Optimization of Pallet Packaging Space and a Robotic SCARA Manipulator for Package Stacking 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. 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 Manipulability Topology Trajectory Link lengths Mass of links Pallet Space Box Locations Randomized boxes

Optimization of pallet space This 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 faced Since 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.

Algorithm The 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

Robot Arm Configuration Optimization for Maximum Manipulability 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. Link-2 Link-3

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 decrease Effect of parameter on joint length

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 joint Constraint Max: Stress Objective Function (Goal) Min: Mass Assumptions Material of the robot: Al-Alloy The height of the Robot

Design Study of the links Link 3 Link 2

Optimization Difficulties How 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.

Graphs End Load vs Mass of the links

Trajectory/Control Optimization Total $ lost from energy consumption Total $ made from all stacked boxes

Trajectory Difficulties Encountered Not 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

Results 15 th order selected

Resulting 15 th order Trajectory

Improvement of the optimized trajectory compared to the linear case Money Lost due to energy consumption Linear ($)Optimized ($) Link 214e e-4 Link e e-4 Total-15e e-04

Sensitivity and Parameter Analysis

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