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Research Papers

Design for Additive Manufacturing: Optimization of Piping Network in Compact System With Enhanced Path-Finding Approach

[+] Author and Article Information
Pei Cao

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269

Zhaoyan Fan

Department of Mechanical,
Industrial and Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97331

Robert X. Gao

Cady Staley Professor of Engineering,
Department of Mechanical and
Aerospace Engineering,
Case Western Reserve University,
Cleveland, OH 44106

J. Tang

Professor
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: jiong.tang@uconn.edu

1Corresponding author.

Manuscript received November 20, 2017; final manuscript received May 11, 2018; published online June 4, 2018. Assoc. Editor: Sam Anand.

J. Manuf. Sci. Eng 140(8), 081013 (Jun 04, 2018) (15 pages) Paper No: MANU-17-1724; doi: 10.1115/1.4040320 History: Received November 20, 2017; Revised May 11, 2018

This research aims at unleashing the potential of additive manufacturing technology in industrial design that can produce structures/devices with irregular component geometries to reduce sizes/weights. We explore, by means of path-finding, the length minimization of freeform hydraulic piping network in compact space under given constraints. Previous studies on path-finding have mainly focused on enhancing computational efficiency due to the need to produce rapid results in such as navigation and video-game applications. In this research, we develop a new Focal Any-Angle A* approach that combines the merits of grid-based method and visibility graph-based method. Specifically, we formulate pruned visibility graphs preserving only the useful portion of the vertices and then find the optimal path based on the candidate vertices using A*. The reduced visibility graphs enable us to outperform approximations and maintain the optimality of exact algorithms in a more efficient manner. The algorithm proposed is compared to the traditional A* on Grids, Theta* and A* on visibility graphs in terms of path length, number of nodes evaluated, as well as computational time. As demonstrated and validated through case studies, the proposed method is capable of finding the shortest path with tractable computational cost, which provides a viable design tool for the additive manufacturing of piping network systems.

