2-D Directed Formation Control Based on Bipolar Coordinates
This work addresses formation control for multi-agent systems, particularly in robotics, with practical applications using low-cost sensors, but it appears incremental as it builds on existing graph and control methods.
The paper tackled the problem of 2-D formation control for directed graphs by proposing a decentralized scheme based on bipolar coordinates, achieving almost global convergence to desired shapes and enabling simultaneous maneuvering, scaling, and orientation with robustness to disturbances.
This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach.