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2016 | OriginalPaper | Chapter

Towards a Comparative Measure of Legged Agility

Authors : J. M. Duperret, G. D. Kenneally, J. L. Pusey, D. E. Koditschek

Published in: Experimental Robotics

Publisher: Springer International Publishing

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Abstract

We introduce an agility measure enabling the comparison of two very different leaping-from-rest transitions by two comparably powered but morphologically different legged robots. We use the measure to show that a flexible spine outperforms a rigid back in the leaping-from-rest task. The agility measure also sheds light on the source of this benefit: core actuation through a sufficiently powerful parallel elastic actuated spine outperforms a similar power budget applied either only to preload the spine or only to actuate the spine during the leap, as well as a rigid backed configuration of the identical machine.

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Appendix
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Footnotes
1
Steady state motions such as running or hopping that can be approximated with Hamiltonian systems will have negligible agility according to our metric in accordance with biological observations that these motions require significantly less muscle power output as compared to leaping accelerations [22, 28].
 
2
Likely it will be useful in later work to consider a notion of integrated specific agility accumulated over a sequence of stance events, such as when evaluating the agility of an accelerating bound containing a brief aerial phase between front and rear leg-ground contacts.
 
3
Vicon motion capture data is used to back out the kinetic and potential energy of the robots. Neglecting air resistance, the apex specific extrinsic body energy minus the starting specific extrinsic body energy gives a very close approximation to the specific agility (1) of the leap. The method used to calculate endurance is given in Appendix 1.
 
