0
Research Papers

On the Technological Instantiation of a Biomimetic Leg Concept for Agile Quadrupedal Locomotion

[+] Author and Article Information
Elena Garcia

Senior Researcher
Centre for Automation and Robotics,
CSIC-UPM,
Madrid 28500, Spain
e-mail: elena.garcia@csic.es

Juan C. Arevalo

Centre for Automation and Robotics,
CSIC-UPM,
Madrid 28500, Spain
e-mail: juan.arevalo@csic.es

Manuel Cestari

Centre for Automation and Robotics,
CSIC-UPM,
Madrid 28500, Spain
e-mail: m.cestari@csic.es

Daniel Sanz-Merodio

Research Engineer
Marsi Bionics,
Madrid 28500, Spain
e-mail: daniel.sanz@marsibionics.com

1Corresponding author.

Manuscript received July 3, 2013; final manuscript received August 6, 2014; published online December 4, 2014. Assoc. Editor: Xilun Ding.

J. Mechanisms Robotics 7(3), 031005 (Aug 01, 2015) (12 pages) Paper No: JMR-13-1124; doi: 10.1115/1.4028306 History: Received July 03, 2013; Revised August 06, 2014; Online December 04, 2014

The legged locomotion system of biological quadrupeds has proven to be the most efficient in natural, complex terrain. Particularly, horses' legs have been evolved to provide speed, endurance, and strength superior to any other animal of equal size. Quadruped robots, emulating their biological counterparts, could become the best choice for field missions in complex or natural environments; however, they should be provided with optimum performance against mobility, payload, and endurance. The design of the leg mechanism is of paramount importance to achieve the targeted performance, and in order to design a leg mechanism able to provide the robot with such agile capabilities nature is the best source for inspiration. In this work, key principles underlying horse legs' power capabilities have been extracted and translated to a biomimetic leg concept. Afterwards, a real prototype has been designed following the biomimetic concept proposed. A key element in the biomimetic concept is the multifunctionality of the natural musculotendinous system, which has been mimicked by combining series elastic actuation and passive elements. This work provides an assessment of the benefits that bio-inspired solutions can provide versus the purely engineering approaches. The experimental evaluation of the bio-inspired prototype shows an improvement on the performance compared to a leg design based on purely engineering principles.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Thornhill, L. D., Walls, A., Arkin, R. C., Beno, J. H., Bergh, C., Bresie, D., Giovannetti, A., Gothard, B. M., Matthies, L. H., Nogueiro, P., Scanlon, J., Scott, R., Simon, M., Smith, W., and Waldron, K. J., 2003, “Design of an Agile Unmanned Combat Vehicle—A Product of the DARPA UGCV Program,” Proc. SPIE, 5083, pp. 258–270.
Griffin, T. M., Kram, R., Wickler, S. J., and Hoyt, D. F., 2004, “Biomechanical and Energetic Determinants of the Walk-Trot Transition in Horses,” J. Exp. Biol., 207(24), pp. 4215–4223. [CrossRef] [PubMed]
Alexander, R. M., and Jayes, A. S., 1983, “A Dynamic Similarity Hypothesis for the Gaits of Quadrupedal Mammals,” J. Zool., 201(1), pp. 135–152. [CrossRef]
Garcia, E., Arevalo, J., Muñoz, G., and Gonzalez-de-Santos, P., 2011, “Combining Series-Elastic Actuation and Magneto-Rheological Damping for the Control of Agile Locomotion,” Rob. Auton. Syst., 59(10), pp. 827–839. [CrossRef]
Poulakakis, I., Smith, J. A., and Buehler, M., 2005, “Modeling and Experiments of Untethered Quadrupedal Running With a Bounding Gait: The Scout II Robot,” Int. J. Rob. Res., 24(4), pp. 239–256. [CrossRef]
Hodoshima, R., Doi, T., Fukuda, Y., Hirose, S., Okamoto, T., and Mori, J., 2007, “Development of a Quadruped Walking Robot TITAN XI for Steep Slope Operation—Step Over Gait to Avoid Concrete Frames on Steep Slopes,” J. Rob. Mechatronics, 19(1), pp. 13–26.
Murphy, M. P., Saunders, A., Moreira, C., Rizzi, A. A., and Raibert, M., 2011, “The LittleDog Robot,” Int. J. Rob. Res., 30(2), pp. 145–149. [CrossRef]
Fukuoka, Y., Katabuchi, H., and Kimura, H., 2010, “Dynamic Locomotion of Quadrupeds Tekken3&4 Using Simple Navigation System,” J. Rob. Mechatronics, 22(1), pp. 36–42.
Singh, S. P. N., and Waldron, K. J., 2006, “Towards High-Fidelity On-Board Attitude Estimation for Legged Locomotion Via a Hybrid Range and Inertial Approach,” Experimental Robots IX (Springer Tracts in Advanced Robotics, Vol. 21), M. H.Ang and O.Khatib, eds., Springer, Berlin, pp. 589–598.
Raibert, M., Blankespoor, K., Nelson, G., and Playter, R., 2008, “BigDog, The Rough-Terrain Quadruped Robot,” 17th World Congress International Federation of Automation Control (IFAC), Seoul, South Korea, July 6–11, pp. 10822–10825.
