Swing-up control based on virtual composite links for n-link underactuated robot with passive first joint

This paper concerns a swing-up control problem for an n-link revolute robot in a vertical plane with its first joint being passive and the rest being active. The objectives of this paper are: 1) to design a controller under which the robot can be brought into any arbitrarily small neighborhood of the upright equilibrium point, where all links of the robot remain in their upright positions; 2) to attain a global analysis of the motion of the robot under the controller. To achieve the above challenging objectives, first, this paper addresses how to devise iteratively a series of virtually composite links for designing a coordinate transformation on the angles of all active joints. Second, this paper constructs a novel Lyapunov function based on the transformation, and proposes an energy based swing-up controller. Third, this paper carries out a global analysis of the motion of the robot under the controller, and establishes some conditions on control parameters for achieving the swing-up control objective. This paper provides insight into the energy or passivity based control to underactuated multi-degree-of-freedom systems.