Trajectory control of Cartesian type industrial manipulators with flexible joints

In this paper, a method for PTP and trajectory control of Cartesian type three DOF industrial manipulator with flexible joints are proposed. The elasticity of the manipulator is modeled using the spring-mass model. To establish the equation of motion, the Lagrangian formulation is used. The state equation is derived. Then it is linearized approximately. The PTP control system is formulated. A minimal order observer is used in this PTP control system, and the trajectory control is realized based on the optimal control theory. Furthermore, the desired trajectory is modified to improve the tracking performance. Finally, computer simulation results are given to show the validity of the proposed tracking controller