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

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Group-4. 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

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

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Optimization of Pallet Packaging Space and a Robotic SCARA Manipulator for Package StackingGroup-4
Puneet JethaniErica NeupergerSiddharth KodgiZarvan Damania
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
Introduction to subsystems
ManipulabilityTopology
Trajectory
Joint angles:
Link lengths
Mass of links
Assume max
Pallet Space
Box Locations
Randomized boxes
Assume max
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 specified
Constraints
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.
Goal
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.
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.
Results
Violates constraints
Removed from the solution
Violates constraints
Removed from the solution
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 =
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
0
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 Robot
1
Design Study of the links
Link 3
Link
2
2
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.
3
Graphs
End Load vs Mass of the links
4
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 boxes
5
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 function
6
Results
15
th
order selected
7
Resulting 15th order Trajectory
8
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-04
9
Sensitivity and Parameter Analysis
0
Thank you