Rest-to-rest motion of a one-link flexible arm

We present a solution to the problem of finding the torque command that provides rest-to-rest motion in a given time for a one-link flexible arm. The basic idea is to design an auxiliary output such that the associated transfer function has no zeros. Planning a smooth interpolating trajectory for this output imposes a unique rest-to-rest motion to the whole arm, with automatically bounded link deformation. The nominal torque is then obtained by inverse dynamics computation in the time domain. The method is presented for a linear model based on the Euler-Bernoulli beam description of the flexible link with dynamic boundary conditions. This approach lends itself to nonlinear extensions and feedback solutions.