Stabilization of a class of underactuated parallel robots via energy shaping: Application to cable driven manipulators

In this brief paper, potential energy shaping of underactuated parallel robots (UPRs) based on the method called interconnection and damping assignment passivity-based control (IDA-PBC) is presented. To this aim, to assign a new Hamiltonian to the closed-loop system, due to fewer actuators than degrees of freedom, a set of partial differential equations (PDEs) related to assigning a desired potential energy should be solved analytically, which are basically the stumbling block of IDA-PBC approach. Although in UPRs, the input mapping matrix is complex and configuration-dependent, a general solution for the potential energy PDE is derived such that it is independent of degrees of underactuation.