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References

Gibson, I. , Rosen, D. W. , and Stucker, B. , 2010, Additive Manufacturing Technologies, Vol. 238, Springer, New York. [CrossRef]
Frazier, W. E. , 2014, “ Metal Additive Manufacturing: A Review,” J. Mater. Eng. Perform., 23(6), pp. 1917–1928. [CrossRef]
Zhou, C. , 2014, “ A Direct Tool Path Planning Algorithm for Line Scanning Based Stereolithography,” ASME J. Manuf. Sci. Eng., 136(6), p. 061023. [CrossRef]
Cao, P. , Fan, Z. , Gao, R. , and Tang, J. , 2016, “ A Framework of a Fast Any-Angle Path Finding Algorithm on Visibility Graphs Based on a* for Plumbing Design,” IEEE International Symposium on Flexible Automation (ISFA), Cleveland, OH, Aug. 1–3, pp. 333–339.
Lipson, H. , 2013, Fabricated: The New World of 3D Printing, Kurman, M. , Wiley, Indianapolis, IN.
Rabin, S. , 2002, “ Implementing a State Machine Language,” AI Game Programming Wisdom, Charles River Media, Rockland, MA, pp. 314–320.
Sturtevant, N. R. , and Geisberger, R. , 2010, “ A Comparison of High-Level Approaches for Speeding Up Pathfinding,” Conference on Artificial Intelligence and Interactive Digital Entertainment (AIIDE), Palo Alto, CA, Oct. 11–13, pp. 76–82.
Konar, A. , Chakraborty, I. G. , Singh, S. J. , Jain, L. C. , and Nagar, A. K. , 2013, “ A Deterministic Improved Q-Learning for Path Planning of a Mobile Robot,” IEEE Trans. Syst., Man, Cybern. Syst., 43(5), pp. 1141–1153. [CrossRef]
Rakshit, P. , Konar, A. , Bhowmik, P. , Goswami, I. , Das, S. , Jain, L. C. , and Nagar, A. K. , 2013, “ Realization of an Adaptive Memetic Algorithm Using Differential Evolution and q-Learning: A Case Study in Multirobot Path Planning,” IEEE Trans. Syst., Man, Cybern.: Syst., 43(4), pp. 814–831. [CrossRef]
LaValle, S. M. , 2006, Planning Algorithms, Cambridge University Press, Cambridge, UK. [CrossRef]
Cui, R. , Li, Y. , and Yan, W. , 2016, “ Mutual Information-Based Multi-AUV Path Planning for Scalar Field Sampling Using Multidimensional RRT,” IEEE Trans. Syst., Man, Cybern. Syst., 46(7), pp. 993–1004. [CrossRef]
Algfoor, Z. A. , Sunar, M. S. , and Kolivand, H. , 2015, “ A Comprehensive Study on Pathfinding Techniques for Robotics and Video Games,” Int. J. Comput. Games Technol., 2015(7), p. 736138.
Dijkstra, E. W. , 1959, “ A Note on Two Problems in Connexion With Graphs,” Numer. Math., 1(1), pp. 269–271. [CrossRef]
Hart, P. E. , Nilsson, N. J. , and Raphael, B. , 1968, “ A Formal Basis for the Heuristic Determination of Minimum Cost Paths,” IEEE Trans. Syst. Sci. Cybern., 4(2), pp. 100–107. [CrossRef]
Rabin, S. , 2000, “ A* Speed Optimizations,” Game Programming Gems, M. DeLoura, ed., Charles River Media, Rockland, MA, pp. 272–287.
Thorpe, C. , and Matthies, L. , 1984, “ Path Relaxation: Path Planning for a Mobile Robot,” IEEE OCEANS, Washington, DC, Sept. 10–12, pp. 576–581.
Botea, A. , Müller, M. , and Schaeffer, J. , 2004, “ Near Optimal Hierarchical Path-Finding,” J. Game Dev., 1(1), pp. 7–28. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.314
Daniel, K. , Nash, A. , Koenig, S. , and Felner, A. , 2010, “ Theta*: Any-Angle Path Planning on Grids,” J. Artif. Intell. Res., 39, pp. 533–579.
Ferguson, D. , and Stentz, A. , 2006, “ Using Interpolation to Improve Path Planning: The Field D* Algorithm,” J. Field Rob., 23(2), pp. 79–101. [CrossRef]
Koenig, S. , and Likhachev, M. , 2002, “ D* Lite,” Association for the Advancement of Artificial Intelligence/IAAI, Menlo Park, CA, pp. 476–483.
Nash, A. , and Koenig, S. , 2013, “ Any-Angle Path Planning,” AI Mag., 34(4), pp. 85–107. [CrossRef]
Nash, A. , Daniel, K. , Koenig, S. , and Felner, A. , 2007, “ Theta*: Any-Angle Path Planning on Grids,” National Conference on Artificial Intelligence, Vancover, BC, Canada, July 22–26, pp. 1177–1183. http://idm-lab.org/bib/abstracts/papers/aaai07a.pdf
Nash, A. , Koenig, S. , and Tovey, C. , 2010, “ Lazy Theta*: Any-Angle Path Planning and Path Length Analysis in 3D,” Third Annual Symposium on Combinatorial Search, Atlanta, GA, July 8–10, pp. 153–154.
Dang, V. H. , Thang, N. D. , Viet, H. H. , and Tuan, L. A. , 2015, “ Batch-Theta* for Path Planning to the Best Goal in a Goal Set,” Adv. Rob., 29(23), pp. 1537–1550. [CrossRef]
Šišlák, D. , Premysl, V. , and Michal, P. , 2009, “ Accelerated a* Trajectory Planning: Grid-Based Path Planning Comparison,” 19th International Conference on Automated Planning and Scheduling (ICAPS), Thessaloniki, Greece, Sept. 19–23, pp. 74–81. https://pdfs.semanticscholar.org/77f1/306116d27fdce4b911d6b9451e6c37f81812.pdf
Harabor, D. D. , and Grastien, A. , 2013, “ An Optimal Any-Angle Pathfinding Algorithm,” International Conference on Automated Planning and Scheduling (ICAPS), Rome, Italy, June 10–14, pp. 308–311. https://www.aaai.org/ocs/index.php/ICAPS/ICAPS13/paper/download/6060/6194
Lozano-Pérez, T. , and Wesley, M. A. , 1979, “ An Algorithm for Planning Collision-Free Paths Among Polyhedral Obstacles,” Commun. ACM, 22(10), pp. 560–570. [CrossRef]
Mitchell, J. S. B. , and Papadimitriou, C. H. , 1991, “ The Weighted Region Problem: Finding Shortest Paths Through a Weighted Planar Subdivision,” J. ACM (JACM), 38(1), pp. 18–73. [CrossRef]
Liu, Y. , and Arimoto, S. , 1992, “ Path Planning Using a Tangent Graph for Mobile Robots Among Polygonal and Curved Obstacles Communication,” Int. J. Rob. Res., 11(4), pp. 376–382. [CrossRef]
Mitchell, J. S. B. , David, D. M. , and Papadimitriou, C. H. , 1987, “ The Discrete Geodesic Problem,” SIAM J. Comput., 16(4), pp. 647–668. [CrossRef]
Hershberger, J. , and Suri, S. , 1999, “ An Optimal Algorithm for Euclidean Shortest Paths in the Plane,” SIAM J. Comput., 28(6), pp. 2215–2256. [CrossRef]
Jain, A. K. , and Richard, C. D. , 1988, Algorithms for Clustering Data, Prentice Hall, Englewood Cliffs, NJ, pp. 50–70.
Hormann, K. , and Agathos, A. , 2001, “ The Point in Polygon Problem for Arbitrary Polygons,” Comput. Geometry, 20(3), pp. 131–144. [CrossRef]
Bresenham, J. E. , 1965, “ Algorithm for Computer Control of a Digital Plotter,” IBM Syst. J., 4(1), pp. 25–30. [CrossRef]
Amanatides, J. , and Woo, A. , 1987, “ A Fast Voxel Traversal Algorithm for Ray Tracing,” Eurographics, 87(3), pp. 3–10. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.42.3443&rep=rep1&type=pdf
Yap, P. , Burch, N. , Holte, R. C. , and Schaeffer, J. , 2011, “ Block a*: Database-Driven Search With Applications in Any-Angle Path-Planning,” Twenty-Fifth AAAI Conference on Artificial Intelligence, San Francisco, CA, Aug. 7–11. https://webdocs.cs.ualberta.ca/~holte/Publications/aaai11PeterYapFinal.pdf

