Research Papers: Design Automation

A Spatial Grammar Method for the Computational Design Synthesis of Virtual Soft Locomotion Robots

[+] Author and Article Information
Merel van Diepen

Engineering Design and Computing Laboratory,
Department of Mechanical and Process Engineering,
ETH Zürich,
8092 Zürich, Switzerland
e-mail: merelvandiepen@ethz.ch

Kristina Shea

Engineering Design and Computing Laboratory,
Department of Mechanical and Process Engineering,
ETH Zürich,
8092 Zürich, Switzerland
e-mail: kshea@ethz.ch

1Corresponding author.

An earlier iteration of this work was accepted to the 2018 ASME IDETC conference (van Diepen et al. 2018).

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received October 22, 2018; final manuscript received March 15, 2019; published online May 14, 2019. Assoc. Editor: Gary Wang.

J. Mech. Des 141(10), 101402 (May 14, 2019) (10 pages) Paper No: MD-18-1778; doi: 10.1115/1.4043314 History: Received October 22, 2018; Accepted March 15, 2019

Soft locomotion robots are intrinsically compliant and have a large number of degrees of freedom. They lack rigid components that provide them with higher flexibility, and they have no joints that need protection from liquids or dirt. However, the hand-design of soft robots is often a lengthy trail-and-error process. This work presents the computational design of virtual, soft locomotion robots using an approach that integrates simulation feedback. The computational approach consists of three stages: (1) generation, (2) evaluation through simulation, and (3) optimization. Here, designs are generated using a spatial grammar to explicitly guide the type of solutions generated and exclude infeasible designs. The soft material simulation method developed and integrated is stable and sufficiently fast for use in a highly iterative simulated annealing search process. The resulting virtual designs exhibit a large variety of expected and unexpected gaits, thus demonstrating the method capabilities. Finally, the optimization results and the spatial grammar are analyzed to understand and map the challenges of the problem and the search space.

