Handling shape variability in a class of multi-agent dynamical systems with a time-varying diffeomorphism

This paper presents a novel framework for the formation and trajectory tracking of multi-agent systems in time-varying tasks. The proposed approach leverages a time-varying diffeomorphism to simplify the control design, decoupling the complexity of reaching a desired trajectory from adhering to motion profiles along it. This framework ensures aggregation and stability in a virtual reference frame, which is then mapped to the real frame to achieve the desired dynamic behavior. The method is demonstrated on agents modeled as double integrators, showcasing its scalability and adaptability to various time-varying scenarios. Numerical results validate the effectiveness of the approach in achieving desired formations and adapting to evolving environments, while maintaining proper performance and predictable behavior. The proposed strategy offers a promising tool for dynamic applications such as surveillance, monitoring, and coordinated motion planning.