Abstract
This paper develops an approach for the control of the motion of a multiple-link manipulator possessing unactuated joints. A three-rigid-link arm with its shoulder joint actuated and two elbow joints unactuated is modeled as a nonlinear Affine system. The system is a case of second-order nonholonomy since the constraints at the passive joints contain terms of accelerations. In the proposed method to solve the problem of optimal positioning the control input is expressed 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. Numerical simulations were carried out and tests with an experimental setting demonstrate the effectiveness of the approach.
