Cooperative Control of Integrator Negative Imaginary Systems with Application to Rendezvous Multiple Mobile Robots

This paper contributes to the solution of mobile robots rendezvous problem via the negative imaginary (NI) systems theory. Cooperative control strategies are proposed for integrator NI systems. These control strategies are beneficial because they can be directly applied to wheeled mobile robots. First, we show that the NI property is preserved for multiple multi-input multi-output (MIMO) integrator systems with directional information flow that is balanced and strongly connected. Then, we derive conditions that guarantee output consensus and output tracking for strongly connected, balanced and directed networks of integrators subject to energy-bounded disturbances using the NI internal stability theorems. Finally, experimental and simulation results are provided to validate the effectiveness of the proposed NI cooperative tracking results to achieve rendezvous of multiple nonholonomic wheeled mobile robots.