Locomotion Locomotion Definition 127 Locomotion and...
Transcript of Locomotion Locomotion Definition 127 Locomotion and...
excerpt from the book: Marko B. Popovic, Biomechanics and Robotics, Pan Stanford Publishing Pte. Ltd., 2013 (No of pages 351) Print ISBN: 9789814411370, eBook ISBN: 9789814411387, DOI: 10.4032/9789814411387 Copyright © 2014 by Pan Stanford Publishing Pte. Ltd.
Chapter 5.
Locomotion
Chapter outline:
Locomotion Definition 127
Locomotion and General Principles of Physics 128
Physics of Locomotion in Fluids 128
Buoyancy 128
The Bernoulli’s Principle 129
Drag 130
Viscosity 134
Navier–Stokes Equations and Reynolds Number 134
Locomotion in Fluids 137
Locomotion in Fluids and Reynolds Number 139
Aquatic Locomotion 140
Aircraft Flying 142
Birds Flying 143
Drag-Induced Motion 143
Biologically Inspired Ornithopters 145
Ornithopters capable of carrying a human 147
Flying Power Requirements: Flapping vs. Fixed Wings 148
Bacterial Flagella and Biological Rotary Motors 153
Physics of Terrestrial Locomotion 154
Why Legs? 154
Zero-Moment Point (ZMP) and Center of Pressure (CP) 155
The Equivalence of the ZMP and the CP for Horizontal Contact Surfaces 158
The Uniqueness of the ZMP and the CP for Complex Contact Topologies 160
Centroidal Moment Pivot (CMP) Point 161
Physics of Balance and Stability 162
Human Walking and Optimal Trajectories 167
Human Walking Energy Considerations 167
Angular Momentum 169
Balance, Stability, Energy 171
Spring Mass Model for Running and Allometry 172
Allometric Observations 173
Examples of Biological Legged Locomotion 176
A Few Records in the Legged Animal Kingdom 176
Various Gaits 179
References and Suggested Reading 184
[chapter content intentionally omitted]
References:
Alerstam, T., Rosén, M., Bäckman, J., Ericson, P. G. P., and Hellgren, O., “Flight speeds among bird species:
Allometric and phylogenetic effects”, PLoS Biol. 5(8), 2007.
Alexander, R. McN., “The gaits of bipedal and quadrupedal animals”, Int. J. Robot. Res., 3(2), 1984.
Alexander, R. McN., “Optimization of structure and movement of the legs of animals”, J. Biomech., 26,
1993.
Alexander, R. McN., “Principles of animal locomotion”, Princeton University Press, 2003.
Allometry— Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Allometry. Retrieved July
2012.
Anderson, F. C., ‘‘A Dynamic Optimization Solution for a Complete Cycle of Normal Gait,’’ Ph.D. thesis, The
University of Texas at Austin, Austin, Texas, 1999.
Anderson, F. C., and Pandy, M. G., ‘‘A dynamic optimization solution for vertical jumping in three
dimensions,’’ Comput. Meth. Biomech. Biomed. Eng., 2, 1999.
Anderson, F. C., and Pandy, M. G., “Dynamic optimization of human walking”, J. Biomech. Eng., 123, 2001.
Arakawa, T. and Fukuda, T., “Natural motion generation of biped locomotion robot using hierarchical
trajectory generation method consisting of GA, EP layers”, Proceedings of the IEEE International
Conference on Robotics and Automation, 1997.
Barth, F. G., A Spider’s World: Senses and Behavior, Springer-Verlag, Berlin 2002.
BBC Nature—Blue whale videos, news and facts, http://www.bbc.co.uk/nature/life/Blue_Whale.
Retrieved July 2012.
Biggest Bird in the World, http://exploredia.com/biggest-bird-in-theworld/. Retrieved 07/12.
Blickhan, R., “The spring-mass model for running and hopping”, J. Biomech., 22, 1989.
Borelli, G. A. 1680. “De Motu Animalium”, P. Maquet (trans.), Springer-Verlag, Berlin, Heidelberg, 1989.
Buoyancy—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Buoyancy. Retrieved July
2012.
Butchart, D., Living Library, Ostrich—Longest Legs, Largest Eyes, Article on Birds,
http://www.wildwatch.com/living_library/birds-1/ostrichlongest-legs-largest-eyes. Retrieved July 2012.
