a b s t r a c  t Keywords: Industrial robot Vibration control Flexible beam ARX modeling PID  controller System identification

The vibration control problem of flexible objects manipulated by industrial robots under normal production conditions is investigated. This is an important problem as the quick and precise manipulation of such objects may reduce the production lead time and thus its cost. The problem is in the present study tackled for flexible beams via a novel method which overcomes various practical difficulties and can be easily applied in industrial environments with the least human intervention. The method is based on: (i) AutoRegressive with eXogenous (ARX) input stochastic modeling of the robot-beam system using exclusively experimental data, (ii) the design of an appropriate control system consisting of a typical feedforward PID-type controller and a feedback that enables the attenuation of the force at the robot’s wrist and thus the suppression of the vibration at the beam’s free- end and, (iii) a synthetic environment within which the performance of the control system may be tested under realistic operating conditions through simulation before its final implementation in the robot. The effectiveness of the method is experimentally assessed through the vibration control of a flexible metallic beam that is manipulated by an industrial robot for its insertion into a slot, testing additionally the control system’s performance under various operating conditions for which it is not designed to deal with.

1. Introduction

Oftentimes the minimization of the production lead time demands the rapid manipulation of various objects by industrial robots during normal production conditions. In the case of flexible objects manipu- lation such as rods, beams, coils and others, the robots’ rapid point to point (PtP) motions increase significantly the amplitude of the object’s free-end vibration. This leads also to increased cycle time for each in- pidual production process as for instance a peg-in-hole insertion, a laying-down action and so forth, since the robot, for a safe and precise placement of the object, must wait until the amplitude of its free-end vi- bration is significantly reduced. For production lines including several processes with flexible objects, this fact results obviously in significantly longer production lead times and thus higher total  cost.

In robotics, this vibration control problem is tackled based on two main families of methods: (i) this which uses physics-based models rep- resenting the object and/or the robot dynamics, and (ii) this which em- ploys empirical knowledge and/or experimental measurements from the robot-object system without resorting on physics-based modeling.

Methods from the first family commonly combine a detailed physics- based model of the robot and/or the flexible object using additional sen- sors and/or other mechanisms installed on the industrial robot. For in- stance, the vibration control at the free-end of a flexible metallic beam is achieved in [1] via a robot’s end-effector trajectory planning procedure and the use of a passive mechanism incorporated in the robot gripper so as to attenuate the vibration at the beam’s free-end. An Euler–Bernoulli model of a beam combined with a robot-action learning strategy that determines the appropriate robot trajectory to complete a peg-in-hole operation are used in [2]. A method that includes physics-based model- ing and prediction of the flexible object’s response in conjunction with a procedure for object’s material properties determination and additional robot’s vision equipment is presented in [3]. Alternatively, a common concept is the use of a Finite Element (FE) model for the representation of the considered flexible object dynamics. A scheme for the elimina- tion of vibration at the free-end of a 2D linear flexible object, where its dynamic deformation is represented in a closed-loop of adaptive slid- ing mode control with input saturation via a FE model and Lagrange equations, has been studied through simulations in [4]. This modeling procedure for the 2D linear flexible object is adopted by the same au- thors in [5] for the design of a position-control system that is based on a fuzzy controller appropriately switched to a PI-controller, and its effectiveness is assessed via simulations as well.