# Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments

arXiv: https://arxiv.org/abs/2508.03428 · HTML: https://mlsanity.com/paper/2508.03428/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 18 of 18)

- [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)
- [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020)
- [Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraints](https://mlsanity.com/paper/1410.6445/) (2014)
- [Review of Pedestrian Trajectory Prediction Methods: Comparing Deep Learning and Knowledge-based Approaches](https://mlsanity.com/paper/2111.06740/) (2021)
- [Optimization-Based Collision Avoidance](https://mlsanity.com/paper/1711.03449/) (2017)
- [Statistical Guarantees for Regularized Neural Networks](https://mlsanity.com/paper/2006.00294/) (2020)
- [Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systems](https://mlsanity.com/paper/1611.00122/) (2016)
- [Online Update of Safety Assurances Using Confidence-Based Predictions](https://mlsanity.com/paper/2210.01199/) (2022)
- [SICNav: Safe and Interactive Crowd Navigation using Model Predictive Control and Bilevel Optimization](https://mlsanity.com/paper/2310.10982/) (2023)
- [Learning Interaction-Aware Trajectory Predictions for Decentralized Multi-Robot Motion Planning in Dynamic Environments](https://mlsanity.com/paper/2102.05382/) (2021)
- [Parameter-Conditioned Reachable Sets for Updating Safety Assurances Online](https://mlsanity.com/paper/2209.14976/) (2022)
- [SICNav-Diffusion: Safe and Interactive Crowd Navigation with Diffusion Trajectory Predictions](https://mlsanity.com/paper/2503.08858/) (2025)
- [Reachability-Based Safety Guarantees using Efficient Initializations](https://mlsanity.com/paper/1903.07715/) (2019)
- [CIAO^star: MPC-based Safe Motion Planning in Predictable Dynamic Environments](https://mlsanity.com/paper/2001.05449/) (2020)
- [Trajectory Generation by Chance Constrained Nonlinear MPC with Probabilistic Prediction](https://mlsanity.com/paper/2006.07907/) (2020)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Parameterized Fast and Safe Tracking (FaSTrack) using Deepreach](https://mlsanity.com/paper/2404.07431/) (2024)

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

- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)
- [CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2603.06921/) (2026)
- [VertexCBF: Improving Neural Control Barrier Functions via Vertex-Restricted Control Search](https://mlsanity.com/paper/2609.12831/) (2026)

## Abstract (arXiv)

In this paper, we propose a hybrid MPC local planner that uses a learning-based approximation of a time-varying safe set, derived from local observations and applied as the MPC terminal constraint. This set can be represented as a zero-superlevel set of the value function computed via Hamilton-Jacobi (HJ) reachability analysis, which is infeasible in real-time. We exploit the property that the HJ value function can be expressed as a difference of the corresponding signed distance function (SDF) and a non-negative residual function. The residual component is modeled as a neural network with non-negative output and subtracted from the computed SDF, resulting in a real-time value function estimate that is at least as safe as the SDF by design. Additionally, we parametrize the neural residual by a hypernetwork to improve real-time performance and generalization properties. The proposed method is compared with three state-of-the-art methods in simulations and hardware experiments, achieving up to 30% higher success rates compared to the best baseline while requiring a similar computational effort and producing high-quality (low travel-time) solutions.