Murad Muradi - Quantum Annealing based Optimization of Robotic Movement in Manufacturing

Murad Muradi
04.04.2019
WORKING DRAFT.
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BLOCKCHAIN.
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LT-1 RUNDE.
DAQARI CORP.
HARD- UND SOFTWARE
QUANTUM INSPIRED OPTIMIZATION OF ROBOTIC
MOVEMENTS IN MANUFACTURING.
04.04.2019

Seite 2Quantum inspired optimizationof roboticprocesses in manufacturing | 04.04.2019
AGENDA.
Experimental Setup3
Results4
Use Case Introduction1
Formal Description2

Use-Case
Introduction

USE-CASE INTRODUCTION.
PVC SEALING PROCESS.
PVC Sealing servesto sealthe gaps of joined sheets,thereby preventing the ingress of corrosive media.

USE-CASE INTRODUCTION.
DEFINITION OF TASK.
RoboticTask
Calculation of a production plan in which all seams are processed within a given cycle time.
b
c
1
a
d
f
g
2
e h
3
Scheduling:
Efficient allocation of tasks to available robots.
Sequencing and Motion Planning:
Minimizing the routes for all robots and creation of collision-
free robot movements.
OptimizationTasks
Goals
 Increasing efficiency of existing production facilities.
 Reduction of planning effort for integration of new
workloads.
 Increasing flexibility in production.
 Improved dynamic design of robot movements.

Formal
Description

FORMAL DESCRIPTION.
PROBLEM MODELLING*.
Modelling as weighted graph
 𝐺 = 𝑉, 𝐸, 𝑊
 𝑉 = 𝑉𝑟 ∪ 𝑖=1
𝑁
𝑉𝑖
1
, 𝑉𝑖
2
 𝐸 = 𝑖=1
𝑁
𝑗=1
𝑗≠𝑖
𝑁
𝑉𝑖
1
, 𝑉𝑗
1
, 𝑉𝑖
1
, 𝑉𝑗
2
, 𝑉𝑖
2
, 𝑉𝑗
1
, 𝑉𝑖
2
, 𝑉𝑗
2
∪ 𝑖=1
𝑁
𝑉𝑟, 𝑉𝑖
1
, 𝑉𝑟, 𝑉𝑖
2
 𝑊: 𝐸 → [0, ∞)
Logical variables
 𝒙 = 0, 1 2𝑁2
 Meaning of logical variable 𝑥𝑖,𝑡
𝑑
:
Robot should process ith task at stept in direction d
taks 1
taks 2
*) QC Ware

FORMAL DESCRIPTION.
OBJECTIVE FUNCTION*.
𝑓 𝒙 = 𝑓𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝒙 + 𝑓𝑡𝑎𝑠𝑘𝑠 𝒙 + 𝑓𝑡𝑖𝑚𝑒 𝒙
Distance travelled by the robot betweenthetasks.
𝑓𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝒙 =
𝑘,𝑙=1
2
𝑖=1
𝑁
𝑗=1
𝑗≠𝑖
𝑁
𝑡=1
𝑁
𝑊 𝑣𝑖
𝑙
, 𝑣𝑗
𝑘
2
𝑥𝑖,𝑡
𝑙
𝑥𝑗,𝑡+1
𝑘′
+ 𝑥𝑗,𝑡
𝑘
𝑥𝑖,𝑡+1
𝑙′
+
𝑖=1
𝑁
𝑊 𝑣𝑟, 𝑣𝑖
2
𝑥𝑖,1
1
+ 𝑊 𝑣𝑟, 𝑣𝑖
1
𝑥𝑖,1
2
Constraint that alltasks are performed exactly once.
𝑓𝑡𝑎𝑠𝑘 𝒙 =
𝑖=1
𝑁
𝑃𝑡𝑎𝑠𝑘
𝑖
1 −
𝑡=1
𝑁
𝑥𝑖,𝑡
1
+ 𝑥𝑖,𝑡
2
2
Constraint that at eachtime step, exactly one task is performed.
𝑓𝑡𝑖𝑚𝑒 𝒙 = 𝑃𝑡𝑖𝑚𝑒
𝑡=1
𝑁
1 −
𝑖=1
𝑁
𝑥𝑖,𝑡
1
+ 𝑥𝑖,𝑡
2
2
*) QC Ware

