Inversion-Based Nonlinear Control of Robot Arms with Flexible Links

The design of inversion-based nonlinear control laws solving the problem of accurate trajectory tracking for robot arms having flexible links is considered. It is shown that smooth joint trajectories can always be exactly reproduced preserving internal stability of the closed-loop system. The interaction between the Lagrangian/assumed modes modeling approach and the complexity of the resulting inversion control laws is stressed. The adoption of clamped boundary conditions at the actuation side of the flexible links allows considerable simplification with respect to the case of pinned boundary conditions. The resulting control is composed of a nonlinear state feedback compensation term and of a linear feedback stabilization term. A feedforward strategy for the nonlinear part is also investigated. Simulation results are presented for a planar manipulator with two flexible links, displaying the performance of the proposed controllers also in terms of end-effector behavior.