Research Papers

Variable Stiffness Legs for Robust, Efficient, and Stable Dynamic Running

[+] Author and Article Information
Kevin C. Galloway

Wyss Institute for Biologically
Inspired Engineering,
Harvard University,
Cambridge, MA 02138
e-mail: kevin.galloway@wyss.harvard.edu

Jonathan E. Clark

Department of Mechanical Engineering,
Florida A&M University/
Florida State University,
College of Engineering,
Tallahassee, FL 32310
e-mail: clarkj@eng.fsu.edu

Daniel E. Koditschek

GRASP Laboratory,
Department of Electrical and
Systems Engineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: kod@seas.upenn.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received August 2, 2011; final manuscript received September 1, 2012; published online January 24, 2013. Assoc. Editor: Vijay Kumar.

J. Mechanisms Robotics 5(1), 011009 (Jan 24, 2013) (11 pages) Paper No: JMR-11-1087; doi: 10.1115/1.4007843 History: Received August 02, 2011; Revised September 01, 2012

Humans and animals adapt their leg impedance during running for both internal (e.g., loading) and external (e.g., surface) changes. To date, the mechanical complexity of designing usefully robust tunable passive compliance into legs has precluded their implementation on practical running robots. This work describes the design of novel, structure-controlled stiffness legs for a hexapedal running robot to enable runtime modification of leg stiffness in a small, lightweight, and rugged package. As part of this investigation, we also study the effect of varying leg stiffness on the performance of a dynamical running robot.

