Tracking control of elastic joint parallel robots via state-dependent Riccati equation

In this study, a methodology for the tracking control of parallel robots having elastic joints based on the state-dependent Riccati equation is developed. Structural stiffness and damping characteristics of the joints are modeled as torsional springs and dampers, respectively. First an open-tree system is obtained by cutting some joints of the parallel robot open and its dynamic equations are written. Closed loops are then represented as constraint equations. The first and second derivatives of dependent (unactuated) joint variables are expressed in terms of independent (actuated) joint variables by making use of the constraint equations. Taking the independent joint variables, the actuator variables, and their first derivatives as state variables, the dynamic equations are represented in state-dependent coefficient form. Finally, state-dependent Riccati equation tracking control is presented. A 2-RRR planar parallel robot is taken into consideration as an example to illustrate the effectiveness of the state-dependent Riccati equation method for the control of parallel robots having elastic joints.