Realization of Spring Loaded Inverted Pendulum dynamics with a two-link manipulator based on the bio-inspired coordinate system

In this paper, kinematics, statics, and dynamics of a two-link manipulator with a biarticular actuation mechanism are discussed. The biarticular actuation mechanism is inspired from the musculoskeletal structure of animals and is utilized in the controller design, as well as the mechanism design. For an effective and convenient expression of the equation of motion, the rotating coordinate system is adopted unlike the conventional robotic manipulators, the dynamics of which are obtained in the fixed coordinate system. It is proved in this paper that the biarticular actuation mechanism makes the control of the end-effector easier, more robust, and more intuitive than typical actuation mechanisms. Based on the derived equation of motion of a robotic manipulator in the rotating coordinate system, a disturbance-observer-based controller is proposed for realization of the Spring Loaded Inverted Pendulum (SLIP) model, which is a common model of human lower extremities but has seldom been realized in practice. The proposed methods are all verified by simulation studies in this paper.