Consensus tracking control and vibration suppression for nonlinear mobile flexible manipulator multi-agent systems based on PDE model

This paper evaluates the consensus tracking control of nonlinear multi-agent systems (MASs) described by partial differential equations (PDEs). Each agent of the MASs is a mobile flexible manipulator composed of a mobile carrier, a flexible manipulator, and an end load. By utilizing Hamilton’s principle, the characteristics of each agent are described by nonlinear fourth-order PDEs with the coupling of displacement, angle, and vibration. A consensus tracking control strategy is proposed for the MASs based on the obtained PDE model. Under the designed controller, both the angle of the flexible manipulator and the displacement of the mobile carrier of all agents can achieve consensus via mutual communication and track the desired positions and speeds. In addition, the elastic deformation and deformation speed of each agent’s flexible manipulator can be suppressed. The closed-loop system is proven asymptotically stable by constructing the Lyapunov function and applying the extended LaSalle’s invariance principle. A MAS example is numerically simulated to verify the effectiveness of the proposed control strategy.