Desensitized motion planning for underactuated multibody systems

Model-plant mismatches can severely limit the effectiveness of conventional model-based motion design methods. To solve this issue, a method for robust trajectory planning that can reduce the effects of parametric uncertainties is presented in this work. The method is based on an indirect variational formulation, which is translated into a Two-Point Boundary Value Problem (TPBVP) and then solved numerically. Robustness is obtained by incorporating into the problem the sensitivity functions of the plant, and imposing some additional constraints on the initial and final points of the trajectory. A formulation aimed at reducing both the residual and the transient oscillations, as well as keeping small the control effort, is also proposed. The work presents a numerical verification of the effectiveness of the method for an underactuated system, such as a double-pendulum crane, by showing its effectiveness and robustness when performing fast rest-to-rest motions.