Cavagna, G. A., Saibene, F. P., and Margaria, R., “Mechanical work in running”, J. Appl. Physiol., 19, 1964.
Centre Interfacultaire Bernoulli—“Asymptotic Behaviour in Fluid Mechanics”,
http://cib.epfl.ch/poisson2008/index.html. Retrieved July 2012.
Cho, K.-J., Hawkes, E., Quinn, C., and Wood, R. J., “Design, fabrication and analysis of a body-caudal fin
propulsion system for a microrobotic fish”, IEEE International Conference on Robotics and Automation,
ICRA 2008, May 2008.
Claude-Louis-Marie Navier (French engineer)—Britannica Online Encyclopedia,
http://www.britannica.com/EBchecked/topic/406971/Claude-Louis-Marie-
Navier/406971rellinks/Related-Links. Retrieved July 2012.
Cyberneticzoo.com, Bourdon Tube Toys, http://cyberneticzoo.com/?tag=bourdon-tube-toys. Retrieved
July 2012.
Darling, D., The Complete Book of Spaceflight: From Apollo 1 to Zero Gravity, John Wiley & Sons, New York,
2002.
Dasgupta, A. and Nakamura, Y., “Making feasible walking motion of humanoid robots from human motion
capture data”, Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, MI,
USA, 1999.
DeLaurier, J. D. (1993). An aerodynamic model for flapping-wing flight. Aeronautical Journal, 97(964),
125–130.
DeLaurier, J. (1994). An Ornithopter Wing Design. Canadian Aeronautics and Space Journal, 40, 10–18.
DeLaurier, J. D. (1999) “The development and testing of a full-scale piloted ornithopter.” Canadian
aeronautics and space journal 45(2), 72–82.
DeLaurier, J. D. (2005). Project Ornithopter. Project Ornithopter. Retrieved March 27, 2013, from
http://ornithopter.net
Drag (physics)—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Drag_(physics). Retrieved
July 2012.
Elephant—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Elephant. Retrieved July 2012.
Elftman, H., “The measurement of the external force in walking”, Science, 88, 1938.
Endo, K., and Herr, H. M., “Human walking model predicts joint mechanics, electromyography and
mechanical economy”, IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS, 2009.
Farley, C. T., Glasheen, J., and McMahon, T. A., “Running springs: Speed and animal size”, J. Exp. Biol.,
185(1), 1993.
Ferrell, C., “Robust and Adaptive Locomotion of an Autonomous Hexapod”, in Proceedings of Perception
to Action Conference, Lausanne, Switzerland, 1994.
Festo Festo Corporate—SmartBird#id_11468, “SmartBird – bird flight deciphered”,
http://www.festo.com/cms/en_corp/11369_11468.htm#id_11468. Retrieved July 2012.
Flagellum—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Flagellum. Retrieved July
2012.
Froude number, http://www.mecaflux.com/en/Froude%20number.htm. Retrieved July 2012.
Full, R. J. and Tu, M. S., “Mechanics of a rapid running insect: Two-, four-, and six- legged locomotion”, J.
Exp. Biol., 156, 1991.
Gait (dog)—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Gait_(dog). Retrieved July
2012.
Giraffe—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Giraffe. Retrieved July 2012.
Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point”, Int. J. Robot.
Res., 18(6), 1999.
Great Bustard—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Great_Bustard. Retrieved
July 2012.
Herr, H. M., and McMahon, T. A. “A trotting horse model”, Int. J. Robot. Res., 2000.
Herr, H. M., and McMahon, T. A. “A galloping horse model”, Int. J. Robot. Res., 2001.
Herr, H., and Popovic, M. B., “Angular momentum in human walking”, J. Exp. Biol., 211, 2008.
Hildebrand, M., “Motions of the running cheetah and horse,” J. Mammal. 40(4), 1959.
Hirai, K., Hirose, M., Haikawa Y. and Takenaka T., “The Development of Honda Humanoid Robot”,
Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium, 1998.
Hofmann, A., Popovic, M., Massaquoi, S. and Herr, H., “A Sliding Controller for Bipedal Balancing Using
Integrated Movement of Contact and Non-Contact Limbs”, Proceedings of the IEEE/RSJ International
Conference on Intelligent Robots and Systems, Sendai, Japan, 2004.
Hofmann, A., Popovic, M. B., and Herr, H., “Exploiting Angular Momentum to Enhance Bipedal Center-of-
Mass Control”, IEEE International Conference on Robotics and Automation, May 12–17, 2009, Kobe,
Japan, 2009.
