T. Gagarina-Sasiaa *, O. Davida, G. Dubusa, E. Gabellinib, N. Zanardob, F. Nozaisa, Y. Perrota, Ph. Pretotb, A. Riwana (a) CEA, LIST, Interactive Robotics Unit, B.P. 6, Fontenay-aux-Roses, F-92265 France (b) SAMTECH France, 15 rue Emile Baudot, Massy, F-91300, France Heavy load manipulation devices for in-vessel maintenance work in Fusion Tokamak Remote Handling 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. Goal: The main goal of this study is to emphasis the fact that dynamical effects are significant in the structure’s response. 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. Experimental set constituents
Experimental platform
DTSI / Interactive Robotics Unit B.P. 6 F92265 Fontenay-aux-Roses CEDEX TEL 33 1 46 54 86 70 FAX 33 1 46 54 89 80 http://www-list.cea.fr
DIRECTION DE LA RECHERCHE TECHNOLOGIQUE
Remote handling dynamical modelling: assessment on a new approach to enhance positioning accuracy with heavy load manipulation
Physical parameters
Symbol
Value
Length
L
3m
Pipe wall thickness
ew
3.25× 10−3 m
Section area
A
5.92 × 10−5 m2
Density
ρ
7.85 × 103 kg/m3
• Position command input as a sinusoidal signal of amplitude 1.2 Rad
Young modulus
E
210 × 109 N/m2
System responses were monitored for duration of 133s with sampling time of 2ms.
Second moment of area
I
2.37× 10−7 m4
Payload mass
Me
14.1 kg
• Long slender beam • Payload mass fixed at beam’s end-point • Actuator: a single axis robotic joint with speed reducer • Resolver optical sensor for joint angular position measurement • Laser tracker Leica to measure the beam end-point position with 5E10-5 m accuracy
SAMCEF: Computer-Aided Engineering Software for simulation of mechanical systems X2
Analysis purpose: to study the transient response of the structure it is necessary to take into account • stiffness of elements • kinematical effects • inertia effects
Lumped mass
SE n° 1
Gravity
arm Reducer unit
Applied Super element method: decrease the size of the problem to solve by replacing different regions of the structure with their equivalent stiffness and mass properties.
Beam SE n° 2
arm
• provides a complete environment for performing Finite Element Analysis (linear, non linear, modal…). Super elements assembled using kinematic joints
SE n° 3
θ2
θ1
Flange Flange
• uses simultaneously structural elements, kinematical joints (hinge joints, prismatic joints, gear elements…), rigid elements and super-elements in the same model.
Super element use phase: non linear dynamic transient response
Super elements creation phase: 3 dynamic super elements created
Axis
Axis
SAMCEF software:
θi: Relative rotation in the hinge joint n° i. R : Reducer ratio (i.e R = 120).
Real structure modeling particularity: • Speed reducer behavior modeled by means of a kinematical constraint between relative rotations in 2 hinge joints
• Robotic joint replaced by 3 super-elements • Super-elements linked with a flexible beam and a concentrated mass with ideal kinematical joints (rigid hinge joints, rigid bodies).
• Viscous damping is taken into account.
Note that all bearings are assumed to be rigid and replaced by rigid bodies and lumped masses.
• Friction effects are neglected.
• Dynamical equation solved during computation:
• All physical properties (beam length, value of the lumped mass…) and materials characteristics used for the computation are deduced from measurements made on the experimental assembly.
C.q K .q F M .q M - inertia matrix ; C - centrifugal and Coriolis effects matrix; K - stiffness matrix; F - applied torques matrix.
Note that all materials are assumed to remain elastic.
Comparison of experimental and simulation results Vertical direction 2.8
Samcef real position Leica real position Stimulation signal
2.6
2
Horizontal direction 2.4
• Good agreement between experimental values and calculations
1
Y [m]
-1
1.4
Samcef real position Leica real position Stimulation signal
-2
1.2 20
40
60
80
100
-3 0
20
40
time[s]
60
80
Oscillations due control scheme
to
Model input signal = real encoder position
60 80 100 time[s] Tangential errors for both calculation and experiment (real stimulation) 0.1 Leica error Samcef error 0.05
20
40
0 -0.05 -0.1 0
60
80
Tangential error along the movement
0
X[m]
position [m]
0
100
Tangential errors for both calculation and experiment
4
0.08
3.5
0.06
Leica error Samcef error
3
0.5
advance
40
Case of a rigid rod:
3.5
1.2
1.1
20
Tangential error along the movement 4
1.3
1.15
-0.05
time[s]
1
Samcef real position Leica real position Stimulation signal
0
-0.1 0
time[s]
Zoom on the three positions
X [m]
• Necessity to take elastic energy accumulated within the joint into account during movements for good prediction of real position
100
Advance/delay of the real position compared to the stimulation signal 1
1.25
Model input signal = desired position
2.5
0.04
3
2
2.5
X[m]
1 0
to
• Vibrations are coming both from transients and control scheme
0
1.8 1.6
Oscillations due starting phase
Tangential errors for both calculation and experiment (theoretical stimulation) 0.1 Leica error Samcef error 0.05
Tang. error [m]
X [m]
2.2 2
• Displacement of the end-point of the beam essentially in tangent direction (lowest stiffness direction)
Tang. error [m]
Comparison of the three positions: stimulation, calculation, measurements 3
Tang. error [m]
Comparison of the three positions: stimulation, calculation, measurements 3
1.5
Rod movement
1
2
0.02 0 -0.02
1.5
-0.04
1
-0.06
1.05
0.5
-0.5 1 0
10
15
20
time[s]
-1 -1 0
20
40
60 time[s]
80
100
-3
-2
-1
0 Y[m]
1
2
3
0.5
-3
-2
-1
0 Y[m]
1
2
• Dynamical effects • Discharge of the elastic energy of the joint
3
-0.08 0
20
40
60
80
100
time[s]
No rod deflection anymore Still a dynamical effect
30% of the error due to joint flexibility only
Conclusions Experimental results proved the necessity to take into account dynamical loads in the positioning of the end-effector of robotic arms. Dynamical errors and static errors are of the same order of magnitude and therefore can not be underestimated in the control schemes. Expensive experimental mock-up needed for calibration of the control model could take advantage of software like SAMCEF integrating the effect of dynamical loads.
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