Modeling & Simulation of a Spring-Assisted Robot Arm

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

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

Motor Parameters Design


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

Switching Mass


Halfway through trajectory the payload mass is decreased from 60 kg to 1kg simulates picking & placing

Controller Design 1/2 - Inverse Dynamics


Advantage- inverse dynamics automatically calculates needed voltage

for given angle PID controllers have minor work to do to compensate uncertainties and disturbances



But how to realize Inverse Dynamics? - change all inputs to outputs


comicforum.de

But how to realize Inverse Dynamics? - change all inputs to outputs



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


INVERSION of motor & mechanics

Example

Controller Design 2/2 – PID controller used in project


Advantage- SISO control design easy

Disadvantages- PID controllers pull all the weight Trick: make controller extremely stiff: P=40 000 !!

Overall Model Structure

Trajectories, PID Controllers, DC Motors & Mechanics Error & Energy measurement performance attributes

Animation for Fixed Path


What is the Spring good for?


parabolic function for energy consumption more than 50% energy savings possible

Max Motor speed

Ener

gy c

onsu

mpti

on

Spring sti

ffness

Detailed Demand Spreadsheet



Modify Profit in `ProfitUtility´ spreadsheet- For discount factors- Discount Limits


Modify this and drag to right and down

Realize with if statement


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´


Modify this and drag to right and down

change

In TEAM_USE In ProfitUtility using Pre-predictor

Motor Cost & Loop


Motor Cost as design variable ´Loop´ in spreadsheet can be seen in influence diagram

Design Space Exploration & Optimization


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.

Design Problem Results


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

Bomfunk MC‘s - Freestyler


THANK YOU VERY MUCHFOR YOUR ATTENTION!

QUESTIONS?

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Modeling & Simulation of a Spring-Assisted Robot Arm