Analysis and synthesis of global nonlinear \(\mathcal{H}_{\infty}\) controller for robot manipulators (Q1665618)

Summary: The \(\mathcal{H}_{\infty}\) regulation problem for robot manipulators using gravitational force compensation or precompensation has been solved locally while global asymptotical stability (or global stability) has been demonstrated using other methodologies. A solution to the global nonlinear \(\mathcal{H}_{\infty}\) regulation problem for \(l\)-degrees-of-freedom (\(l\)-DOF) robot manipulators, affected by external disturbances, is presented. We showed that the Hamilton-Jacobi-Isaacs (HJI) inequality, inherited in the solution of the \(\mathcal{H}_{\infty}\) control problem, is satisfied by defining a strict Lyapunov function. The performance issues of the nonlinear \(\mathcal{H}_{\infty}\) regulator are illustrated in experimental and simulation studies made for a 3-DOF rigid links robot manipulator.