# Continuous Reachability Task Transition Using Control Barrier Functions

arXiv: https://arxiv.org/abs/2005.12407 · HTML: https://mlsanity.com/paper/2005.12407/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2020.

## Built on by (most cited first, 1 of 1)

- [Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers](https://mlsanity.com/paper/2504.08249/) (2025)

## Abstract (arXiv)

In this paper, a method to achieve smooth transitions between sequential reachability tasks for a continuous time mobile robotic system is presented. Control barrier functions provide formal guarantees of forward invariance of safe sets and finite-time reachability and are able to enforce task execution. Barrier functions used in quadratic programs result in implementation of controllers with real-time performance guarantees. Existing approaches for multi-objective task execution using control barrier functions leverage discretely switched, sequential quadratic programs to achieve successive tasks. However, discrete switching can lead to control input discontinuities which can affect a robot's performance. Hence, we propose a method which ensures continuous transitions between sequential quadratic programs. In particular, a time varying component to the barrier function constraint is introduced which allows for a smooth transition between objectives. Robotic implementation results are also provided.