The Location Of The Planar Underactuated Robot Pendubot Control Strategy Research

The two-link manipulator Pendubot operating in a planar plane is a typical model of underactuated mechanical system, which consists of two joints with a single actuator at the first joint. The control objective is to move it from any initial position to the given equilibrium position and balance it there.As the planar two-link robot poses high-nonlinear property and does not satisfy the STLC (Small Time Local Controllability), the control for this kind of system is still an open problem. The positional control strategy for the spring-coupled planar Pendubot is studied in this thesis. Moreover, simulations are carried out to demonstrate the effectiveness of the proposed strategy.Firstly, the dynamic model of the planar Pendubot is obtained based on Lagrange equation, and the dynamic characteristics of this system are analyzed. Moreover, the effect on the dynamic characteristics due to the spring is also studied in this chapter.Secondly, a control strategy based on Equivalent-Input-Disturbance is proposed to move the planar Pendubot from any initial position to its target position only using the information of the link angels. The design procedure includes two steps:(1) A homeomorphous coordinate transformation is carried out to change the original system to a new nonlinear cascade system, which also changes the problem of positioning the original system into one of stabilizing the new system.(2) The new system is divided into linear and nonlinear parts, and the nonlinear part is regarded as a virtual disturbance, thereby enabling the use of EID (Equivalent-input-disturbance) approach to achieve the robot’s positional objective. The state feedback controller and observer are designed independently based on the separation theorem.Finally, in order to improve the control performance, a control strategy based on the energy of system and the state of actuated joint is proposed. The global stability of the control system is guaranteed based on the largest invariant set theorem. This control strategy has the merits of lower maximum control torque, simpler configuration and easier to be applied in the actual control.