Passive dynamic systems have the advantage over conventional robotic systems that they do not require actuators and control. Brachiating, in particular, involves the swinging motion of an animal from one branch to the next. Such systems are usually designed manually by human designers and often are bio-inspired. However, a computational design approach has the capability to search vast design spaces and find solutions that go beyond those possible by manual design. This paper addresses the automated design of passive dynamic systems by introducing a graph grammar-based method that integrates dynamic simulation to evaluate and evolve configurations. In particular, the method is shown to find different, new solutions to the problem of the design of two-dimensional passive, dynamic, continuous contact, brachiating robots. The presented graph grammar rules preserve symmetry among robot topologies. A separation of parametric multi-objective optimization and topologic synthesis is proposed, considering four objectives: number of successful swings, deviation from cyclic motion, required space, and number of bodies. The results show that multiple solutions with varying complexity are found that trade-off cyclic motion and the space required. Compared to research on automated design synthesis of actuated and controlled robotic systems, this paper contributes a new method for passive dynamic systems that integrates dynamic simulation.

References

References
1.
Collins
,
S.
,
Ruina
,
A.
,
Tedrake
,
R.
, and
Wisse
,
M.
,
2005
, “
Efficient Bipedal Robots Based on Passive-Dynamic Walkers
,”
Science
,
307
(
5712
), pp.
1082
1085
.
2.
Mcgeer
,
T.
,
1990
, “
Passive Dynamic Walking
,”
Int. J. Rob. Res.
,
9
(
2
), pp.
62
82
.
3.
McGeer
,
T.
,
1990
, “
Passive Walking With Knees
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Cincinnati, OH, May 13–18, pp.
1640
1645
.
4.
Gomes
,
M.
, and
Ruina
,
A.
,
2011
, “
Walking Model With No Energy Cost
,”
Phys. Rev. E
,
83
(
3
), p.
032901
.
5.
Gomes
,
M. W.
,
2005
, “
Collisionless Rigid Body Locomotion Models and Physically Based Homotopy Methods for Finding Periodic Motions in High Degree of Freedom Models
,”
Ph.D. thesis
, Cornell University, Ithaca, NY.http://ruina.tam.cornell.edu/research/topics/locomotion_and_robotics/GomesPhDthesis.pdf
6.
Gomes
,
M. W.
, and
Ruina
,
A. L.
,
2005
, “
A Five-Link 2D Brachiating Ape Model With Life-Like Zero-Energy-Cost Motions
,”
J. Theor. Biol.
,
237
(
3
), pp.
265
278
.
7.
Collins
,
S. H.
,
Wisse
,
M.
, and
Ruina
,
A.
,
2001
, “
A Three-Dimensional Passive-Dynamic Walking Robot With Two Legs and Knees
,”
Int. J. Rob. Res.
,
20
(
7
), pp.
607
615
.
8.
Stöckli
,
F. R.
, and
Shea
,
K.
,
2015
, “
A Simulation-Driven Graph Grammar Method for the Automated Synthesis of Passive Dynamic Brachiating Robots
,”
ASME
Paper No. DETC2015-47641.
9.
Bertram
,
J.
,
Ruina
,
A.
,
Cannon
,
C.
,
Chang
,
Y. H.
, and
Coleman
,
M. J.
,
1999
, “
A Point-Mass Model of Gibbon Locomotion
,”
J. Exp. Biol.
,
202
(
19
), pp.
2609
2617
.http://jeb.biologists.org/content/202/19/2609
10.
Chakrabarti
,
A.
,
Shea
,
K.
,
Stone
,
R.
,
Cagan
,
J.
,
Campbell
,
M.
,
Hernandez
,
N. V.
, and
Wood
,
K. L.
,
2011
, “
Computer-Based Design Synthesis Research: An Overview
,”
ASME J. Comput. Inf. Sci. Eng.
,
11
(
2
), p.
021003
.
11.
Radhakrishnan
,
P.