Experimental
Setup

EXPERIMENTAL SETUP.
QUANTUM ANNEALING*.
Hardware: DWave 2000Q
Annealing Cycle:
 Lessthan 4tasks 10.000 cycles.
 Morethan 4tasks 1.000.000 cycles.
For testing the use case the robotic tasks are defined in 2D.
Following isthe definition of thetasks along with start and end coordinate of eachtasks, along withthe velocity of robot.
Task Start End Velocity
a (287, 619) (17, 479) 94
b (595, 627) (592, 52) 58
c (488, 353) (43, 565) 68
d (450, 142) (688, 580 63
e (136, 403) (630, 170) 70
*) QC Ware

EXPERIMENTAL SETUP.
DIGITAL ANNEALING*. 12 fixed seams
for Robot 1
12 fixed seams
for Robot 2
10variable seams
for Robot 1 and 2
24 fixed seams
10variable seams (1024 possible seam allocations)
Examined Scope:
 34 seams
 2 robots
 1 nozzle
 1 position on linear axis
*) Fujitsu

Results

FROM THE MANUFACTURING PROBLEM TO A QUANTUM INSPIRED SOLUTION.
1 2
Build model from
production process
Experimental implementation
3
Comparison of
the solutions
Distance Matrix
Quantum Annealing (QA) Digital Annealing (DA)Simulated Annealing (SA)

QA Hardware is still in a development phase and requires further development for bringing concrete business value.
KEY TAKEAWAYS
• QA approach successfully foundthe optimal solution.
• Dueto hardware limitations only roundtrips with upto 5 seams could be solved.
RESULTS.
QUANTUM ANNEALING.
Performance

RESULTS.
DIGITAL ANNEALING.
Processing Time
KEY TAKEAWAYS
• Roundtrips with upto 22 seams per Robot could be solved.
• Evaluation on 1024 different work distributions between 2 robots
• Computation time is 1-2 magnitudes faster than SA.
• Result quality is similar to SA and up to 7 % better than NN.
Seam Allocation
ProcessingTime
Simulated Annealing
Digital Annealing
Nearest Neighbor
Next Generation of Digital Annealer is capable totackle business relevant problems.
Seam Allocation
KEY TAKEAWAYS
• Notrivial solution for seam allocation.
• There are seams closer to Robot 1, but processed by Robot 2 and
vice versa.
Robot1 Robot2
Midplane

THANKS FORYOUR ATTENTION!
QUESTIONS?
quantumcomputing@bmw.de

QUANTUM COMPUTING TEAM @ BMW.
Murad Muradi
TP-322
Robotics / PVC Sealing
Oliver Wick
LT-7
Research / Scout
Stefan Benesch
FG-250
BigData
Bernhard Pflugfelder
FG-26
Big Data / AI Network
SelamWoldetsadick
FG-250
Big Data
Johannes Müller
FG-845
HPC
Marvin Erdmann
EE-541
CarSharing
Arpit Mehta
FG-250
Machine Learning
Markus Müller
LT-7
Research/DigAnnealer
UseCase
Owner
Core
Team
Khanh-Huy Tan
FG-130
IT Innovation
Thomas Hubregtsen
LT-3
Quantum Computing, AI

RESULTS.
KEY TAKEAWAYS
• Dueto hardware limitations only roundtrips with upto 5 seams
could be solved.
• Found Solution was optimal.
Quantum Annealing
QA Hardware is still in a premature phase and requires
further development to getting a business value.
Digital Annealing
KEY TAKEAWAYS
• Roundtrips with upto 22 seams per Robot could be solved.
• Evaluation on 1024 different work distributions between 2 robots
• Computation time is 1-2 magnitudes faster than SA.
• Result quality is similar to SA and up to 7 % better than NN.
Next Generation of Digital Annealer is capabletotackle
business relevant problems.
Seam Allocation
ProcessingTime
Simulated Annealing
Digital Annealing
Nearest Neighbor

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