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7 <strong>Control</strong> approach – ELAU GmbH ....................................................................................... 33 7.1 MC-4 Drive .................................................................................................................. 34 7.2 Motor ............................................................................................................................ 34 7.3 Tracking Error .............................................................................................................. 34 8 Simulink model.................................................................................................................... 35 8.1 MC-4 ............................................................................................................................ 36 8.2 Motor ............................................................................................................................ 36 8.3 Manipulator .................................................................................................................. 37 9 Parameter estimation ........................................................................................................... 38 10 Experiments ......................................................................................................................... 40 11 Results ................................................................................................................................. 41 11.1 Simulink model compared with real robot ............................................................... 41 11.1.1 Simulink Experiment 1 ......................................................................................... 41 11.1.2 Simulink Experiment 2 ......................................................................................... 46 11.1.3 Simulink Experiment 3 ......................................................................................... 51 11.1.4 Discussion ............................................................................................................. 54 11.2 Jacobian matrix Results in EPAS ............................................................................. 55 11.2.1 Jacobian Experiment 1 .......................................................................................... 55 11.2.2 Jacobian Experiment 2 .......................................................................................... 58 11.2.3 Jacobian Experiment 3 .......................................................................................... 62 11.2.4 Discussion ............................................................................................................. 64 12 Conclusions ......................................................................................................................... 66 13 References ........................................................................................................................... 67 ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 2
1 INTRODUCTION 1.1 MOTIVATION The company ELAU GmbH which is the global Packaging Solution Center for Schneider Electric has developed an own Delta-3 robot controlled with ELAU GmbH own motors, drive units and controller unit. This Master Thesis treats the modeling of the Delta-3 robot actuated with ELAU GmbH own motors and drive units. Also the kinematics for a Delta-3 robot is implemented to be able to see where the traveling plate has for position for different arm angle configurations. 1.2 SOFTWARE AND HARDWARE USED IN THESIS To simulate the Delta-3 robot actuated with ELAU GmbH own controller, drive units and motors Matlab Simulink was used. To create trajectory motions for the Delta-3 robot to use in Simulink ELAU GmbH own programming software EPAS-4 was used. These trajectories was first simulated in EPAS-4 then transferred into Matlab Simulink so the same reference was used in both the Simulink model when simulating the robot and in EPAS-4 when controlling the real robot. When creating trajectories for only one motor simulation ELAU GMBHSs own motion toolkit ECAM-4 was used. The computer software Mathematica was used to solve the equations for kinematic transformation and the dynamics equations for the Delta-3 robot. 1.3 NOTATIONS The following notations are used in the thesis. 1.3.1 ACRONYMS The following acronyms are used: TCP Tool center point DOF Degree of freedom 1.3.2 VARIABLES AND PARAMETERS The following variables and parameters are used in the thesis. {R} reference frame at the base plate {Ri} R iRz reference frame for arm i transformation matrix between frames {Ri} and {R} θ1 angle of the first upper arm attached to motor 1 θ2 angle of the second upper arm attached to motor 2 angle of the third upper arm attached to motor 3 θ3 ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 3
Page 1: ISSN 0280-5316 ISRN LUTFD2/TFRT--58
Page 5: Acknowledgements This Master thesis
Page 10 and 11: α1 frame rotation angle for arm at
Page 12 and 13: 2 BACKGROUND 2.1 ROBOTICS The word
Page 14 and 15: 2.2.2 SOFTWARE - ELAU GMBH EPAS-4 i
Page 16 and 17: 3 KINEMATICS - SERIAL ROBOT In the
Page 18 and 19: 3.2 INVERSE KINEMATICS When the for
Page 20 and 21: 4 KINEMATICS & KINETICS - DELTA-3 R
Page 22 and 23: 4.3 Forward Kinematics The forward
Page 24 and 25: Figure 4.5, inverse kinematics tran
Page 26 and 27: where & ⎡x& n ⎤ ⎡− lA sin(
Page 28 and 29: 4.7 ACTUATOR DYNAMICS In most exist
Page 30 and 31: The inertia contribution of each up
Page 32 and 33: According to d’Alembert’s princ
Page 34 and 35: 5 TRAJECTORY A trajectory is a path
Page 36 and 37: 6 TRAJECTORY - ELAU GMBH C600 is th
Page 38 and 39: 6.2 CIRCULAR INTERPOLATION In the E
Page 40 and 41: 7.1 MC-4 DRIVE The MC-4 drive is a
Page 42 and 43: Figure 8.2, Simulink model with mot
Page 44 and 45: 9 PARAMETER ESTIMATION To simulate
Page 46 and 47: 10 EXPERIMENTS For the experiments
Page 48 and 49: Figure 11.2, shows the motion of th
Page 50 and 51: Figure 11.6, shows the current I ef
Page 52 and 53: 11.1.2 SIMULINK EXPERIMENT 2 Figure
Page 54 and 55: Figure 11.13, shows the acceleratio
Page 56 and 57: measured actual value from the real
Page 58 and 59:
and are shown over the time in seco
Page 60 and 61:
Figure 11.23 shows the x, y and z c
Page 62 and 63:
Figure 11.27, the blue line shows t
Page 64 and 65:
Figure 11.31, the blue line shows t
Page 66 and 67:
In Figure 11.36 the blue line repre
Page 68 and 69:
11.2.3 JACOBIAN EXPERIMENT 3 Figure
Page 70 and 71:
In Figure 11.44 the blue line repre
Page 72 and 73:
12 CONCLUSIONS In section 11.1 one
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