# Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems

arXiv: https://arxiv.org/abs/2003.11500 · HTML: https://mlsanity.com/paper/2003.11500/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2020.

## Built on by (most cited first, 17 of 17)

- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [SafeVLA: Towards Safety Alignment of Vision-Language-Action Model via Constrained Learning](https://mlsanity.com/paper/2503.03480/) (2025)
- [Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.07695/) (2021)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Learning Robust Hybrid Control Barrier Functions for Uncertain Systems](https://mlsanity.com/paper/2101.06492/) (2021)
- [Temporal Logic Imitation: Learning Plan-Satisficing Motion Policies from Demonstrations](https://mlsanity.com/paper/2206.04632/) (2022)
- [Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance](https://mlsanity.com/paper/2307.03015/) (2023)
- [Learning Control Barrier Functions and their application in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2404.16879/) (2024)
- [Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control](https://mlsanity.com/paper/2502.03640/) (2025)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Estimating Control Barriers from Offline Data](https://mlsanity.com/paper/2503.10641/) (2025)
- [EKMP: Generalized Imitation Learning with Adaptation, Nonlinear Hard Constraints and Obstacle Avoidance](https://mlsanity.com/paper/2103.00452/) (2021)
- [Constrained Equation Learner Networks for Precision-Preserving Extrapolation of Robotic Skills](https://mlsanity.com/paper/2311.02475/) (2023)
- [Safe Human Robot Navigation in Warehouse Scenario](https://mlsanity.com/paper/2503.21141/) (2025)
- [A Robust Task-Level Control Architecture for Learned Dynamical Systems](https://mlsanity.com/paper/2511.09790/) (2025)
- [Safe Probabilistic Planning for Human-Robot Interaction using Conformal Risk Control](https://mlsanity.com/paper/2603.10392/) (2026)

## Abstract (arXiv)

Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work presents a novel approach to learn workspace constraints from human demonstrations and to generate motion trajectories for the robot that lie in the constrained workspace. Training data are incrementally clustered into different linear subspaces and used to fit a low dimensional representation of each subspace. By considering the learned constraint subspaces as zeroing barrier functions, we are able to design a control input that keeps the system trajectory within the learned bounds. This control input is effectively combined with the original system dynamics preserving eventual asymptotic properties of the unconstrained system. Simulations and experiments on a real robot show the effectiveness of the proposed approach.