Adaptive total energy shaping of a class of manipulators

Point-to-point control of underactuated mechanical systems is a challenging problem, especially if some of the system's parameters are uncertain. A popular method to stabilize underactuated manipulators is total energy shaping, in which a new Hamiltonian function is assigned to the closed-loop system while a set of partial differential equations (PDEs) should be solved. In this study, an adaptive total energy shaping controller based on the approach called interconnection and damping assignment passivity-based control (IDA-PBC) for some underactuated robots is designed. The proposed method can overcome uncertainties in the dynamical parameters and also the parameters of the input mapping matrix under the satisfaction of the PDEs. The stability of the desired pose is ensured by the Lyapunov approach via suitable design of adaptation laws without the requirement for the persistence of excitation condition or other similar conditions. The results are applied to a 3-DOF underactuated manipulator and verified by simulations.