Fusion Engineering and Design 83 (2008) 1856–1860

Authors' copy - Article presented at the 8th International Symposium on Fusion Nuclear Technology (ISFNT-8), Sept. 2007, Heidelberg, Germany Contents lists available at ScienceDirect

Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes

Remote handling dynamical modelling: Assessment of a new approach to enhance positioning accuracy with heavy load manipulation T. Gagarina-Sasia a,∗ , O. David a , G. Dubus a , E. Gabellini b , F. Nozais a , Y. Perrot a , Ph. Pretot b , A. Riwan a , N. Zanardo b a b

C.E.A., LIST, Interactive Robotics Unit, B.P. 6, Fontenay-aux-Roses F-92265, France SAMTECH France, 15 rue Emile Baudot, Massy F-91300, France

a r t i c l e

i n f o

Article history: Available online 23 August 2008 Keywords: Long-reach robotic systems Heavy load handling structure Flexible manipulator Specific mechanical software Dynamics simulation

a b s t r a c t In-vessel maintenance work in Fusion Tokamak will be carried out by the help of several sets of robotic devices. Handling of heavy loads in constrained space is identified by all players of the RH community as a key-issue in behalf of the ITER. To deal with high-level dexterity tasks, characterized by high payload to mass ratio and limited operating space RH equipment designers propose systems whose mechanical flexibility is no longer negligible and needs to be taken into account in the control scheme. A traditional approach where control system includes a linear model of deformation of the structure only leads to poor positioning accuracy. During maintenance operations in the ITER facility, uncontrolled or under-evaluated errors can damage in-vessel components. To address the control of complex flexible systems, we will investigate the use of specific mechanical software that combines both finite element and kinematical joint analyses with a strong-coupled formulation to perform system dynamics simulations. This approach will be applied to a single axis mock-up of robotic joint, supplied by a highly flexible structure. A comparison of experimental results with the traditional linear approach and the specified software model is carried out.

1. Introduction Activation and contamination of structures submitted to high neutron fluxes or in contact with will prevent any hands on maintenance within the ITER torus, a few years after beginning of operations. Remote handling and robotics means were therefore considered in ITER as the standard maintenance tools and were taken into account since the early beginning in the design of the facility. Access ports or workspace around each part of the facility needing maintenance will be very limited and have a significant impact on the size of the maintenance tools. Heavy loads handling in space constrained environment is therefore identified by all players of the RH community as a key-issue for maintenance. This paper presents theoretical and experimental investigations in the field of remote handling dynamical modelling of systems with significant mechanical flexibility. A lot of efforts have been spent to design the long-reach robotic systems operating in constrained space with heavy load manipulation [1–4]. The remote handling systems are required for

∗ Corresponding author. Tel.: +33 146547879; fax: +33 146548980. E-mail address: [email protected] (T. Gagarina-Sasia).

Authors' copy © 2008 Authors. All rights reserved. doi:10.1016/j.fusengdes.2008.07.011

multifarious tasks, where the successful fulfilment depends on the accuracy of system positioning. However, control of such systems aimed to maintain accurate positioning raises serious difficulties due to their structural and joint flexibility. Its dynamics is highly non-linear and complex thereby inertial effects provided by the manipulation of heavy load handling structure are significant and cannot be neglected. In this respect, a control mechanism that accounts for flexural motions and inertia of the whole system is required. It means that a system model is needed which being included into control schema compensates for the flexibilities in the robotic system and estimates the position of the tool. Several works [5–8] address the problem. To challenge the problem, this paper proposes to use specific mechanical software [9] permitting to replace the cost-bearing experiments with real systems by adequate software models for tuning the corresponding control schemas. Software simulation based on the proposed approach is compared to the results of natural experiments on corresponding laboratory mechanical system and to a theoretical linear model. A single-link flexible manipulator with a lumped heavy load is used to illustrate the inertia and joint flexibility effects for the longreach manipulators. The main goal of this study is to emphasize the fact that elasticity effects of the hinge joint are significant in the structure’s response.

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where qT (t) is the vector of the generalized coordinates describing the motion of the system, ˝ = diag[ω02 , ω12 , . . . , ωn2 ], ωi denoting (n+1)×(n+1)

(n+1)×(n+1)

the ith natural frequency, C a and C w are matrices of shape functions, I(n+1)×(n+1) is the identity matrix and appl is the vector of the applied torques, fric is the vector of joint friction torques. To derive the controller used, the friction is considered as the maximum static (Coulomb) torque. A linearised form of Eq. (1), obtained by setting Ca = 0 and C w = 0, to yield Eq. (2): q¨ + ˝q =  appl +  fric

(2)

is usually employed in control schemas of heavy load handling systems. For interpreting the experimental results we use as reference model a more simplified model, wherein we admit the vector qT (t) to be reduced to rigid components (to angular articulated position q0 in our case).