Havoutis, I., Semini, C., Buchli, J., and Caldwell, D. G., 2013, “Quadrupedal Trotting With Active Compliance,” IEEE International Conference on Mechatronics (ICM), Vicenza, Italy, Feb. 27–Mar. 1, pp. 610–616. [CrossRef]
Hutter, M., Remy, C. D., Hoepflinger, M. A., and Siegwart, R., 2013, “Efficient and Versatile Locomotion With Highly Compliant Legs,” IEEE/ASME Trans. Mechatronics, 18(2), pp. 449–458. [CrossRef]
Ananthanarayanan, A., Azadi, M., and Kim, S., 2012, “Towards the Bio-Inspired Legs Design for High Speed Running,” Bioinspiration Biomimetics, 7(4), p. 046005. [CrossRef] [PubMed]
Arikawa, K., and Hirose, S., 2007, “Mechanical Design of Walking Machines,” Philos. Trans. R. Soc. A365(1850), pp. 171–183. [CrossRef]
Hildebrand, M., 1987, “The Mechanics of Horse Legs,” Am. Sci., 75(6), pp. 594–601.
Bar-Cohen, Y., and Breazeal, C., 2003, Biologically Inspired Intelligent Robots, SPIE Press, Bellingham, WA.
Pontzer, H., 2007, “Effective Limb Length and the Scaling of Locomotor Cost in Terrestrial Animals,” J. Exp. Biol., 210(10), pp. 1752–1761. [CrossRef] [PubMed]
American Institute of Architects, 2000, Architectural Graphic Standards (Version 3), Wiley, New York.
Nauwelaerts, S., Allen, W. A., Lane, J. M., and Clayton, H. M., 2011, “Inertial Properties of Equine Limb Segments,” J. Anat., 218(5), pp. 500–509. [CrossRef] [PubMed]
Gunn, H., 1983, “Morphological Attributes Associated With Speed of Running in Horses,” Equine Exercise Physiology, D.Snow, S.Persson, and R.Rose, eds., Burlington Press, Cambridge, UK, pp. 271–274.
Alexander, R. M., 1988, Elastic Mechanisms in Animal Movement, Cambridge University Press,, Cambridge, UK.
Rapoport, S., Mizrahi, J., Kimmel, E., Verbitsky, O., and Isakov, E., 2003, “Constant and Variable Stiffness and Damping of the Leg Joints in Human Hopping,” ASME J. Biomech. Eng., 125(4), pp. 507–514. [CrossRef]
Buchner, H. H. F., Savelberg, H. H. C. M., Schamhardt, H. C., and Barneveld, A., 1997, “Inertial Properties of Dutch Warmblood Horses,” J. Biomech., 30(6), pp. 653–658. [CrossRef] [PubMed]
Gonzalez de Santos, P., Garcia, E., and Estremera, J., 2006, Quadrupedal Locomotion: An Introduction to the Control of Four-Legged Robots, Springer, London.
Dickinson, M., Farley, C., Full, R., Koehl, M., Kram, R., and Lehman, S., 2000, “How Animals Move: An Integrative View,” Science, 288(5463), pp. 100–106. [CrossRef] [PubMed]
Hyon, S.-H., 2009, “A Motor Control Strategy With Virtual Musculoskeletal Systems for Compliant Anthropomorphic Robots,” IEEE/ASME Trans. Mechatronics, 14(6), pp. 677–688. [CrossRef]
Anderson, I., Ieropoulos, I., McKay, T., O'Brien, B., and Melhuish, C., 2011, “Power for Robotic Artificial Muscles,” IEEE/ASME Trans. Mechatronics, 16(1), pp. 107–111. [CrossRef]
Pratt, J., Krupp, B., and Morse, C., 2002, “Series Elastic Actuators for High Fidelity Force Control,” Ind. Rob.: Int. J., 29(3), pp. 234–241. [CrossRef]
Kong, K., Bae, J., and Tomizuka, M., 2009, “Control of Rotary Series Elastic Actuator for Ideal Force-Mode Actuation in Human-Robot Interaction Applications,” IEEE/ASME Trans. Mechatronics, 14(1), pp. 105–118. [CrossRef]
Parietti, F., Baud-Bovy, G., Gatti, E., Riener, R., Guzzella, L., and Vallery, H., 2011, “Series Viscoelastic Actuators Can Match Human Force Perception,” IEEE/ASME Trans. Mechatronics, 16(5), pp. 853–860. [CrossRef]
Rooney, J. R., 1990, “The Jump Behavior of the Humeroradial and Tarsocrural Joints of the Horse,” J. Equine Vet. Sci., 10(4), pp. 311–314. [CrossRef]
McGuigan, M. P., Yoo, E., Lee, D. V., and Biewener, A. A., 2009, “Dynamics of Goat Distal Hind Limb Muscle-Tendon Function in Response to Locomotor Grade,” J. Exp. Biol., 212(13), pp. 2092–2104. [CrossRef] [PubMed]
Minetti, A., Ardigo, L., Reinach, E., and Saibene, F., 1999, “The Relationship Between Mechanical Work and Energy Expenditure of Locomotion in Horses,” J. Exp. Biol., 202(17), pp. 2329–2338. [PubMed]
Kazerooni, H., Chu, A., and Steger, R., 2007, “That Which Does Not Stabilize, Will Only Make Us Stronger,” Int. J. Rob. Res., 26(1), pp. 75–89. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Iterative optimization of leg mass distribution by minimizing the power required at the joints. Convergence is shown in black thicker line for a mass distribution of 50%, 38%, and 12% at thigh, crus, and hoof, respectively, which for a 5-kg leg yields 2.5 kg, 1.9 kg, and 0.6 kg at thigh, crus, and hoof, respectively: (a) hip power for varying link masses and (b) knee power for varying link masses.

