Funnel formation control for multi-agent systems and its application to satellite formation flight

• Applicant: Professor Dr. Thomas Berger
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics ; Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 524064985

The objective of the proposed research project is the development, numerical implementation and analysis of the novel decentralized control concept Funnel Formation Control (FFC) for multi-agent systems. This method is able to guarantee the evolution of the inter-agent distances within a prescribed range. Additionally, it achieves collision avoidance and velocity synchronization with prescribed performance in the context of so-called “flocking”. As a particular challenge, we consider heterogeneous agents with nonlinear dynamics. Furthermore, the dynamics and initial states of the agents are not assumed to be known, apart from some structural information such as the order of the underlying differential equation. To realize these ambitious goals we utilize methods from funnel control, which is a current research area in control engineering and mathematical systems theory, and it successfully balances theory and application. The funnel controller is able to guarantee the evolution of the output variables within a prespecified margin. This allows for a controller design independent of the specific system parameters, which therefore exhibits inherent robustness properties. The desired control strategy consists of three components: 1.) In the first formation control part the desired position of each agent in the formation is constructed geometrically and used as a reference signal in a recent funnel control method. The FFC constructed in this way achieves that each agent attains its desired position with prescribed performance. Additionally, an input filter is used to avoid the measurements of velocities. 2.) In a second step the FFC is expanded by an additional controller component, which achieves collision avoidance. This component is again based on funnel control techniques. For this combination, feasibility and robustness are to be proved rigorously. 3.) In the last step the collision-avoiding FFC is combined with a so-called edge-wise funnel coupling law, which achieves synchronization of the velocities of the agents with prescribed performance. In this way it is expected to achieve the ultimate objective of flocking with prescribed behavior of the agents. As a proof of concept, the application to satellite formation flight is considered, where each satellite is described by a nonlinear differential equation of second order. In the course of this, the performance and implementability of the developed control methods is to be constantly verified by means of simulation studies. This supports the selection of suitable controller design parameters and thus ensures a continuous feedback between theory and numerical practice.

• DFG Programme: Research Grants