Formation-Containment Control of Euler-Lagrange Systems of Leaders With Bounded Unknown Inputs

Area of Science:

• Robotics and Control Systems
• Applied Mathematics
• Mechanical Engineering

Background:

• Multiple Euler-Lagrange (EL) systems are crucial for complex robotic applications.
• Formation-containment (FC) control is essential for coordinated multi-agent systems, especially for obstacle avoidance.
• Existing methods often struggle with unknown leader inputs and distributed communication constraints.

Purpose of the Study:

• To address the formation-containment (FC) control problem for multiple Euler-Lagrange (EL) systems.
• To develop a distributed control strategy that accommodates bounded unknown control inputs from leader systems.
• To enable cooperative generation of safe trajectories for obstacle avoidance.

Main Methods:

• An algorithm to determine the stress matrix based on desired formation shapes.
• A novel adaptive distributed observer for estimating the convex hull of leader systems.
• A continuous function to mitigate the impact of unknown leader inputs.
• A local control law utilizing the adaptive observer for FC control.

Main Results:

• A fully distributed adaptive observer was developed, eliminating the need for global graph information.
• The observer effectively estimates the convex hull of leader systems.
• The proposed control law ensures that formation-containment errors can be minimized.
• Lyapunov stability theory confirmed the effectiveness of the observer and control law.

Conclusions:

• The proposed adaptive distributed observer and control law effectively achieve formation-containment for multiple EL systems.
• The approach successfully handles bounded unknown control inputs and directed communication topologies.
• This work contributes to safer and more efficient multi-agent coordination in complex environments.