A stable reentry trajectory for flexible manipulators

Trajectory tracking of fast-lightweight manipulators is an emerging topic. These systems often possess an unstable internal dynamics that is related to the inverse dynamics problem. The main contributions of this work are (i) a direct relation between internal dynamics variables and trajectory constraints as state equations in an observer canonical form; (ii) the entry/reentry trajectory defined as input control in order to stabilise the unstable internal dynamics; (iii) the methodology is well-suited for systems modelled in a finite element approach, related to an index-3 differential algebraic equation; (iv) a linearised design is established, but the results are suitable to consider a nonlinear model predictive control of underactuated/flexible manipulators, since a reentry trajectory is often required to minimise the output error recursively. For the application, (a) a planar underactuated manipulator with one passive joint and (b) a planar flexible manipulator on a cart were considered.