Manipulator Dynamic Nonlinearity Approximation Based on Polytopic LPV Modeling for Robot Tracking Control Problem

This article proposes a novel robot control strategy to compensate the robotic manipulator nonlinearity effects by applying the linear parameter-varying (LPV) modeling technique. A polytopic LPV description of the robot is created by the usual Lagrangian linearizing about an arbitrary complex full-scope trajectory. The principal component analysis is implemented for the parameter set mapping and generating a reduced polytopic LPV model to decrease the implementation complexity. An estimation of the required torque is calculated based on the constructed polytopic model to neutralize the nonlinear terms of the robot dynamics. The control gain matrix is involved in a set of linear matrix inequalities to sufficiently decrease the time derivative of a Lyapunov function. A sufficient condition ensures that the proposed controller stabilizes the polytopic LPV system against the torque estimation error. Finally, the proposed scheme is applied to the six-degree-of-freedom PUMA560 manipulator for the tracking control problem.