Koopman Operation-Based Leader-Following Formation Control for Nonholonomic Mobile Robots Under Denial-of-Service Attacks

Abstract

Under denial-of-service (DoS) attacks, achieving a desired formation of networked nonholonomic mobile robots (NMRs) over communication is a nontrivial challenge due to communication disconnecting and recovering at any time. Efforts have been made in prevention, detection, and resilience methods, but existing methods' generalization ability and interpretability still need improvement. This paper proposes the leader-following formation control framework for a group of NMRs under denial-of-service (DoS) attacks. The Koopman operator is utilized to express a linear lifted feature space for the discrete motion of networked NMRs. Based on an event-triggered mechanism, a data-driven loss function is presented to approximate the Koopman operator, enabling a long-term recovery capability under DoS attacks. Furthermore, according to the recovered motion of the leader, the leader-following formation controller with a variable gain is designed to ensure that the formation error converges to the neighborhoods of zero. In numerical simulation, the effectiveness of the proposed method is verified by a DoS attack example.