Energy-based swing-up control for a two-link underactuated robot with flexible first joint

This paper concerns the swing-up control of a two-link robot moving in vertical plane, which has single actuator at second joint and linear torsional spring first joint. First, we present necessary sufficient condition such that is linearly controllable upright equilibrium point (UEP, where two links are both upright). Second, prove without any assumption an provided its actuated angle constant under torque. Third, for with stiffness being not greater than value determined by coefficients gravitational terms, propose energy-based controller singular points. We conduct global motion analysis proposed controller. For case total mechanical energy converges to desired value, phase portrait closed-loop solution. convergence achieved, show solution approaches belonging set points, give check instability. From analysis, can be swung-up close UEP Finally, verify our theoretical results through numerical simulation.