Theoretical and experimental study of dynamic load-carrying capacity for flexible robotic arms in point-to-point motion

This paper involves the study of a general formulation and numerical solution for the dynamic load-carrying capacity of a mechanical manipulator with elastic links. The approach presented in this article is based on an open-loop optimal control. This method results from the Pontryagin minimum principle, which yields a 2-point boundary value problem. The indirect method has been exploited to extract the optimality conditions. The dynamic equations of motion for this system have been obtained by means of the Gibbs-Appell formulation and by applying the assumed modes method. The elastic characteristics of the members have been modeled based on the Timoshenko beam theory and its associated mode shapes. The aim of this research is to calculate the maximum-allowed load that a mechanical manipulator with flexible links can carry while traversing an optimal path. At the end, to evaluate the proposed method, we made a comparison between the simulation results obtained from the presented model and the experimental results obtained from a manipulator with 2 flexible links. The comparison between the simulation and empirical data confirms the credibility of the presented method in computing the dynamic load-carrying capacity and controlling the point-to-point motion of the considered 2-link flexible manipulator.