, 3 of 3)

- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments](https://mlsanity.com/paper/2508.03428/) (2025)
- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)

## Abstract (arXiv)

This paper presents a novel learning-based approach for online estimation of maximal safe sets for local trajectory planning in unknown static environments. The neural representation of a set is used as the terminal set constraint for a model predictive control (MPC) local planner, resulting in improved recursive feasibility and safety. To achieve real-time performance and desired generalization properties, we employ the idea of hypernetworks. We use the Hamilton-Jacobi (HJ) reachability analysis as the source of supervision during the training process, allowing us to consider general nonlinear dynamics and arbitrary constraints. The proposed method is extensively evaluated against relevant baselines in simulations for different environments and robot dynamics. The results show an increase in success rate of up to 52% compared to the best baseline while maintaining comparable execution speed. Additionally, we deploy our proposed method, NTC-MPC, on a physical robot and demonstrate its ability to safely avoid obstacles in scenarios where the baselines fail.