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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]
Cavagna, G. A., Heglund, N. C., and Taylor, C. R., 1977, “Mechanical Work in Terrestrial Locomotion: Two Basic Mechanisms for Minimizing Energy Expenditure,” Am. J. Physiol., 233(5), pp. R243–R261. [PubMed]
Blickhan, R., 1989, “The Spring-Mass Model for Running and Hopping,” J. Biomech., 22(11–12), pp. 1217–1227. [CrossRef] [PubMed]
Blickhan, R., and Full, R. J., 1993, “Similarity in Multilegged Locomotion: Bounding Like a Monopod,” J. Comp. Physiol., 173(5), pp. 509–517. [CrossRef]
Raibert, M. H., 1986, Legged Robots That Balance (MIT Press Series in Artificial Intelligence), MIT Press, Cambridge, MA.
Buehler, M., Battaglia, R., Cocosoc, A., Hawker, G., Sarkis, J., and Yamazaki, K., 1998, “SCOUT: A Simple Quadruped That Walks, Climbs, and Runs,” Int. J. Robot. Res., 13(2), pp. 1707–1712.
Papdopoulos, D., and Buehler, M., 2000, “Stable Running in a Quadruped Robot With Compliant Legs,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 444–449.
Smith, J. A., and Poulakakis, I., 2004, “Rotary Gallop in the Untethered Quadrupedal Robot Scout II,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 3, pp. 2556–2561.
Saranli, U., Buehler, M., and Koditschek, D. E., 2000, “Design, Modeling and Preliminary Control of a Compliant Hexapod Robot,” Proceedings—IEEE International Conference on Robotics and Automation, Vol. 3, pp. 2589–2596.
Cham, J. G., Karpick, J., Clark, J. E., and Cutkosky, M. R., 2001, “Stride Period Adaptation for a Biomimetic Running Hexapod,” International Symposium of Robotics Research.
Full, R. J., and Koditschek, D. E., 1999, “Templates and Anchors: Neuromechanical Hypotheses of Legged Locomotion on Land,” J. Exp. Biol., 202(23), pp. 3325–3332. [PubMed]
Ferris, D., Louie, M., and Farley, C., 1998, “Running in the Real World: Adjusting Leg Stiffness for Different Surfaces,” Proc. R. Soc. London, 265, pp. 989–993. [CrossRef]
Brown, I., and Loeb, G., 2000, “A Reductionist Approach to Creating and Using Neuromusculoskeletal Models,” Biomechanics and Neural Control of Posture and Movement, J.Winters and P.Crago, eds., Springer-Verlag, Berlin, pp. 148–163.
Holmes, P., Full, R., Koditschek, D., and Guckenheimer, J., 2006, “The Dynamics of Legged Locomotion: Models, Analyses, and Challenges,” SIAM Rev., 48(2), pp. 207–304. [CrossRef]
Jindrich, D., and Full, R., 2002, “Dynamic Stabilization of Rapid Hexapedal Locomotion,” J. Exp. Biol., 205(18), pp. 2803–2823. [PubMed]
Van Ham, R., Van Damme, M., Vanderborght, B., Verrelst, B., and Lefeber, D., 2006, “MACCEPA: The Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator,” Proceedings of CLAWAR, pp. 196–203.
Daerden, F., and Lefeber, D., 2001, “The Concept and Design of Pleated Pneumatic Artificial Muscles,” Int. J. Fluid Power, 2(3), pp. 41–50.
Hurst, W., Chestnutt, J., E., and Rizzi, A., A., 2004, “An Actuator With Physically Variable Stiffness for Highly Dynamic Legged Locomotion,” Proceedings—IEEE International Conference on Robotics and Automation, pp. 4662–4667.
Hurst, J., 2008, “The Role and Implementation of Compliance in Legged Locomotion,” Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA.
Alexander, R. M., 1990, “Three Uses for Springs in Legged Locomotion,” Int. J. Robot. Res., 9(2), pp. 53–61. [CrossRef]
Weingarten, J., Koditschek, D., Komsuoglu, H., and Massey, C., 2007, “Robotics as the Delivery Vehicle: A Contextualized, Social, Self Paced, Engineering Education for Life-Long Learners,” RSS: Robot Science and Systems, p. 314. Available at http://kodlab.seas.upenn.edu/Haldunk/RSS2007-2
Komsuoglu, H., 2007, “Towards a Comprehensive Infrastructure for Construction of Modular and Extensible Robotic Systems,” Technical Report MS-CIS-07-04, Department of Computer and Information Science, University of Pennsylvania.
Pratt, G., and Williamson, M., 1995, “Series Elastic Actuators,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 1, p. 399.
Fukuoka, Y., Kimuar, H., and Cohen, A. H., 2003, “Adaptive Dynamics Walking of a Quadruped Robot on Irregular Terrain Based on Biological Concepts,” Int. J. Robot. Res., 22(3–4), pp. 187–202. [CrossRef]
Nichol, J. G., Palmer, L., Singh, S., Orin, D., and Waldron, K., 2004, “System Design of a Quadrupedal Galloping Machine,” Int. J. Robot. Res., 23, pp. 1013–1027. [CrossRef]
Lambrecht, B. G. A., Horchler, A. D., and Quinn, R. D., 2005, “A Small, Insect-Inspired Robot That Runs and Jumps,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1252–1257.
Quinn, R. D., Nelson, G. M., Bachmann, R. J., Kingsley, D. A., Offi, J., and Ritzmann, R. E., 2001, “Insect Designs for Improved Robot Mobility,” Proceedings of CLAWAR 2001, D.Berns, ed., Karlsruhe, Germany, pp. 69–76.
Cham, J. G., 2002, “On Stability and Performance in Open-Loop Running,” Ph.D. thesis, Stanford University, Stanford, CA.
Saranli, U., Buehler, M., and Koditschek, D. E., 2001, “RHex: A Simple and Highly Mobile Hexapod Robot,” Int. J. Robot. Res., 20(7), pp. 616–631. [CrossRef]
Altendorfer, R., Moore, N., Komsuoglu, H., Buehler, M., Brown, Jr., H. B., McMordie, D., Saranli, U., Full, R., and Koditschek, D. E., 2001, “RHex: A Biologically Inspired Hexapod Runner,” Auton. Rob., 11(3), pp. 207–213. [CrossRef]
