LAUSR

Abstract This paper proposes the theory and the experimental assessment of a robust model-based trajectory planning algorithm for underactuated nonlinear systems in point-to-point motion. The method has been developed to increase the insensitivity of the resulting trajectory to parametric uncertainties of the plant. The proposed method is based on an augmented model that considers an approximate dynamics of the servo-controlled axis driving the actuated degrees of freedom. Trajectory planning is accomplished by computing the motion reference for the actuated degrees of freedom to reduce the effects of the uncertainty on the dynamic model. By exploiting an indirect variational formulation method, the necessary optimality conditions deriving from the Pontryagin’s minimum principle are imposed, thus leading to a differential Two-Point Boundary Value Problem (TPBVP). Numerical solution of the latter is accomplished by means of collocation techniques to handle model nonlinearities. Robustness is achieved by including additional conditions on the sensitivity functions for the initial and final points of the trajectory. The experimental evaluation of the effectiveness of the proposed method is performed on a double-pendulum crane, by comparing the transient and residual vibration. A comparison is provided with three well-established input-shaping methods, and robustness against unmodeled parametric perturbations and tracking errors is evaluated. The experimental evidence indicates that the inclusion of the additional constrains results in an effective reduction of the residual vibration, and that the proposed method is well suited to perform high speed motion.