Holland, J. M., Basic Robotic Concepts (Blacksburg Continuing Education), 1st Ed., Financial Times Prentice
Hall, 1983.
Horse gait—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Horse_gait. Retrieved July
2012.
Howe, R. D., and Kronauer, R. E., “THOMAS MCMAHON: A Dedication in Memoriam”, Ann. Rev. Biomed.
Eng., 3, xv–xxxix, 2001.
Hutchinson, J. R., Famini, D., Lair, R., and Kram, R., “Biomechanics: Are fast moving elephants really
running?”, Nature, Brief Communications, 422, 2003.
Inman, V. T., Ralston, H. J., and Todd, F., “Human walking”; Lieberman, J. C. (ed.), Williams & Wilkins,
Baltimore, 1981.
International Society of Biomechanics (ISB); Did You Know? From the Archives March 2011, ISB Now,
http://isbnow.isbweb.org/?p=783. Retrieved July 2012.
Isaac Newton—Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Isaac_Newton. Retrieved
July 2012.
Jackowski, Z.J., “Design and Construction of an Autonomous Ornithopter”, MIT SB Thesis, 2009.
Jean le Rond d’Alembert—Wikipedia, the free encyclopedia,
http://en.wikipedia.org/wiki/Jean_le_Rond_d’Alembert. Retrieved July 2012.
Klaassen, B., Linnemann, R., Spenneberg, D., and Kirchner, F., “Biomimetic Walking Robot Scorpion:
Control and Modelling”, 9th International Symposium on Intelligent Robotic Systems, SIRS 2001, Toulouse,
France, 2001.
Koffeman, H. 1992 “The Reynolds Number, About Rowing and Flying”,
http://www.aerodrag.com/Articles/ReynoldsNumber.htm. Retrieved July 2012.
Kondak, K., and Hommel, G., “Control and online computation of stable movement for biped robots”,
Proceedings of the International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA,
2003.
Lee, L. K., Ginsburg, M. A., Crovace, C., Donohoe, M., and Stock D., “Structure of the torque ring of the
flagellar motor and the molecular basis for rotational switching”, Nature, 466, 2010.
Malkevitch, J., “Mathematics and Climate” American Mathematical Society, Feature Column— Monthly
Essays on Mathematical Topics, http://www.ams.org/samplings/feature-column/fcarc-climate. Retrieved
July 2012.
Man Flies Like a Bird Flapping His Own Wings (Update 6), [story on Dutch mechanical engineer Smeets, J.]
posted by Diaz, J., March 21, 2012, http://gizmodo.com/5894904/man-flies-like-a-bird-flapping-hisown-
wings. Retrieved July 2012.
Mastiff Galloping, http://bowlingsite.mcf.com/movement/MGal.html. Retrieved July 2012.
McMahon, T. A. and Cheng, G. C., “The mechanics of running: How does stiffness couple with speed?” J.
Biomech., 23(Suppl. 1), 1990.
Megafauna Size Comparison Mk2 by ~Harry-the-Fox on deviantART, Harry Wilson 2010, http://harry-the-
fox.deviantart.com/gallery/29526515#/d2xt9nb. Retrieved July 2012.
Merritt, Thomas M. “Book of Insects Records”, University of Florida, 1999.
Plants, Nature, PBS, “The Seedy Side of Plants: Video: Shooting Seeds, Burrowing Seeds”, Feb 10th, 2008,
http://www.pbs.org/wnet/nature/tag/plants/. Retrieved July 2012.
Popovic, M., “Designing Large Ornithopter for Human Transport via ExoMusculature and Sensitive
Robotics”, Robotics Science and Systems conference, Sensitive Robotics Workshop, Berlin, Germany, June
24–28, 2013.
Popovic, M., Hofmann, A. and Herr, H., “Angular momentum regulation during human walking:
Biomechanics and control”, Proceedings of the IEEE International Conference on Robotics and
Automation, New Orleans, LA, USA, 2004.
Popovic, M., Hofmann, A. and Herr, H., “Zero spin angular momentum control: definition and
applicability”, Proceedings of the IEEE-RAS/RSJ International Conference on Humanoid Robots, Los
Angeles, CA, USA, 2004.
Popovic, M. B., Goswami, A., and Herr, H., “Ground reference points in legged locomotion: Definitions,
biological trajectories and control implications”, Int. J. Robot. Res., 24(12), 2005.
