Acceleration of Formation Control Based on Hessian Matrix of Artificial Potential Field

The formation control of multi-agent system has become a hotspot in recent years. One of the most commonly used methods is to use artificial potential field (APF) to generate the attractive and repulsive force to organize the agents into a low-energy and stable formation. In this paper, we regard the APF as the difference in the desired position, and introduce the derivative of the gradient of the APF with respect to time, which is simplified as the Hessian matrix of the APF, into the formation control from the perspective of trajectory tracking. The energy-based Lyapunov function is selected to prove the stability and collision avoidance ability of the proposed control law. Moreover, we show that the maneuverability of the multi-agent system is enormously improved with the additional Hessian matrix term.