A coupled relationship between control toques is constructed for an underactuated four-link gymnast robot (UFGR). It changes the nonlinear UFGR system into a cascade-connected system.
We transform the stabilization of the UFGR into that of an underactuated two-link acrobot.
An energy-based stabilizing controller is designed for the two-link acrobot.
The structure of the proposed control system is simple. And our proposed strategy is easy to extend to the stabilization control of n-DOF class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0020746215001651&_mathId=si0069.gif&_user=111111111&_pii=S0020746215001651&_rdoc=1&_issn=00207462&md5=022fb4209dbb3692f0a47db31940701c" title="Click to view the MathML source">(n>4)class="mathContainer hidden">class="mathCode"> underactuated manipulator.