Modelling and control of a three degree of freedom manipulator with two flexible links

The authors propose a model that is useful for real-time control of a robot with two flexible links moving in three dimensions. Each link is described by using a 3D spring/mass model; then, the whole arm is modeled by connecting the models of the individual links so as to treat change in feedback gain easily. By using this model, the equation of motion and the state equation of a 3D flexible robot are derived with Lagrange´s method. It is shown that accelerometers attached to the tips of elastic links are adequate for observing the state variables that represent flexibility in the model. Finally, a controller designed by applying optimal regulator theory is described, and experimental results demonstrate that the proposed controller can suppress vibrations of the arm