Motion control of flexible manipulator possessing unactuated joints

This paper aims at developing an approach for the motion control and trajectory planning of a lightweighted three-link manipulator possessing two unactuated joints. The system is a case of second-order nonholonomy due to the presence of dynamical constraints. A three-flexible-link arm with a single actuator at the shoulder joint is modeled as a nonlinear Affine system, where the deflection is approximated as static bending. The way to attain the optimal positioning of this nonlinear system subjected to extreme conditions is to express the control input as a general function of a Fourier basis parameter acquired by using the Ritz method. Then this parameter is optimized through the application of the Newton method. To demonstrate the validity of this approach, simulations are carried out.