Abstract
This paper presents a hybrid control strategy for an underactuated three-link manipulator with its second joint being passive. The motion space of the manipulator is divided into three stages: order-reduced stage, swing-up stage and balancing stage. Firstly, in the order-reduced stage, a Lyapunov function is constructed for the third joint, and a control law is designed to force the third link to stretch out toward the second one in a natural way. Meanwhile, another control law is designed for the first joint based on the idea of increasing the system energy continuously. Consequently, the manipulator is reduced to a Pendubot-like system. Then, in the swing-up stage, by retaining the designed control law for the third joint, two different control law design methods are proposed for the first joint to force the manipulator to enter into the balancing stage. One method is only based on the system energy, while another one is based on both the energy and the angular velocity of the first joint. Finally, a linear control is employed for the reduced Pendubot-like system, which stabilizes the manipulator at the straight-up unstable equilibrium position. Numerical simulations show that the proposed strategy has the advantages of short settling time and small control torques.
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