Enhancing Collision-Free Formation Control in Multiagent Systems: An Approach Based on Time-Derivative of Artificial Potential Functions

The artificial potential function (APF) is a widely applied algorithm in collision-free formation control in multiagent systems (MASs). However, it suffers from oscillations and acceleration surges, particularly when the current formation and the desired one conflict. To address this problem and enhance collision-free formation control in MAS, this article introduces the time-derivative of APFs. This approach unifies attractive and repulsive APFs. The gradients of the APFs transform potential and kinetic energy, and the time-derivative of the APF gradients serve as damping terms to dissipate energy. This article discusses the general properties of APFs and introduces a time-variant formation tracking scheme that encompasses existing algorithms as specific instances. Then, a collision-free formation control algorithm is presented. This article gives proof of its Lyapunov stability and collision avoidance ability, followed by a maneuverability analysis from the geometry perspective. By incorporating the time-derivatives of repulsive APF gradients as damping terms, the proposed method mitigates oscillations and acceleration surges caused by conflicting attractive and repulsive effects.