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

2024-03-23

AI Summary

The theoretical relationship between Artificial Potential Field (APF) controllers and Reciprocal Control Barrier Function-based Quadratic Programming safety filters (RCBF-QP) remains unclear, limiting rigorous analysis of APF’s safety and stability guarantees. Method: We introduce Tightened Control Lyapunov Functions and Reciprocal Control Barrier Functions (T-CLF/T-RCBF) to formally characterize APF as a specific instance of RCBF-QP. This framework unifies attractive/repulsive potential fields and safety constraints within a single optimization-based control structure, eliminating reliance on ad hoc auxiliary functions inherent in classical APF design. Contribution/Results: We provide the first rigorous proof of mathematical equivalence between APF and RCBF-QP. The unified formulation enables joint synthesis of stability and safety, extends APF to general safety-critical scenarios beyond collision avoidance, and enhances robustness and theoretical soundness. Experimental validation confirms behavioral consistency between APF and RCBF-QP in obstacle avoidance tasks.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Intelligent Robots: Behavior Learning & Control
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Security and Privacy: Security and privacy of machine learning and AI applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Relate APF controllers to RCBF-QP safety filters
• Generalize APF-based controllers for broader scenarios
• Demonstrate equivalence via collision avoidance example

Innovation

• Integrates APFs within RCBF-QP framework
• Uses T-CLFs and T-RCBFs with auxiliary functions
• Generalizes APF-based controllers to broader scenarios