Copyright © 2019 by ASME
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Hiller, J. D., and Lipson, H., “Evolving Amorphous Robots,” Proceedings of the 12th International Conference on the Synthesis and Simulation of Living Systems, Odense, Denmark, Aug. 19–23, 2010.
Rieffel, J., Knox, D., Smith, S., and Trimmer, B., 2013, “Growing and Evolving Soft Robots,” Artif. Life, 20(1), pp. 143–162. [CrossRef] [PubMed]
Deimel, R., and Brock, O., 2014, “A Novel Type of Compliant, Underactuated Robotic Hand for Dexterous Grasping,” Proc. Rob.: Sci. Syst., 35(1-3), pp. 161–185.
Wang, J.-Y., and Lan, C.-C., 2014, “A Constant-Force Compliant Gripper for Handling Objects of Various Sizes,” ASME J. Mech. Des., 136(7), p. 071008. [CrossRef]
Ilievski, F., Mazzeo, A. D., Shepherd, R. F., Chen, X., and Whitesides, G. M., 2011, “Soft Robotics for Chemists,” Angew. Chem.- Int. Edition, 123(8), pp. 1930–1935. [CrossRef]
Trivedi, D., Dienno, D., and Rahn, C. D., 2008, “Optimal, Model-Based Design of Soft Robotic Manipulators,” ASME J. Mech. Des., 130(9), pp. 091402. [CrossRef]
Calisti, M., Picardi, G., and Laschi, C., 2017, “Fundamentals of Soft Robot Locomotion,” J. R. Soc. Interface, 14(130).
Rus, D., and Tolley, M. T., 2015, “Design, Fabrication and Control of Soft Robots,” Nature, 521(7553), pp. 467–475. [CrossRef] [PubMed]
Tolley, M. T., Shepherd, R. F., Mosadegh, B., Galloway, K. C., Wehner, M., Karpelson, M., Wood, R. J., and Whitesides, G. M., 2014, “A Resilient, Untethered Soft Robot,” Soft Rob., 1(3), pp. 213–223. [CrossRef]
Du Pasquier, C., 2017, “Modular Pneumatic Toolkit: An Application of 4d-Printing,” Master’s thesis, ETH Zürich.
Mao, S., Dong, E., Jin, H., Xu, M., and Low, K. H., “Locomotion and Gait Analysis of Multi-limb Soft Robots Driven by Smart Actuators,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Daejeon, Korea, Oct. 9–14, 2016.
Sugiyama, Y., and Sugiyama, Y., “Crawling and Jumping of Deformable Soft Robot,” 2004 IEEE/RSJ International Conference on Itelligent Robots and Systems, Sendai, Japan, Sept. 28–Oct. 2, 2004.
Sims, K., “Evolving virtual creatures,” SIGGRAPH '94 Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, Orlando, Florida, USA, July 24–29, 1994.
Hiller, J., and Lipson, H., 2012, “Automatic Design and Manufacture of Soft Robots,” IEEE Trans. Rob., 28(2), pp. 457–466. [CrossRef]
Stiny, G., 1980, “Introduction to Shape and Shape Grammars,” Environ. Planning B, 7( Nov.), pp. 343–351. [CrossRef]
McKay, A., Chase, S., Shea, K., and Chau, H. H., 2012, “Spatial Grammar Implementation: From Theory to Useable Software,” Artif. Intell. Eng. Design, Anal. Manuf. 26(2), pp. 143–159. [CrossRef]
Hsiao, S.-W., and Chen, C.-H., 1997, “A Semantic and Shape Grammar Based Approach for Product Design,” Design Stud. 18(3), pp. 275–296. [CrossRef]
Pugliese, M. J., and Cagan, J., 2002, “Capturing a Rebel: Modeling the Harley-Davidson Brand Through a Motorcycle Shape Grammar,” Res. Eng. Design, 13(Apr.), pp. 139–156. [CrossRef]
Teboul, O., Kokkinos, I., Simon, L., Koutsourakis, P., and Paragios, N., “Shape Parsing via Reinforcement Learning,” Conference on Computer Vision and Pattern Recognition, Colorado Spring, CO, USA, June 20–25, 2011.
Shea, K., and Cagan, J., 1997, “Innovative Dome Design-Applying Geodesic Patterns with Shape Annealing.pdf,” Artif. Intell. Eng., Design, Anal. Manuf., 11(05), pp. 379–394. [CrossRef]
Zimmermann, L., Chen, T., and Shea, K., 2017, “Generative Shape Design using 3D Spatial Grammars, Simulation and Optimization,” Design Computing and Cognition’16, pp. 297–316.
Königseder, C., and Shea, K., 2016, “Visualizing Relations Between Grammar Rules, Objectives, and Search Space Exploration in Grammar-Based Computational Design Synthesis,” ASME J. Mech. Des., 138(10), p. 101101. [CrossRef]
Moseley, P., Florez, J. M., Sonar, H. A., Agarwal, G., Curtin, W., and Paik, J., 2016, “Modeling, Design, and Development of Soft Pneumatic Actuators with Finite Element Method,” Adv. Eng. Mater., 18(6), pp. 978–988. [CrossRef]
Suzumori, K., Endo, S., Kanda, T., Kato, N., and Suzuki, H., “A Bending Pneumatic Rubber Actuator Realizing Soft-Bodied Manta Swimming Robot,” Proceedings of the IEEE International Conference on Robotics and Automation, Roma, Italy, April 10–14, 2007.
Fang, G., Matte, C.-D., Kwok, T.-H., and Wang, C. C., “Geometry-based direct simulation for multi-material soft robots,” 2018 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Brisbane, Australia, May 21–25, 2018.
Cheney, N., MacCurdy, R., Clune, J., and Lipson, H., “Unshackling Evolution: Evolving Soft Robots with Multiple Materials and a Powerful Generative Encoding,” Proceeding of the Fifteenth Annual Conference on Genetic and Evolutionary Computation - GECCO ’13, Amsterdam, Netherlands, July 6–10, 2013.
Couman, E.,2017, Bullet Real-Time Physics Simulation, https://pybullet.org.
Bender, J., Koschier, D., Charrier, P., and Weber, D., 2014, “Position-Based Simulation of Continuous Materials,” Comput. Graph. (Pergamon), 44(1), pp. 1–10.
Jansson, J., and Vergeest, J. S., 2002, “A Discrete Mechanics Model for Deformable Bodies,” Comput.-Aided Design, 34(12), pp. 913–928. [CrossRef]
van Diepen, M., and Shea, K., “A Spatial Grammar Method for the Computational Design Synthesis,” ASME DETC Conference 2018., Quebec City, Canada, Aug. 26–29, 2018.
Triki, E., Collette, Y., and Siarry, P., 2005, “A Theoretical Study on the Behavior of Simulated Annealing Leading to a New Cooling Schedule,” Eur. J. Oper. Res., 166(1 SPEC. ISS.), pp. 77–92. [CrossRef]


