# Sampling-based Motion Planning via Control Barrier Functions

arXiv: https://arxiv.org/abs/1907.06722 · HTML: https://mlsanity.com/paper/1907.06722/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Efficient Motion Planning for Manipulators with Control Barrier Function-Induced Neural Controller](https://mlsanity.com/paper/2404.01184/) (2024)
- [Composable Model-Free RL for Navigation with Input-Affine Systems](https://mlsanity.com/paper/2602.12492/) (2026)

## Abstract (arXiv)

Robot motion planning is central to real-world autonomous applications, such as self-driving cars, persistence surveillance, and robotic arm manipulation. One challenge in motion planning is generating control signals for nonlinear systems that result in obstacle free paths through dynamic environments. In this paper, we propose Control Barrier Function guided Rapidly-exploring Random Trees (CBF-RRT), a sampling-based motion planning algorithm for continuous-time nonlinear systems in dynamic environments. The algorithm focuses on two objectives: efficiently generating feasible controls that steer the system toward a goal region, and handling environments with dynamical obstacles in continuous time. We formulate the control synthesis problem as a Quadratic Program (QP) that enforces Control Barrier Function (CBF) constraints to achieve obstacle avoidance. Additionally, CBF-RRT does not require nearest neighbor or collision checks when sampling, which greatly reduce the run-time overhead when compared to standard RRT variants.