Figures

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Fig. 1

Piping design for traditional manufacturing versus piping design for additive manufacturing: (a) a piping design blueprint for traditional manufacturing; (b) a piping design prototype for traditional manufacturing; (c) a piping design prototype for additive manufacturing (implemented by the proposed approach)

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Fig. 2

(a) The shortest graph path and (b) the shortest continuous path

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Fig. 3

Path found by Theta* versus true shortest path

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Fig. 4

Visibility graph of two nodes and two obstacles and the shortest path

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Fig. 5

Diagonal move between obstacles

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Fig. 6

An example of finding candidate vertices: (a) vertices in V1, (b) blocking cluster and V2 (inside the box), (c) vertex corresponding to the largest angle, (d) vertices in V3, and (e) candidate vertices (marked with dotted circles)

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Fig. 7

Flowchart of finding the candidate vertices as part of path-finding

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Fig. 8

The obstacles in between starting node and target node

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Fig. 9

Visibility check example

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Fig. 10

Node evaluations comparison between A* on grids and FA-A*

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Fig. 11

Random 50*50 maps with different proportion of obstacles

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Fig. 12

Runtime versus path length: (a) 50*50: 5%, (b) 100*100: 5%, (c) 50*50: 10%, (d) 100*100: 10%, (e) 50*50: 20%, (f) 100*100: 20%, (g) 50*50: 30%, (h) 100*100: 30%, (i) 50*50: 50%, and (j) 100*100: 50%

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Fig. 13

Random 100*100 maps with different proportion of obstacles

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Fig. 14

Paths found and nodes evaluated by each algorithm (100*100, 50%): (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 15

Paths comparison of FA-A* with and without post smoothing (100*100, 50%)

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Fig. 16

Random 300*300 maps with different proportion of obstacles

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Fig. 17

Paths found and nodes evaluated by each algorithm (300*300, 5%): (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 18

Performance comparison (50*50)

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Fig. 19

Paths found and nodes evaluated by each algorithm (300*300, 35 clusters): (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 20

Path found for 511*511 maze routing: (a) A* on G, (b) Theta*, (c) A* on V, and (d) FA-A*

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Fig. 21

Number of evaluations comparison: (a) 50*50, (b) 100*100, (c) 300*300, and (d) 50*50 with different number of clusters

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Fig. 22

Piping design example: (a) CAD model of prespecified components, (b) geometry model, (c) gridding, and (d) optimal paths

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Fig. 23

Piping design comparison: (a) A* on G and (b) FA-A*

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Fig. 24

Optimal piping design. Inlet and outlet locations of the system are prespecified at the top-right and bottom-right in the figure.

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Fig. 25

Path refinement through perturbation

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Fig. 26

Stereolithography prototype of a freeform piping network designed by FA-A*

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