Lin, P.-C., Komsuoglu, H., and Koditschek, D., 2005, “Sensor Data Fusion for Body State Estimation in a Hexapod Robot With Dynamical Gaits,” ICRA, pp. 4733–4738.
Lopes, G., and Koditschek, D., 2007, “Visual Servoing for Nonholonomically Constrained Three Degree of Freedom Kinematic Systems,” Int. J. Robot. Res., 26(7), pp. 715–736. [CrossRef]
Clark, J. E., 2004, “Design, Simulation, and Stability of a Hexapedal Running Robot,” Ph.D. thesis, Stanford University, Stanford, CA.
Burden, S., Clark, J. E., Weingarten, J., Komsouglu, H., and Koditschek, D. E., 2007, “Heterogeneous Leg Stiffness and Roll in Dynamic Running,” IEEE—International Conference of Robotics and Automation.
Moore, E. Z., 2002, “Leg Design and Stair Climbing Control for the RHex Robotic Hexapod,” Master's thesis, McGill University, Montreal, Quebec, Canada.
Vanderborght, B., Van Ham, R., Lefeber, D., Sugar, T., and Hollander, K., 2009, “Comparison of Mechanical Design and Energy Consumption of Adaptable, Passive-Compliant Actuators,” Int. J. Robot. Res., 28(1), pp. 90–103. [CrossRef]
Beyl, P., Vanderborght, B., Van Ham, R., Van Damme, M., Versluys, R., and Lefeber, D., 2006, “Compliant Actuation in New Robotic Applications,” NCTAM06—7th National Congress on Theoretical and Applied Mechanics.
Morita, T., and Sugano, S., 1995, “Design and Development of a New Robotic Joint Using a Mechanical Impedance Adjuster,” IEEE International Conference on Robotics and Automation, Vol. 3, pp. 2469–2475.
Hollander, K., Sugar, T., and Herring, D., 2005, “Adjustable Robotic Tendon Using a ‘Jack Spring’ TM,” IEEE International Conference on Rehabilitation Robotics.
Tabata, O., Konishi, S., Cusin, P., Ito, Y., Kawai, F., Hirai, S., and Kawamura, S., 1999, “Microfabricated Tunable Stiffness Device,” Proceedings of the 13th Annual International Conference on Micro Electro Mechanical Systems.
Moore, E. Z., Campbell, D., Grimminger, F., and Buehler, M., 2002, “Reliable Stair Climbing in the Simple Hexapod ‘RHex’,” Proceedings—IEEE International Conference on Robotics and Automation, Vol. 3, pp. 2222–2227.
Lin, P.-C., 2005, “Proprioceptive Sensing for a Legged Robot,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
Lin, P.-C., Komsuoglu, H., and Koditschek, D. E., 2005, “A Leg Configuration Measurement System for Full Body Posture Estimates in a Hexapod Robot,” IEEE Trans. Rob., 21(3), pp. 411–422. [CrossRef]
Howell, L. L., 2001, Compliant Mechanisms, Wiley, New York.
Howell, L. L., and Midha, A., 1996, “Parametric Deflection Approximations for Initially Curved, Large-Deflection Beams in Compliant Mechanisms,” Proceedings of the ASME Design Engineering Technical Conference.
Merz, R., Prinz, F. B., Ramaswami, K., Terk, M., and Weiss, L. E., 1994, “Shape Deposition Manufacturing,” Proceedings of the Solid Freeform Fabrication Symposium.
Cham, J. G., Bailey, S. A., and Cutkosky, M. R., 2000, “Robust Dynamic Locomotion Through Feedforward-Preflex Interaction,” ASME IMECE Proceedings.
Chitta, S., Karabas, M., Galloway, K., and Kumar, V., 2006, “RoboTrikke: Design, Modeling and Experimentation With a Robotic Trikke,” Proceedings of the ASME Design Engineering Technical Conference.
Dollar, A., and Howe, R., 2005, “Design and Evaluation of a Robust Compliant Grasper Using Shape Deposition Manufacturing,” Proceedings of the ASME Design Engineering Technical Conference.
Shigley, J., 1977, Mechanical Engineering Design, McGraw-Hill, New York.
Barbero, E., 1999, Introduction to Composite Materials Design, Taylor & Francis Inc., London.
Kawamura, S., Yamamoto, T., Ishida, D., Ogata, T., Nakayama, Y., Tabata, O., and Sugiyama, S., 2002, “Development of Passive Elements With Variable Mechanical Impedance for Wearable Robots,” IEEE Interternational Conference on Robotics and Automation, pp. 248–253.
Weingarten, J., Groff, R., and Koditschek, D., 2004, “A Framework for the Coordination of Legged Robot Gaits,” IEEE International Conference of Robotics, Automation and Mechatronics, Singapore.
Galloway, K., 2010, “Passive Variable Compliance for Dynamic Legged Robots,” Ph.D. thesis, University of Pennsylvania, Philadelphia, PA.
Ghigliazza, R. M., Altendorfer, R., Holmes, P., and Koditschek, D., 2005, “A Simply Stabilized Running Model,” SIAM Rev., 47, pp. 519–549. [CrossRef]
Altendorfer, R., Koditschek, D., and Holmes, P., 2004, “Stability Analysis of a Clock-Driven Rigid-Body SLIP Model for RHex,” Int. J. Robot. Res., 23(10–11), pp. 1001–1012. [CrossRef]
Galloway, K., Clark, J., and Koditschek, D., 2007, “Design of a Multi-Directional Variable Stiffness Leg for Dynamic Runnings,” ASME International Mechanical Engineering Congress and Exposition.
Galloway, K. C., Clark, J. E., and Koditschek, D. E., 2009, “Design of a Tunable Stiffness Composite Leg for Dynamic Locomotion,” ASME Conf. Proc., 2009(49040), pp. 215–222.
Galloway, K., Clark, J., Yim, M., and Koditschek, D., 2011, “Experimental Investigations Into the Role of Passive Variable Compliant Legs for Dynamic Robotic Locomotion,” 2011 IEEE International Conference on Robotics and Automation (ICRA), pp. 1243–1249.