Literature
1.
go back to reference Zhou, X., Bi, S.: A survey of bio-inspired compliant legged robot designs. Bioinspiration Biomimetics 7(4), 041001 (2012)CrossRef Zhou, X., Bi, S.: A survey of bio-inspired compliant legged robot designs. Bioinspiration Biomimetics 7(4), 041001 (2012)CrossRef
3.
go back to reference Seok, S., Wang, A., Chuah, M.Y., Otten, D., Lang, J., Kim, S.: Design principles for highly efficient quadrupeds and implementation on the mit cheetah robot. In: Proceedings—IEEE International Conference on Robotics and Automation (2013) pp. 3307–3312 Seok, S., Wang, A., Chuah, M.Y., Otten, D., Lang, J., Kim, S.: Design principles for highly efficient quadrupeds and implementation on the mit cheetah robot. In: Proceedings—IEEE International Conference on Robotics and Automation (2013) pp. 3307–3312
4.
go back to reference Ananthanarayanan, A., Azadi, M., Kim, S.: Towards a bio-inspired leg design for high-speed running. Bioinspiration Biomimetics 7(4), 046005 (2012)CrossRef Ananthanarayanan, A., Azadi, M., Kim, S.: Towards a bio-inspired leg design for high-speed running. Bioinspiration Biomimetics 7(4), 046005 (2012)CrossRef
5.
go back to reference Sreenath, K., Park, H., Poulakakis, I., Grizzle, J.W.: A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on mabel. Int. J. Robot. Res. 30(9), 1170–1193 (2011)CrossRef Sreenath, K., Park, H., Poulakakis, I., Grizzle, J.W.: A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on mabel. Int. J. Robot. Res. 30(9), 1170–1193 (2011)CrossRef
6.
go back to reference Grimes J.A., Hurst, J.W.: The design of atrias 1.0 a unique monopod, hopping robot. In: Adaptive Mobile Robotics—Proceedings of the 15th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, CLAWAR 2012 (2012) pp. 548–554 Grimes J.A., Hurst, J.W.: The design of atrias 1.0 a unique monopod, hopping robot. In: Adaptive Mobile Robotics—Proceedings of the 15th International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, CLAWAR 2012 (2012) pp. 548–554
7.
go back to reference Pasupuleti, M., Nadubettu Yadukumar, S., Ames, A.: Human-inspired underactuated bipedal robotic walking with amber on flat-ground, up-slope and uneven terrain. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Algarve, Portugal (2012) Pasupuleti, M., Nadubettu Yadukumar, S., Ames, A.: Human-inspired underactuated bipedal robotic walking with amber on flat-ground, up-slope and uneven terrain. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Algarve, Portugal (2012)
8.
go back to reference Holmes, P., Full, R.J., Koditschek, D.E., Guckenheimer, J.: The dynamics of legged locomotion: models, analyses, and challenges. SIAM Rev. 48(2), 207304 (2006)MathSciNetCrossRefMATH Holmes, P., Full, R.J., Koditschek, D.E., Guckenheimer, J.: The dynamics of legged locomotion: models, analyses, and challenges. SIAM Rev. 48(2), 207304 (2006)MathSciNetCrossRefMATH
9.
go back to reference Koditschek, D.E., Full, R.J., Buehler, M.: Mechanical aspects of legged locomotion control. Arthropod Struct. Dev. 33(3), 251272 (2004)CrossRef Koditschek, D.E., Full, R.J., Buehler, M.: Mechanical aspects of legged locomotion control. Arthropod Struct. Dev. 33(3), 251272 (2004)CrossRef
10.
go back to reference Johnson, A.M., Koditschek, D.E.: Toward a vocabulary of legged leaping. In: Proceedings of the 2013 IEEE International Conference on Robotics and Automation, May 2013, pp. 2553–2560 Johnson, A.M., Koditschek, D.E.: Toward a vocabulary of legged leaping. In: Proceedings of the 2013 IEEE International Conference on Robotics and Automation, May 2013, pp. 2553–2560
11.
go back to reference Libby, T., Moore, T.Y., Chang-Siu, E., Li, D., Cohen, D.J., Jusufi, A., Full, R.J.: Tail-assisted pitch control in lizards, robots and dinosaurs. Nature 481(7380), 181–184 (2012)CrossRef Libby, T., Moore, T.Y., Chang-Siu, E., Li, D., Cohen, D.J., Jusufi, A., Full, R.J.: Tail-assisted pitch control in lizards, robots and dinosaurs. Nature 481(7380), 181–184 (2012)CrossRef
12.
go back to reference Degani, A., Feng, S., Brown, H., Lynch, K., Choset, H., Mason, M.: The parkourbot-a dynamic bowleg climbing robot. In: 2011 IEEE International Conference on IEEE, Robotics and Automation (ICRA) (2011) pp. 795–801 Degani, A., Feng, S., Brown, H., Lynch, K., Choset, H., Mason, M.: The parkourbot-a dynamic bowleg climbing robot. In: 2011 IEEE International Conference on IEEE, Robotics and Automation (ICRA) (2011) pp. 795–801
13.
