Robust control using recursive design method for flexible joint robot manipulators

A flexible joint robot manipulator can be regarded as a cascade of two subsystems: link dynamics and the motor dynamics. Using this structural characteristic, we propose a robust nonlinear recursive control method for flexible manipulators. The recursive design is done in two steps. First, a fictitious robust control for the link dynamics is designed as if it has a direct control input. As the fictitious control, a nonlinear H∞-control using energy dissipation is designed in the sense of L2-gain attenuation from the disturbance caused by uncertainties to performance. In the process, Hamilton-Jacobi (HJ) inequality is solved by a more tractable nonlinear matrix inequality (NLMI) method. In the second step, the other fictitious and the actual robust control are designed recursively by using the Lyapunov’s second method. The proposed robust control is applied to a two-link robot manipulator with flexible joints in computer simulations. The simulation results show that the proposed robust control has robustness to the model uncertainty caused by changes in the link inertia and the joint stiffness.