Analysis and synthesis of global nonlinear H ∞ controller for robot manipulators

Abstract

The H ∞ 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 H ∞ 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 H ∞ control problem, is satisfied by defining a strict Lyapunov function. The performance issues of the nonlinear H ∞ regulator are illustrated in experimental and simulation studies made for a 3-DOF rigid links robot manipulator.