Motion control of underactuated three-link gymnast robot based on combination of energy and posture

This study discusses the motion control of an underactuated 3-link gymnast robot moving in a vertical plane. The motion space of the robot is divided into two subspaces (swing-up area, attractive area), and a different type of motion control (swing-up control, balancing control) is applied to each. To enable efficient motion control, the swing-up area is further divided into two subspaces, and a different control law is designed for each. These two laws are employed sequentially and make the robot enter the attractive area with a suitable posture and energy. In the attractive area, the balancing-control law captures the robot and stabilises it at the straight-up equilibrium position. Simulations and a comparison demonstrate the validity of this control method.