A numerical method to minimize tracking error of multi-link elastic robot

The tracking error of robot manipulators based on flexible arm models are presented in this study. The number of actuator is equal to the dimension of the task space which is usually equal to the rigid body degrees of freedom. Actuator torques required for a flexible arm to track a given trajectory are formulated and computed by an iterative algorithm which is based on path planning method. The formulation is complete in the sense that it also considers the full nonlinear dynamics of the manipulator arm. The Euler-Bernoulli beam theory is used to model the dynamics of flexible links and the resulting equations of motion are derived by Lagrange´s equation using finite element discretization technique. The algorithm is simple to implement but computationally expensive. The performance and capabilities of the proposed method are tested on a two-link arm through simulation and the results show the potential use of this method not only for feedforward open-loop control but also for closed-loop control strategies