Grahic Jump Location
Fig. 2

Hill's muscle model. F: force; CE: contractile element; SE: series element; and PE: parallel element.

Grahic Jump Location
Fig. 3

Simplified block diagram of neuromuscular control system based on proprioceptive organs

Grahic Jump Location
Fig. 4

Block diagram of a force controlled SEA, adapted from Ref. [27]. Xd: reference output position; Xa: actual output position; Fd: reference force on the load; Fa: actual force on the load; and KS: spring stiffness.

Grahic Jump Location
Fig. 5

Curves of SDF stiffness versus maximum SDF deflection for achieving elastic energy ranging between 10 J (slow trot) and 26 J (fast trot)

Grahic Jump Location
Fig. 6

Biomimetic model of a leg for agile locomotion. SEA: series elastic actuator, and SDF: superficial digital flexor.

Grahic Jump Location
Fig. 7

(a) HADE2 leg prototype for agile locomotion and (b) HADE2 leg kinematics

Grahic Jump Location
Fig. 8

Hip joint kinematics

Grahic Jump Location
Fig. 9

(a) Knee joint kinematics and (b) fetlock joint kinematics

Grahic Jump Location
Fig. 10

Control states of the locomotion cycle

Grahic Jump Location
Fig. 11

SEA23-23 motor torque–speed diagram overlapped with joint requirements for average nondimensional leg speed of 0.54 considering a biomimetic leg

Grahic Jump Location
Fig. 12

SEA compliance control scheme block diagram

Grahic Jump Location
Fig. 13

Bode diagram of the actuator impedance (thin line) overlapped with the ideal spring–damper system (thick line)

Grahic Jump Location
Fig. 14

Measurements on the HADE2 leg during seven locomotion cycles: (a) potential energy stored in the SDF during the support phase; (b) linear force exerted by the SDF; and (c) Deflection of the SDF. The duration of the support phase is shown in black thick lines.

Grahic Jump Location
Fig. 15

(a) Experimental testbed and (b) close up view of hip, linear rail, carriage, and carriage stop

Grahic Jump Location
Fig. 16

Sequence of the locomotion cycle of the HADE2 leg

Grahic Jump Location
Fig. 17

Linear speed of the tread mill: (a) HADE2 leg with passive ankle and SDF and (b) previous HADE leg prototype with actuated ankle

Grahic Jump Location
Fig. 18

Fetlock joint curves for an actuated fetlock: (a) torque; (b) angle; and (c) power. The duration of the support phase is shown in black thick line.

Grahic Jump Location
Fig. 19

Fetlock joint curves for the passive fetlock with SDF: (a) torque; (b) angle; and (c) power. The duration of the support phase is shown in black thick line.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In