Non-linear Observer-based Control of Flexible-joint Manipulators Used in Machine Processing

This paper proposes to use a non-linear observer to build the state and the external force of flexible manipulator robots during their machining (composite materials) processes or Friction Stir Welding (FSW) processes. These two different processes have a problem in common: the flexibility of the robot can not be neglected, that is to say, the errors due to the deformation of the links should be taken into account. However, in most industrial robots, the real positions and velocities of each link are not measured, so in this study, an observer is proposed to reconstruct the real angular positions and velocities of links by using the measured angular positions and the velocities of actuators. A simulation by Matlab/Simulink has been carried out with a 2 axis Robot during its machining processes: the proposed observer showed great performances in estimating the state of the robot (position and velocity). Then, in order to improve the tracking accuracy in the tool frame, the state of the external force along the forward direction (x) and its normal direction (y) are required, while they are also not measured by our robot. A disturbance observer has been added to reconstruct the processing force. A good precision during the proposed processes have been obtained using the latter. This study contributes to solve the problem from the point of ∗THIS WORK IS SUPPORTED BY FRENCH NATIONAL RESEARCH AGENCY UNDER THE PROJECT NUMBER ANR-2010-SEGI-003-01COROUSSO †Address all correspondence to this author view of accuracies during the machining processes. INTRODUCTION Manufacturing processes such as machining and welding are widely applied in production industry. This study focus on two special processes: machining of composite materials and the Friction Stir Welding (FSW) process. These two applications have an innovative character: the first one concerns an application of composite materials, and the second one is a new development of welding. Composite materials are used extensively for their high specific properties of strength and stiffness, however, these materials are difficult to machine due to nonhomogeneous, anisotropic and reinforced by very abrasive components. The FSW is a solid state welding technology that can be used for many joining applications. The process uses a nonconsumable rotation tool consisting of a pin extending below a shoulder, plunges into the work piece such that both the pin and the shoulder are in contact with the piece [1, 2]. The technical and economic performances of some manufacturing processes can be greatly improved by using a manipulator or a robotic system as holder of the production tooling. However, using robot to do these two processes is a challenge: the natural rigidities of industrial robots are not sufficient to perform the tasks in the requirements of the processes. Actually, those processes are carried out by some special developed machines which need a great investment. In the sector of aeronautic industry, these two processes need to be strongly applied. New technologies are demand to reduce the investment and to improve the quality of the products. Due to a strong external force during the operations, the deformations of the robot cannot be neglected, therefore, the real angular positions and velocities of links are different from those determined by the geometric model of the robot. Moreover, to make an accurate machining or welding, the forces exerted on the material should be measured. Unfortunately, most of the industrial robots have only motor side measurements, thus a new approach to estimate link side states as well as the external force is required. Nevertheless, in case of welding, a force sensor is added to get at least the axial effort to the work plan, but the path effort Fx and normal effort Fy are still unknown. There are many control methods available for the flexible robots [3] such as iterative learning control, adaptive control, backstepping, sliding mode control, neural networks, singular perturbations, composite control, pole placement, input shaping, passivity-based control, robustification by Lyapunov’s second method, model-based feedforward control [4]. A good description of these control methods can be found in [5–8]. Disturbance observer technique is widely used in mechanical servo systems and observers are often used for the state estimations [9, 10]. An adaptive robust control of FSW and an observer-based adaptive robust control (ARC) approach is discussed in [11] where it is proved that the axial force can be also estimated by an observer. An application of disturbance observers to nonlinear systems is reported in [12]. An accelerationbased state observer is presented in [13]. Subrahmanya and Shin [14] propose a method of state estimation. There are a lot of observer methods proposed by other researchers such as highgain observers, sliding mode observers [15], extended state observers, Kalman Filter and the Luenberger observer. In order to realize these operations, we propose an improved observer which can estimate not only the unmeasured states but also the external force. This paper is organized as follows: a simplified model of flexible manipulators and the model of processing force for the two processes that mentioned above will be presented in the first part. The second part proposes a new observer which uses motor side measurements to reconstruct the state of robot as well as the external force. In the third part, a simulation is carried out by Matlab/Simulink to verify the tracking performance with the proposed observer. And finally, a conclusion and some further applications of this study will be presented. MODELING OF ROBOT AND PROCESSES Robotic manipulators are highly nonlinear and coupled dynamic systems, there also subjected to different external disturbances. This study is a part of the project COROUSSO (see acknowledgment). The objective of this project is to realize maTABLE 1. Model parameters of the robot IBM7545. Name Description (unit) Value l1, l2 length of link (m) 0.40 ; 0.25 m1,m2 mass of link (kg) 12.70 ; 4.35 ml mass of the spindle (kg) 1.34 N1,N2 gear transmission factor 157 ; 80 K1,K2 elasticity constante (N m−1) 3.67 104 ; 8.90 103 r1,r2 distance between axis 0.153 ; and center of gravity (m) 0.084 Ke1,Ke2 motor torque constant 0.1099 ; (Nm V−1) 8.90 103 Jm1,Jm2 motor inertia (kg m2) 1.50 10−4 ; 0.0496 fm1, fm2 coefficients of viscous friction 7.18 10−5 ; on the motor side (Nm s rad−1) 2.58 10−5 fq1, fq2 viscous friction of the joints 10 ; 10 (Nm s rad−1) chining process and FSW process with industrial robots. In a first step, in order to simplify the approach, the tool is considered to stay in a horizontal plan during the machining process, the considered robot is a Scara robot which has two joint axis in parallel. The necessary parameters are taken from a robot IBM7545 that presents in [16]. It is a robot not well adapted to this task, but we will study firstly the problems addressed. Hereafter, the flexibility of joints, the efforts applied by the robot, the gravity and the frictions are taken into account. A. Model of two axis flexible joint robot The model parameters of two-link flexible manipulator used in the simulations are given in Table 1. It is supposed that the tool is fixed at the end of the second axis and its rotation axis is assumed perpendicular to the work plan (x,y), and the tool moves only in the plan (see Figure 1). Assuming that the links are rigid and only the joints have torsional stiffness due to the gearbox that are taken into account. The position of the tool (x2,y2) is calculated with the articular positions of each link q = [q1 q2] by using the geometric model: { x2 = l1 cos(q1)+ l2 cos(q1+q2) y2 = l1 sin(q1)+ l2 sin(q1+q2) (1) FIGURE 1. Geometric model of robot