Boundary Stabilization of Underground Multirobot System with Virtual String Constraints

Abstract

The manipulation of multiple physical connected objects can be described by virtual connected string system. We proposed a Lyapunov-based stabilization control approach for virtual connected string with midway discontinue vertical force. The system is with Riemannian boundary. We use the backstepping method to transform the system into a stable system with Dirichlet boundary. In this way, we get the controller to make sure the closed-loop system converge to the zero point exponentially. Then, we construct a Lyapunov function to analyze the stability for the closed-loop system. We also show the system is well-posedness. Also, we use the active disturbance rejection control (ADRC) to reject the disturbance when disturbance is present. Some numerical stimulations show that the control law is the effective.