An energy-based position control and asymptotic stability analysis for manipulator handling a flexible payload

In this paper, an exact dynamic model of manipulator handling a flexible payload is derived by Hamiton´s principle. On the basis of the distributed parameter model, a position controller is designed by using Lyapunov function related to the total energy of the system. The controller can achieve the given desired link angles and suppress the vibrations of flexible payload. Using the LaSalle´s invariance principle and the characteristic of the differential operator, the asymptotic stability in the neighbor-hood of the desired states of the closed-loop system is proved. The effectiveness of the control strategy proposed is supported by some simulations.