Fig. 1. A heavy load flexible manipulator.

2. Mathematical modelling of highly flexible loaded structures

3. Software for simulation of mechanical systems

The conceptual structure considered in this work is shown in Fig. 1 where X0 OY0 and xOy represent the stationary and moving frames, respectively. It is composed of a single axis robotic joint locked at O point. A single-arm flexible structure has been connected to the joint and modelled as a pinned-free long-reach tubular beam with small circular cross-section. The arm has length L and mass Mb. The beam has been designed so that it justified Euler–Bernoulli assumption when the beam thickness e is much smaller than its length L: |e/L| < 1/10, thus allowing it to be flexible dominantly in the transverse direction. The beam is assumed to be not extensible, i.e. the length of its neutral line is constant during the motion. It is considered to have constant (rigid) cross-section and uniform material properties throughout. At the free end of the beam a lumped mass Me has been attached to represent a heavy load. The tubular beam can bend freely in the X0 OY0 plane. The moment of inertia of the arm about the hub O is denoted by Jf , and  is the linear mass density. The angular displacement of the manipulator, moving in the X0 OY0 plane, is denoted by q0. The parametric values of the considered system are given in Table 1. The dynamic equations describing the motion of a one-degreeof-freedom (DOF) flexible manipulator carrying a load can be obtained by developing the Hamiltonian from the expressions for kinetic energy, potential energy and work. The governing Euler equations with cantilever boundary conditions are derived from the Hamiltonian and the vibration or modal frequencies are calculated from these. The non-linear partial differential equation model is expanded along a finite truncated set of these modal frequencies which yields an ordinary differential equation model. A representation of the displacement field with n vibration modes yield to the non-linear differential equation of motion: (I + qT C w qC a )q¨ + (q˙ T Cw qI − C w qq˙ T )C a q˙ + ˝q =  appl +  fric

(1)

Table 1 Parametric values for the flexible system Physical parameters

Symbol

Value

Rod length Pipe wall thickness Section area Density Young modulus Second moment of area Payload mass

L ew A  E I Me

3m 3.25 × 10−3 m 5.92 × 10−5 m2 7.85 × 103 kg/m3 210 × 109 N/m2 2.37 × 10−7 m4 14.1 kg

As we want to study the transient response of the structure, we have to take into account not only the stiffness but also kinematical and inertia effects for the computation. From a numerical point of view, solving this kind of analysis with a good accuracy is very time consuming if a large finite element model is used. That is why a super-element method is used in this study [10]. The principle of this method is to decrease the size of the problem to solve by replacing different regions of the structure by their equivalent stiffness and mass properties. These equivalent properties are evaluated in prior fast computations, called super-elements creations. So, a single time consuming calculation is replaced by several faster ones. And a super-element is no more than a region of the structure replaced by its equivalent stiffness and mass properties and which the representation in the global model is reduced to the nodes required to express the boundary conditions (fixations, loading, links with other super-elements, etc.). Computer-Aided Engineering Environment SAMCEF field V6.108 software [9], developed and marketed by SAMTECH, provides a complete environment for performing finite element analysis (linear, non-linear, modal, etc.). One can in particular use simultaneously structural elements, kinematical joints (hinge joints, prismatic joints, gear elements, etc.), rigid elements and superelements in the same model. These capabilities are exploited in this study. Indeed, parts are sorted in three groups as detailed in Fig. 2 and a super-element is created for each group. Note that bearing and cross-rolling ring are assumed to be rigid and replaced by rigid bodies and lumped masses. Then, super-elements are imported in the final model in order to be linked with a flexible beam and a concentrated mass, as explained on the right side of Fig. 2. All parts are linked together with ideal kinematical joints (rigid hinge joints and rigid bodies). Friction effects are neglected. The speed reducer behavior is modelled by means of a kinematical constraint between relative rotations in two hinge joints, as detailed Fig. 3. 3.1. Physical data and materials properties All physical properties (beam length, value of the lumped mass, etc.) and materials characteristics used for the computation are deduced from measurements made on the experimental assembly. Note that all materials are assumed to remain elastic. Moreover, a viscous damping is taken into account.

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Fig. 2. Description of the finite element model.

Fig. 3. Speed reducer model.

3.2. Boundary conditions and loading As the system is considered fixed on the test bench, flanges’ bases are clamped. A hinge joint with a ×120 reduction ratio is created between the motor input and the output connected to the rod. A gravity field is applied to the whole model. We applied to the rod the trajectory assured by a sinusoidal signal with amplitude ± 1.2 rad (vertical position = zero). To take into account the hinge deformation within the computation a 120 multiplication ratio is applied to this signal to the reducer’s input resulting in the application of the signal as shown in Fig. 4. The vertical axis shows amplified angular articulated position of the rod q(t). 3.3. Run management The equation solved during the dynamic computation is the following: M q¨ + C q˙ + Kq = F. Note in particular that the stiffness

Fig. 4. Position of the input shaft versus time.

