# Sampling-based Motion Planning via Control Barrier Functions

## TL;DR

This paper introduces CBF-RRT, a sampling-based motion planning algorithm that uses control barrier functions to efficiently generate obstacle-free paths for nonlinear systems in dynamic environments, reducing computational overhead.

## Contribution

The paper presents a novel CBF-guided RRT algorithm that integrates control barrier functions into sampling-based planning for nonlinear systems, enabling real-time obstacle avoidance without collision checks.

## Key findings

- Reduces run-time compared to standard RRT methods.
- Handles dynamic obstacles in continuous time.
- Enforces obstacle avoidance via quadratic programming.

## Abstract

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.