Development of New Nonlinear Control Theory for Underactuated Mechanical Systems with Its Application to Robot Control

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This research concerns a swing-up control problem for an n-link revolute planar robot with any one of the joints being a passive joint. The goal of this study is to design and analyze a swing-up controller that can bring the robot into any small neighborhood of the upright equilibrium point with all links in the upright position. First, we address how to iteratively devise two series of virtual composite links separated by the passive joint to be used for designing a coordinate transformation on the angles of all active joints. Second, we devise an energy based swing-up controller that uses a new Lyapunov function based on that transformation. Third, we analyze the global motion of the robot under the controller and establish conditions on control parameters that ensure attainment of the swing-up control objective. The results obtained not only unify some previous results for some underactuated robots with a passive first joint, but also provide insight into the energy-based control of underactuated multi-degree-of-freedom systems.