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Fig. 5. Experimental mock-up. Fig. 6. Mock-up deformation.

K varies during the analysis as the problem is non-linear. From a numerical point of view, the time integration of the equation of the motion is done using a Hilber–Hugues–Taylor implicit scheme. In the static case, kinematic and inertial effects are neglected so that the equation is reduced to Kq = F. 4. Experimental set The experimental platform shown in Fig. 5 used in this work consisted of three principal parts: a long slender beam with a load concentrated mass at its end-point, the robotic joint which is driven by a motor through a speed reducer, measuring devices and a processor. The positioning errors of the robot arm in the operation plan can be easily measured, since it works in the two dimensional space. 4.1. Measuring devices The measuring devices used in this work are the optical encoder to measure the hub – angle of the actuator (joint position) and a laser tracker Leica LTD800 to measure the position of the endpoint of the beam. The accuracy of the laser measuring system is 5E 10−5 m. The laser tracker system measures the three dimensional coordinates of robot’s reference point by tracking laser rays to a retro reflector fixed to the robot arm. In this study, to measure the translational deflections of the arm in the working plane, a set of two retro reflectors were mounted at the system. One was fixed at the hub of the articulated joint and the other one on the tip of the beam at the lumped mass location. The retro reflector movements are surveyed by means of the laser rays with data acquisition frequency being 2–10 Hz. This frequency is sufficiently high to detect each oscillation of the flexible beam. The robotic joint is driven by a sinusoidal signal of amplitude 1.2 rad as position command input for the motor. Joint position is measured by optical encoder and fed back for position control. System responses were monitored for duration of 133 s with sampling time of 2 ms.

Fig. 7. End-point’s vertical and horizontal positions.

Results of the experiments carried out in time and frequency domain are shown in Fig. 7 represent the deviation between the referenced linear model, calculated position and measurements on the experimental platform.

5. Comparison of experimental and simulation results We compared the three following positions of the rod endpoint see Fig. 6: (1) That issued from computations with SAMCEF model (2) That issued from measurements with the laser tracker (3) The theoretical position of the end-point of rigid rod with an angular position equivalent to the one supplied by the encoder.

Fig. 8. Zoom on vertical position.

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direction that is the direction tangent to the trajectory of the axis. This signal error is composed of a carrying signal (main error) and oscillations around this carrying signal. The main error is due to the own stiffness of the mock-up (both rod and hinge joint flexibility) and could be assumed to a static error. Oscillations are coming from: dynamical effects, starts, stops, acceleration, etc., the control scheme. This is clearly demonstrated by the graph of Fig. 10. In that simulation, we no longer used the encoder signal as input position signal for the numerical FE model but we used the theoretical pure sinus signal. We see on the green graph of Fig. 10 that, starting point excepted, there are no longer any oscillations of the green curve. The first oscillations are therefore due to the dynamical effect during starting phase and the oscillations observed in the following phase are responses to excitations due to the control scheme. Elasticity of the hinge joint is a major contributor to the deflection of the whole system. 6. Conclusions Fig. 9. Vertical and horizontal errors for both model and measurements compared to rigid position.

Definition and assembly of a mock-up installation was made to study the effects of the control scheme on positioning accuracy. With help of a numerical finite element model of the installation, preliminary investigations were made to identify the main contributors to the positioning error. As expected deflection of the articulation due to elasticity of the reducer of the hinge joint is one of the major errors. It was also proved that oscillations of the control scheme have a non-negligible impact on the positioning error and on dynamical behavior of the system. Further investigations will concentrate on improvements of the numerical model of the installation and analysis of all phenomenons playing an active role in the deflection of the structure, modeling and study of complete and complex robotic structures without developing building expensive mock-ups. References

Fig. 10. Tangential errors with an input signal of the numerical model equivalent to the stimulation signal.

Significant differences appear between the theoretical linear position compared to the real one and the prediction of the model. Although the agreement between measurements and model seems correct, a position error of about a few centimeters is observed between the real one and the one of a linear system. Zooming on all three positions (see Fig. 8) show that vibration of the structure can be observed on both measurements and model during movement of the rod. We defined two errors: an experimental one defined as the difference between the position of the rigid system (according to stimulation signal) and the experimental measurements; a model error defined as the difference between the position of the rigid system (according to stimulation signal) and the estimation of the model according to the stiffness of the reducer unit and the structure’s geometry. Representation of these two errors is given in Fig. 9. In this figure expression of these errors are given along the vertical and horizontal axis of the fixed coordinates system. Due to its geometry, deformation of our mock-up is essentially made in one

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