# A Comparative Study of Artificial Potential Fields and Reciprocal Control Barrier Function-based Safety Filters

arXiv: https://arxiv.org/abs/2403.15743 · HTML: https://mlsanity.com/paper/2403.15743/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 23 Mar 2024.

## Builds on (most cited first, 6 of 6)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Comparative Analysis of Control Barrier Functions and Artificial Potential Fields for Obstacle Avoidance](https://mlsanity.com/paper/2010.09819/) (2020)
- [Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models](https://mlsanity.com/paper/2403.09865/) (2024)
- [Multi-agent systems with CBF-based controllers -- collision avoidance and liveness from instability](https://mlsanity.com/paper/2207.04915/) (2022)
- [A Tunable Universal Formula for Safety-Critical Control](https://mlsanity.com/paper/2403.06285/) (2024)

## Abstract (arXiv)

In this paper, we demonstrate that controllers designed by artificial potential fields (APFs) can be derived from reciprocal control barrier function quadratic program (RCBF-QP) safety filters. By integrating APFs within the RCBF-QP framework, we explicitly establish the relationship between these two approaches. Specifically, we first introduce the concepts of tightened control Lyapunov functions (T-CLFs) and tightened reciprocal control barrier functions (T-RCBFs), each of which incorporates a flexible auxiliary function. We then utilize an attractive potential field as a T-CLF to guide the nominal controller design, and a repulsive potential field as a T-RCBF to formulate an RCBF-QP safety filter. With appropriately chosen auxiliary functions, we show that controllers designed by APFs and those derived by RCBF-QP safety filters are equivalent. Based on this insight, we further generalize the APF-based controllers (equivalently, RCBF-QP safety filter-based controllers) to more general scenarios without restricting the choice of auxiliary functions. Finally, we present a collision avoidance example to clearly illustrate the connection and equivalence between the two methods.