Linear Parameter Varying (LPV) modeling for PUMA560 arm to estimate the computed torque in trajectory control

This paper proposes a new computed torque strategy to control the robotic manipulators using polytopic linear parameter varying (LPV) modeling method. An LPV representation of the robot is generated by identification of its dynamic in different workspace points about an arbitrary full-path trajectory. Identification of the models is done by using the least square of errors  algorithm. By utilization of parameter set mapping based on parameter component analysis (PCA) a reduced polytopic LPV model is obtained that reduces the complexity of the implementation. In the conventional computed torque control, it is necessary to know the dynamical model of the robot while in the proposed method an estimation of the required torque is computed based on the obtained LPV model. The control gain matrix is derived by solving a set of linear matrix inequalities (LMIs) that takes the time derivative of the Lyapunov function to the sufficiently small value. Sufficient conditions are provided to ensure the asymptotic stability of the closed loop LPV system against the torque estimation error. The proposed scheme is applied to trajectory tracking control of a six degree of freedom (DOF) PUMA 560 robot manipulator.