A Comparative Study of Artificial Potential Fields and Reciprocal Control Barrier Function-based Safety Filters
This work provides a theoretical link between two control methods for safety-critical systems, but it is incremental as it primarily establishes equivalence rather than introducing new capabilities.
The paper tackles the problem of relating artificial potential fields (APFs) and reciprocal control barrier function (RCBF) safety filters in control design, showing that APF-based controllers can be derived from RCBF-QP safety filters and are equivalent under certain conditions, with a collision avoidance example used to illustrate this connection.
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.