, and
Campbell
,
M. I.
,
2011
, “
A Graph Grammar Based Scheme for Generating and Evaluating Planar Mechanisms
,” Fourth International Conference on
Design Computing and Cognition
(
DCC
), Stuttgart, Germany, July 12–14, pp.
663
679
.https://link.springer.com/chapter/10.1007/978-94-007-0510-4_35
12.
Czech
,
C.
,
2014
, “
Automated Synthesis of Orthotic Devices Using a Graph Grammar
,” Master's thesis, ETH Zurich, Zurich, Switzerland.
13.
Schmidt
,
L. C.
,
Shetty
,
H.
, and
Chase
,
S. C.
,
2000
, “
A Graph Grammar Approach for Structure Synthesis of Mechanisms
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
371
376
.
14.
Campbell
,
M. I.
,
Rai
,
R.
, and
Kurtoglu
,
T.
,
2009
, “
A Stochastic Graph Grammar Algorithm for Interactive Search
,”
ASME
Paper No. DETC2009-86804.
15.
Kurtoglu
,
T.
, and
Campbell
,
M.
, 2016, “
A Graph Grammar Based Framework for Automated Concept Generation
,”
Ninth International Design Conference
, Dubrovnik, Croatia, May 15–18, pp. 61–68.https://www.designsociety.org/publication/18985/a_graph_grammar_based_framework_for_automated_concept_generation
16.
Königseder
,
C.
, and
Shea
,
K.
,
2014
, “
Strategies for Topologic and Parametric Rule Application in Automated Design Synthesis Using Graph Grammars
,”
ASME
Paper No. DETC2014-34691.
17.
Freudenstein
,
F.
,
1954
, “
Design of Four-Link Mechanisms
,” Ph.D. thesis, Columbia University, New York.
18.
Freudenstein
,
F.
, and
Maki
,
E.
,
1979
, “
The Creation of Mechanisms According to Kinematic Structure and Function
,”
Environ. Plann.
,
6
(
4
), pp.
375
391
.
19.
Freudenstein
,
F.
, and
Dobrjanskyj
,
L.
,
1966
, “
On a Theory for the Type Synthesis of Mechanisms
,”
Applied Mechanics
,
Springer
, Berlin, pp.
420
428
.
20.
Tsai
,
L.-W.
,
2000
,
Mechanism Design: Enumeration of Kinematic Structures According to Function
,
CRC Press
, Boca Raton, FL.
21.
McCarthy
,
J. M.
, and
Song Soh
,
G.
,
2011
, “
Geometric Design of Linkages
,”
2nd ed.
,
Interdisciplinary Applied Mathematics
,
Springer
,
Berlin
.
22.
Lipson
,
H.
,
2006
, “
A Relaxation Method for Simulating the Kinematics of Compound Nonlinear Mechanisms
,”
ASME J. Mech. Des.
,
128
(
4
), pp.
719
728
.
23.
Coros
,
S.
,
Thomaszewski
,
B.
,
Noris
,
G.
,
Sueda
,
S.
,
Forberg
,
M.
,
Sumner
,
R. W.
,
Matusik
,
W.
, and
Bickel
,
B.
,
2013
, “
Computational Design of Mechanical Characters
,”
ACM Trans. Graphics
,
32
(
4
), p. 83.
24.
Thomaszewski
,
B.
,
Coros
,
S.
,
Gauge
,
D.
,
Megaro
,
V.
,
Grinspun
,
E.
, and
Gross
,
M.
,
2014
, “
Computational Design of Linkage-Based Characters
,”
ACM Trans. Graphics
,
33
(
4
), p.
64
.
25.
Cabrera
,
J. A.
,
Simon
,
A.
, and
Prado
,
M.
,
2002
, “
Optimal Synthesis of Mechanisms With Genetic Algorithms
,”
Mech. Mach. Theory
,
37
(
10
), pp.
1165
1177
.
26.
Lipson
,
H.
,
2008
, “
Evolutionary Synthesis of Kinematic Mechanisms
,”
Artificial Intell. Eng. Des., Anal. Manuf.