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Fig. 1

EduBot [22], a hexapod robot considered for studying the effect of the legs with variable stiffness on the robot's dynamic stability

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Fig. 2

Illustrations of the different spring models used to understand C-leg compliance under load a load, P. (a) Linear model, (b) 2-orthogonal spring model, (c) pseduo-rigid-body model where stiffness is characterized by a single torsional spring.

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Fig. 3

Pseudo-rigid-body model applied to the C-leg. Adapted from Ref. [44].

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Fig. 4

An implementation of a structure-controlled stiffness mechanism applied to a C-leg

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Fig. 5

Application of PRB-model to tunable leg where leg stiffness can be defined by the slider position and the loading point

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Fig. 7

Experimental validation of the PRB model for estimating torsional spring constant

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Fig. 8

Experimental validation of the cantilever beam bending model for estimating lateral leg stiffness

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Fig. 6

Relaxed and compressed images of a C-leg in the experimental set-up

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Fig. 9

Proposed new design: side view of tunable stiffness composite leg design. (a) Rotation directions of gears. (b) Slider adjusted to a higher stiffness setting.

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Fig. 10

Photograph of the prototyped variable stiffness C-leg

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Fig. 11

Close-up of the active component

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Fig. 12

Older design alternative: C-leg with a Nitinol spring element

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Fig. 13

Top view of experimental set-up. (a) Linear stage is in the home position and leg is undeflected. (b) Platform has been moved a distance, d, and the leg is deflected.

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Fig. 14

Spring force response at four different leg stiffness settings each with a curve fit (dotted line) applied to the loading phase

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Fig. 15

Deflection path of leg for various stiffness settings

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Fig. 18

Final leg design: (left) illustration of mechanical stop, (right) photo of final assembly

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Fig. 16

Preliminary experimental results showing specific resistance against relative leg stiffness

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Fig. 17

Preliminary experimental results comparing relative leg stiffness against top forward speed




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