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Modeling & Simulation of a Spring-Assisted Robot Arm
ME 6105 Fall 2012 – 12/06/2012 Lewis Lo, Benjamin Daniels, Matthew Rosen, Merlin Morlock
abb.com
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4 axis robot based on the ABB IRB660 palletizing & materials handling up to 250 kg load Torsional spring at lower arm Goal: design a motor with spring at lower arm joint to maximize utility
performance attributes: 1. Energy consumption 2. End-
effector position error
Introduction & Domain
ME6105 - Spring Assisted Robot Arm
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Motor Parameters Design
ME6105 - Spring Assisted Robot Arm
Back calculating Torque (~20kN) to find k and R, motor paramters Use of gear box (~182/1)to increase Torque
Thanks for help from Prof. Paredis in Motor Cost estimation
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Switching Mass
ME6105 - Spring Assisted Robot Arm
Halfway through trajectory the payload mass is decreased from 60 kg to 1kg simulates picking & placing
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Controller Design 1/2 - Inverse Dynamics
ME6105 - Spring Assisted Robot Arm
Advantage- inverse dynamics automatically calculates needed voltage
for given angle PID controllers have minor work to do to compensate uncertainties and disturbances
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Controller Design 1/2 - Inverse Dynamics
ME6105 - Spring Assisted Robot Arm
But how to realize Inverse Dynamics? - change all inputs to outputs
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Controller Design 1/2 - Inverse Dynamics
comicforum.de
But how to realize Inverse Dynamics? - change all inputs to outputs
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Controller Design 1/2 - Inverse Dynamics
ME6105 - Spring Assisted Robot Arm
But how to realize Inverse Dynamics? Let Dymola do the work!- copy model- change all inputs to outputs and vice versa e.g sensors to actuators and vice versa- make resistance negative- make damping negative
Disadvantage of Dymola Trick- problems occured with multiple inputs and outputs when
there is damping & resistance
PhysicallyNot meaningfulBut does the job
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ME6105 - Spring Assisted Robot Arm
INVERSION of motor & mechanics
Example
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Controller Design 2/2 – PID controller used in project
ME6105 - Spring Assisted Robot Arm
Advantage- SISO control design easy
Disadvantages- PID controllers pull all the weight Trick: make controller extremely stiff: P=40 000 !!
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Overall Model Structure
Trajectories, PID Controllers, DC Motors & Mechanics Error & Energy measurement performance attributes
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Animation for Fixed Path
ME6105 - Spring Assisted Robot Arm
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What is the Spring good for?
ME6105 - Spring Assisted Robot Arm
parabolic function for energy consumption more than 50% energy savings possible
Max Motor speed
Ener
gy c
onsu
mpti
on
Spring sti
ffness
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Detailed Demand Spreadsheet
ME6105 - Spring Assisted Robot Arm
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Detailed Demand Spreadsheet
Modify Profit in `ProfitUtility´ spreadsheet- For discount factors- Discount Limits
ME6105 - Spring Assisted Robot Arm
Modify this and drag to right and down
Realize with if statement
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Detailed Demand Spreadsheet
Modify Utility in `ProfitUtility´ spreadsheet- introduce time preference discount profit and plug in into utility function
But don‘t forget to change the calculation of expected demand since cost depends on demand now = `loop´
ME6105 - Spring Assisted Robot Arm
Modify this and drag to right and down
change
In TEAM_USE In ProfitUtility using Pre-predictor
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Motor Cost & Loop
ME6105 - Spring Assisted Robot Arm
Motor Cost as design variable ´Loop´ in spreadsheet can be seen in influence diagram
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Design Space Exploration & Optimization
ME6105 - Spring Assisted Robot Arm
Optimum Under Uncertainty at:
Max Motor Speed 760.91
Motor Cost $703.83
Spring Stiffness 302.33
Utility $246874000
Error 0.16875
Energy (kJ) 70
• Changed of modification cost at zero spring size to exponential function to ensure smooth design surface
• Optimization results not too close to design space bounds.
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Design Problem Results
ME6105 - Spring Assisted Robot Arm
Profit
Attribute Certainty UncertaintyProfit $352,485,298 $351,495,061
Optimal Price $59,589 $59,347Unit Cost $33,824.83 $33,901.00Demand 0.43683 0.44436
Market Share 14272 14487Energy - KJ 70 70
Error 0.16813 0.16804
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Bomfunk MC‘s - Freestyler
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ME6105 - Spring Assisted Robot Arm
THANK YOU VERY MUCHFOR YOUR ATTENTION!
QUESTIONS?