,
22
(
3
), pp.
195
205
.
27.
Bouma
,
W.
,
Fudos
,
I.
,
Hoffmann
,
C.
,
Cai
,
J.
, and
Paige
,
R.
,
1995
, “
Geometric Constraint Solver
,”
Comput.-Aided Des.
,
27
(
6
), pp.
487
501
.
28.
Sims
,
K.
,
1994
, “
Evolving Virtual Creatures
,” 21st Annual Conference on Computer Graphics and Interactive Techniques (
SIGGRAPH
), Orlando, FL, July 24–29, pp.
15
22
.
29.
Sims
,
K.
,
1994
, “
Evolving 3D Morphology and Behavior by Competition
,”
Artif. Life
,
1
(
4
), pp.
353
372
.
30.
Lipson
,
H.
, and
Pollack
,
J.
,
2000
, “
Evolving Physical Creatures
,”
Artificial Life VII: Seventh International Conference on Artificial Life
, Portland, OR, pp.
282
287
.https://pdfs.semanticscholar.org/1254/f7b7c00b99dcf481cdb2c3fac73ac7e511ba.pdf
31.
Auerbach
,
J. E.
, and
Bongard
,
J. C.
,
2014
, “
Environmental Influence on the Evolution of Morphological Complexity in Machines
,”
PLoS Comput. Biol.
,
10
(
1
), p.
e1003399
.
32.
Leger
,
C.
,
1999
, “
Automated Synthesis and Optimization of Robot Configurations: An Evolutionary Approach
,”
Ph.D. thesis
, Carnegie Mellon University, Pittsburgh, PA.http://darwin2k.sourceforge.net/thesis.pdf
33.
Leger
,
C.
,
2000
,
Darwin2K: An Evolutionary Approach to Automated Design for Robotics
,
Springer Science +Business Media
, New York.
34.
Matsushita
,
K.
,
Yokoi
,
H.
, and
Arai
,
T.
,
2006
, “
Pseudo-Passive Dynamic Walkers Designed by Coupled Evolution of the Controller and Morphology
,”
Rob. Auton. Syst.
,
54
(
8
), pp.
674
685
.
35.
Matsushita
,
K.
,
Lungarella
,
M.
,
Paul
,
C.
, and
Yokoi
,
H.
,
2005
, “
Locomoting With Less Computation But More Morphology
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Barcelona, Spain, Apr. 18–22, pp.
2008
2013
.
36.
Bolognini
,
F.
,
Shea
,
K.
,
Vale
,
C. W.
, and
Seshia
,
A. A.
, “
A Multicriteria System-Based Method for Simulation-Driven Design Synthesis
,”
ASME
Paper No. DETC2006-99354.
37.
Geiss
,
R.
,
Batz
,
G. V.
,
Grund
,
D.
,
Hack
,
S.
, and
Szalkowski
,
A.
,
2006
,
GrGen: A Fast SPO-Based Graph Rewriting Tool
,
Springer
, Berlin, pp.
383
397
.
38.
MATLAB
,
2013
, “
Version R2013a
,” The MathWorks, Inc., Natick, MA.
39.
Featherstone
,
R.
,
2008
,
Rigid Body Dynamics Algorithms
, Vol.
49
,
Springer
,
New York
.
40.
Bolognini
,
F.
,
Seshia
,
A. A.
, and
Shea
,
K.
,
2007
, “
Exploring the Application of Multidomain Simulation-Based Computational Synthesis Methods in MEMS Design
,”
International Conference on Engineering Design (ICED), Paris, France, July 28–31
, Paper No.
DS42_P_305
.https://www.designsociety.org/publication/25362/exploring_the_application_of_a_multi-domain_simulation-based_computational_synthesis_method_in_mems_design
41.
Deb
,
K.
,
2001
,
Multi-Objective Optimization Using Evolutionary Algorithms
,
Wiley
, Hoboken, NJ.
You do not currently have access to this content.