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Optimization of Pallet Packaging Space and a Robotic SCARA Manipulator for Package Stacking Optimization of Pallet Packaging Space and a Robotic SCARA Manipulator for Package Stacking

Optimization of Pallet Packaging Space and a Robotic SCARA Manipulator for Package Stacking - PowerPoint Presentation

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Uploaded On 2018-11-07

Optimization of Pallet Packaging Space and a Robotic SCARA Manipulator for Package Stacking - PPT Presentation

Group4 Puneet Jethani Erica Neuperger Siddharth Kodgi Zarvan Damania Abstract and Inspiration for the Idea The number of robotic manipulators used in industry grows with each year ID: 720264

boxes link mass length link boxes length mass pallet constraints optimization robot order trajectory joint goal function objective number

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Slide1

Optimization of Pallet Packaging Space and a Robotic SCARA Manipulator for Package StackingGroup-4

Puneet JethaniErica NeupergerSiddharth KodgiZarvan DamaniaSlide2

Abstract and Inspiration for the IdeaThe number of robotic manipulators used in industry grows with each year

. Need to be able to perform repetitive tasks both quickly and precisely Goal: Optimization of stacking boxes in an industrial setting, using a SCARA robot. The robot will perform the task of picking up boxes and placing them onto a shipping pallet.

Pallet

Box

 

 

L

 

 

 

 

 Slide3

Introduction to subsystems

ManipulabilityTopology

Trajectory

Joint angles:

 

Link lengths

Mass of links

Assume max

 

Pallet Space

Box Locations

Randomized boxes

Assume max

 Slide4

Optimization of pallet spaceThis part of the project deals with the logistics part of the project.The inputs for the system are a bunch of boxes that need to be arranged in a manner that utilizes maximum volume of the pallet.

This order is then given to the robot which then places them in the order specifiedConstraints

The constraints were mainly the standard dimension of the pallet. So the height of the stacked boxes cannot go higher than the acceptable height.

The following is the standard dimension of the pallet.

Lp

= 48 inches,

Wp

= 40 inches,

Hp

= 60 inches when transported by air,

Hp

= 85 inches when transported by sea.

The

goal of this subsystem is to determine the arrangement of the boxes which maximum utilizes the space of the pallet.

GoalSlide5

Challenges facedSince this is a discrete optimization problem, there is no direct objective function which could be solved using a standard solver.

The problem was solved using an Generic algorithm and heuristics.The most difficult was part of the subsystem was to code the algorithm to work for random bunch of boxes.

Algorithm

Assumptions

For implementation purpose, the result shows just one vertical layer of the boxes placed.

The boxes placed at the bottom are heavier and have large lengths as compared to boxes on top.

The method:

We initialize an 1-D array of size equal to the length of the base.

When no boxes are placed, all the elements are zero.

As and when we keep placing the boxes, the elements of the array reflect the height of boxes at those locations.Slide6

AlgorithmThe minimum number on the array gives the lowest gap available to us.The number of times these elements occur gives the width of the gap.Slide7

Results

Violates constraints

Removed from the solution

Violates constraints

Removed from the solutionSlide8

Constraints

: 𝜏2.≤𝜏𝑚𝑎𝑥2

: 𝜏3

.

𝜏𝑚𝑎𝑥3

:

:

:

 

Robot Arm

C

onfiguration

O

ptimization for Maximum

M

anipulability

To design robotic arm for specific purpose( Pallet packing, Car assembly etc…)

Advantages:- Increased workspace, reduced working cost, higher efficiency.

Manipulability

is the ability of manipulating or moving robotic arm to some arbitrary position at minimum effort

To fix the parameter value (mass).

Used neural network to calculate mass of link for each iteration

Non-linear constraints, Used fmincon to optimize.

Objective function

w=

Dependent on joint angles and joint lengths

 

Link-2

Link-3

Variables

Link length 2 =

Link length 3 =

Joint angle two =

 Slide9

Torque motor 3 increases, link length 3 will increase, and link length 2 will decrease.Torque motor 2 increases, link length

2 will increase, and link length 3 will decreaseEffect of parameter on joint length

Results

=

34 in

=

30 in

 Slide10

Structure & Topology Optimization

Topology optimization is carried out on different parts of the robot.Design Variables Width Thickness Inner Width Inner Length Diameter of the jointConstraint Max: Stress

Objective Function (Goal)

Min: Mass

Assumptions

Material of the robot: Al-Alloy

The height of the RobotSlide11

Design Study of the links

Link 3

Link

2Slide12

Optimization DifficultiesHow to relate the mass of link 2 with mass of link 3 ?

The difficulty was overcome by using Neural Network.The training algorithm used was Levenberg - Marqardt.Length of link 3 was used as input and the mass of the link 3 was used as output. Length of link 2 and Mass of Link 3 was used as inputs and the Mass of link 2 was used as the output.Slide13

Graphs

End Load vs Mass of the links Slide14

Trajectory/Control Optimization

Goal: Determine time of trajectory

and

over time for the 1

st

two links, where

Objective:

Constraints:

- 4 equality constraints for initial and final joint angles and velocity

-3 inequality constraints that must be satisfied at every point in time

 

Total $ lost from energy consumption

Total $ made from all stacked boxesSlide15

Trajectory Difficulties EncounteredNot easy to explicitly write function for the gradient and hessian AMPL is used in order to perform “automatic differentiation”

The KNITRO solver was used in order to deal with the large number of nonlinear inequality constraints and nonlinear objective functionSlide16

Results

15

th

order selected Slide17

Resulting 15th order TrajectorySlide18

Improvement of the optimized trajectory compared to the linear case

Money

Lost due to energy consumption

Linear ($)

Optimized ($)

Link

2

14e-4

6.812e-4

Link

3

7.886e-6

2.316e-4

Total

-15e-4

-9.1357e-04Slide19

Sensitivity and Parameter AnalysisSlide20

Thank you