An imaginary robot model and double-PD control for redundant robotic systems

The theory and applications of an imaginary robot model with a double-PD control law for redundant robotic systems are presented. The imaginary robot model is based on a special Riemannian metric decomposition for general nonlinear dynamic systems. This model offers an effective way for reducing nonlinear feedback formulation while preserving the linearized system equation. The developed procedure is also applicable to redundant robots. A three-dimensional redundant robot main-frame having three revolute joints plus a prismatic joint is used in the paper to illustrate the design procedure based on the imaginary robot model with the double-PD control scheme. The entire dynamic control algorithm is also verified by a simulation study on the four-joint three-dimensional robot arm.