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Fig. 1

Two manually designed soft locomotion robots: (a) manually designed soft walker from Ref. [9] and (b) manually designed soft crawler from Ref. [10]

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Fig. 2

Overview of the computational design synthesis process and the methods used

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Fig. 3

To bend, rows of balls are expanded and contracted. The rest-length of the connecting springs of the top row is increased, as is the size of the balls. The rest-length of the connecting springs and the size of the balls of the bottom row are decreased.

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Fig. 4

The four patterns used for activation. One side of an activated subassembly is activated with the positive pattern and therefore extends, the opposite side is activated with the negative of the pattern and contracts. As a result, the subassembly bends.

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Fig. 5

The seven rules of the rule set. Rules 0–5 add material, rule 6 removes material. The rule parameters are listed in the right column, the activation directions are shown by the arrows. Dark shaded balls have a higher friction value than the light shaded balls.

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Fig. 6

The generation of a design created by hand picking rules. For every transition, the rule and the used parameters are given.

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Fig. 7

Example of self-collision. The left picture shows a 2D example of one point of a model penetrating an edge belonging to the same model. The right picture shows the effect of a failed detection of self-collision during a previous time step. After a failed detection, correct detection in subsequent time-steps will maintain the point on the wrong side of the face.

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Fig. 8

The motion and objective function value of the hand-built design from Fig. 6

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Fig. 9

The average accepted objective function value and the average best objective function value of 24 runs with 150 iteration and 50 moves with reheating. The standard deviation of the average accepted value is shown.

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Fig. 10

The average accepted objective function value and the average best objective function value of 24 runs with 150 iteration and 50 moves without reheating. The standard deviation of the average accepted value is shown.

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Fig. 11

The average accepted objective function value and the average best objective function value of 24 runs with 250 iteration and 50 moves with reheating. The standard deviation of the average accepted value is shown.

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Fig. 12

The average temperature and acceptance rate for the processes with and without reheating: (a) the average temperature over the iterations for the processes with and without reheating and (b) the average acceptance rate for the processes with and without reheating

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Fig. 13

Top: maximum objective function value as a function of the design size, grouped in bins. Bottom: the number of designs per design size bin. The x-axis values of the plotted points are the right side borders of the bins. Designs with between 200 and 600 balls have better performance than the smaller and bigger designs. The majority of the generated designs have between 180 and 850 balls.

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Fig. 14

Designs showing hopping locomotion. Design A uses the impulse of its arms to lift its base of the ground. Design B hops by lifting off and rotating before landing. The locomotion of design C is comparable with design A. Design D pushes off with its only leg and balances using a tail-like structure.

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Fig. 15

Walking designs. Although the propulsion of design A is very similar to that of hopping designs A and C, here, the legs are lifted off the ground alternating, resulting in steps. Designs B, C, and D show legged locomotion where the leg is lifted of the floor just enough to reduce the friction.

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Fig. 16

A crawling and a rolling design. Design A crawls and has minimal lift-off of the ground. Design B rolls.

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Fig. 17

Average improvement of the objective function value for the different rules. All rules have, on average, a negative effect on the objective function value. A small percentage of rule applications improves the designs. The median is shown as a dot, the standard deviation as a bar.

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Fig. 18

The average design entropy versus the objective function value. The objective values of the designs are grouped in bins with bin size 1. The x-axis values of the plotted points are the right side borders of the bins. The standard deviation is shown in gray. The design entropy is defined as the average of the local diversity within a design. For every ball in the design, the local diversity is defined by the fraction of identical neighboring balls.



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