Formation Control With Size Scaling Via a Complex Laplacian-Based Approach.

Area of Science:

• Robotics
• Control Theory
• Networked Systems

Background:

• Coordinated control of multi-agent systems is crucial for tasks like formation flying and swarm robotics.
• Existing methods often struggle with dynamically scaling formations or require centralized control.

Purpose of the Study:

• To develop a distributed linear control strategy for mobile agents to achieve variable-sized formations.
• To enable leader agents to dictate formation size while followers adapt.
• To ensure velocity consensus among all agents within the formation.

Main Methods:

• A distributed linear control law is designed based on a leader-follower network architecture.
• The control strategy utilizes a complex-valued Laplacian to represent the desired formation shape.
• Velocity consensus is achieved via a separate communication network, independent of the sensing graph topology.

Main Results:

• Agents successfully converge to the desired formation shape, with size determined by two designated leaders.
• The control strategy ensures all agents move with a common velocity.
• The framework accommodates both single-integrator and double-integrator agent dynamics.

Conclusions:

• The proposed distributed control strategy effectively manages variable-sized formations in multi-agent systems.
• The method allows for decentralized control of formation shape and size.
• The approach is robust and applicable to different agent dynamics and network topologies.