End-point position control of multi-link flexible manipulator arms

In this thesis the problem of positioning the end-effector of a flexible manipulator arm along a desired path is discussed. The application of nonlinear inversion method as a potential solution is considered first. Since the inverse system is not stable, an alternative approach is presented: based on the assumption of small elastic deflection of the flexible links, the equations of motion are linearized. The solution of linear optimal control equations yields a noncausal control, which approximately reproduces the end-point trajectory for the nominal nonlinear system.;The assumed mode method is used to model the elastic deformation in the links of the manipulator. Simulation results for very flexible single-link and two-link arms are given. Convergence of the optimal solution with the number of modes used in the modal expansion is shown. Accurate tracking is achieved for fast motion of the end-point.;To have accurate and stable tracking for an off-nominal flexible arm, several closed-loop control schemes are presented. The optimal tracking control, viewed as a closed-loop scheme is shown to be stable despite uncertainties in the model. To avoid the measurement of flexible coordinates, a closed-loop scheme is given which uses a simple proportional plus derivative (PD) joint feedback. The optimal solution, used as a feedforward, is essential for the implementation of this method. Simulation results for a single-link flexible arm are shown to illustrate the above ideas.