Pressure measurement—Wikipedia, the free encyclopedia,
http://en.wikipedia.org/wiki/Pressure_measurement. Retrieved July 2012.
Psychiatrische Klinik Lüneburg, Geschichte, “Der erste Direktor in Lüneburg: Dr. Otto Snell”,
http://www.pk.lueneburg.de/hist-notizen2.html. Retrieved July 2012.
Raibert, M. H., Legged Robots That Balance, MIT Press, Cambridge, MA, 1986.
Ren, L., and Hutchinson, J. R., “The three-dimensional locomotor dynamics of African (Loxodonta africana)
and Asian (Elephas maximus) elephants reveal a smooth gait transition at moderate speed”, J. R. Soc.
Interface, 5(19), 2008.
Rose, J., and Gamble, J. G., Human Walking, 2nd Ed., Baltimore, Maryland, Williams and Wilkins, 1994.
Sardain, P. and Bessonnet, G., “Forces acting on a biped robot. Center of pressure—zero moment point”,
IEEE Trans. Syst., Man and Cybern., Part A, 34(5), 2004.
Send, W., Fischer, M., Jebens, K., Mugrauer, R., Nagarathinam, A., and Scharstein, F. (2012). “Artificial
Hinged-Wing Bird with Active Torsion and Partially linear kinematics”. 28th International Congress of the
Aeronautical Sciences, Göttingen, Germany 2012
Sfakiotakis, M., Lane, D. M., and Davies, J. B. C., “Review of fish swimming modes for aquatic locomotion”,
IEEE J. Oceanic Eng., 24(2), 1999.
Sir George Stokes, 1st Baronet—Wikipedia, the free encyclopedia,
http://en.wikipedia.org/wiki/George_Gabriel_Stokes. Retrieved July 2012.
SmartBird - bird flight deciphered, Presented at TED Global 2011, Edinburgh, UK, July 11-15, 2011. [Online:
http://www.festo.com/cmslen_corp/11369.htm ]. Retrieved July 2012.
Surfbirds Online Photo Gallery Search Results,
http://www.surfbirds.com/gallery/search2.php?species=great%20bustard&photographer=&location=&c
ountry=&start=41. Retrieved July 2012.
Swilling, B. J., “Human Walking Adaptations to Distal Limb Mass Disturbances: Investigating Biomimetic
Performance Objectives”, Master of Science in Mechanical Engineering at the Massachusetts Institute of
Technology, September 2005
Takanishi, A., Lim, H.-ok, Tsuda, M. and Kato, I., “Realization of Dynamic Biped Walking Stabilized by Trunk
Motion on a Sagitally Uneven Surface”, Proceedings of the IEEE/RSJ International Conference on
Intelligent Robots and Systems, 1990.
The Ornithopter Zone—Fly Like A Bird—Flapping Wing Flight, http://www.ornithopter.org/. Retrieved July
2012.
Todd, D. J., Walking machines: An introduction to legged robots, Kogan Page, London, 1985.
Videler, J. J., Fish Swimming, Springer, 1993.
Vogel, S., “Life in Moving Fluids: The Physical Biology of Flow”, 2nd Ed., Princeton University Press, 1996.
Vukobratovic, M. and Juricic, D., “Contributions to the synthesis of biped gait”, IEEE Trans. Biomed. Eng.,
BME-16, 1969.
Vukobratovic, M. and Borovac, B., “Zero-moment point—thirty-five years of its life”, Int. J. Humanoid
Robot., 1(1), 2004.
Vukobratovic, M., Herr, H., Borovac, B., Rakovic, M., Popovic, M. B., Hofmann, A., Jovanovic M., and
Potkonjak, V., “Biological principles of control selection for a humanoid robot’s dynamic balance
preservation”, Int. J. Humanoid Robot., 5(4), 2008.
Wang M. C., Liu C. Y., Shiao A. S., Wang T. “Ear problems in swimmers”, J. Chin. Med. Assoc., 68(8), 2005.
Webb, P. W., and Weihs, D., “Hydrostatic stability of fish with swim bladders: Not all fish are unstable”,
Can. J. Zool. 72, 1994.
Winter, D., Biomechanics and Motor Control of Human Movement, John Wiley, New York, 1990.
Young, M. C. (ed.), The Guinness Book of Records 1998, Bantam Books, New York, 1998.