go back to reference Urata J., Nakanishi, Y., Okada, K., Inaba, M.: Design of high torque and high speed leg module for high power humanoid. In: 2010 IEEE/RSJ International Conference on IEEE, Intelligent Robots and Systems (IROS) (2010), pp. 4497–4502 Urata J., Nakanishi, Y., Okada, K., Inaba, M.: Design of high torque and high speed leg module for high power humanoid. In: 2010 IEEE/RSJ International Conference on IEEE, Intelligent Robots and Systems (IROS) (2010), pp. 4497–4502
14.
go back to reference Dickson, J.D., Patel, J., Clark, J.E.: Towards maneuverability in plane with a dynamic climbing platform. In: 2013 IEEE International Conference on IEEE, Robotics and Automation (ICRA), (2013), pp. 1355–1361 Dickson, J.D., Patel, J., Clark, J.E.: Towards maneuverability in plane with a dynamic climbing platform. In: 2013 IEEE International Conference on IEEE, Robotics and Automation (ICRA), (2013), pp. 1355–1361
15.
go back to reference Bowling, A.P.: Dynamic performance, mobility, and agility of multilegged robots. J. Dyn. Syst. Meas. Control, Trans. ASME 128(4), 765–777 (2006)CrossRef Bowling, A.P.: Dynamic performance, mobility, and agility of multilegged robots. J. Dyn. Syst. Meas. Control, Trans. ASME 128(4), 765–777 (2006)CrossRef
16.
go back to reference Pusey, J.L., Duperret, J.M., Haynes, G.C., Knopf, R., Koditschek, D.E.: Free-standing leaping experiments with a power-autonomous elastic-spined quadruped. In: SPIE Defense, Security, and Sensing, International Society for Optics and Photonics, (2013), vol. 8741, pp. 87 410W–87 410W Pusey, J.L., Duperret, J.M., Haynes, G.C., Knopf, R., Koditschek, D.E.: Free-standing leaping experiments with a power-autonomous elastic-spined quadruped. In: SPIE Defense, Security, and Sensing, International Society for Optics and Photonics, (2013), vol. 8741, pp. 87 410W–87 410W
17.
go back to reference Haynes, G.C., Pusey, J., Knopf, R., Johnson, A.M., Koditschek, D.E.: Laboratory on legs: an architecture for adjustable morphology with legged robots. In: Karlsen, R.E., Gage, D.W., Shoemaker, C.M., Gerhart, G.R. (eds.) Unmanned Systems Technology XIV, vol. 8387, p. 83870W. SPIE (2012) Haynes, G.C., Pusey, J., Knopf, R., Johnson, A.M., Koditschek, D.E.: Laboratory on legs: an architecture for adjustable morphology with legged robots. In: Karlsen, R.E., Gage, D.W., Shoemaker, C.M., Gerhart, G.R. (eds.) Unmanned Systems Technology XIV, vol. 8387, p. 83870W. SPIE (2012)
18.
go back to reference Sheppard, J., Young, W.: Agility literature review: classifications, training and testing. J. Sports Sci. 24(9), 919–932 (2006)CrossRef Sheppard, J., Young, W.: Agility literature review: classifications, training and testing. J. Sports Sci. 24(9), 919–932 (2006)CrossRef
19.
go back to reference Jindrich, D.L., Qiao, M.: Maneuvers during legged locomotion. Chaos: An Interdisc. J. Nonlinear Sci. 19(2), 026 105–026 105 (2009) Jindrich, D.L., Qiao, M.: Maneuvers during legged locomotion. Chaos: An Interdisc. J. Nonlinear Sci. 19(2), 026 105–026 105 (2009)
20.
go back to reference Bennet, H.C.: Clark, The energetics of the jump of the locust schistocerca gregaria. J. Exp. Biol. 63(1), 53–83 (1975) Bennet, H.C.: Clark, The energetics of the jump of the locust schistocerca gregaria. J. Exp. Biol. 63(1), 53–83 (1975)
21.
go back to reference Bennet-Clark, H.C., Lucey, E.C.: The jump of the flea: a study of the energetics and a model of the mechanism. J. Exp. Biol. 47(1), 59–67 (1967) Bennet-Clark, H.C., Lucey, E.C.: The jump of the flea: a study of the energetics and a model of the mechanism. J. Exp. Biol. 47(1), 59–67 (1967)
22.
go back to reference Roberts, T.J., Abbott, E.M., Azizi, E.: The weak link: do muscle properties determine locomotor performance in frogs? Philos. Trans. R. Soc. B: Biol. Sci. 366(1570), 1488–1495 (2011)CrossRef Roberts, T.J., Abbott, E.M., Azizi, E.: The weak link: do muscle properties determine locomotor performance in frogs? Philos. Trans. R. Soc. B: Biol. Sci. 366(1570), 1488–1495 (2011)CrossRef
23.
go back to reference Moore, D., Deuel, N., Drevemo, S., Van den Bogert, A.: Kinematic analysis of world championship three-day event horses jumping a cross-country drop fence. J. Equine Vet. Sci. 15(12), 527–531 (1995)CrossRef Moore, D., Deuel, N., Drevemo, S., Van den Bogert, A.: Kinematic analysis of world championship three-day event horses jumping a cross-country drop fence. J. Equine Vet. Sci. 15(12), 527–531 (1995)CrossRef
24.
go back to reference Pfau, T., Garland de Rivaz, A., Brighton, S., Weller, R.: Kinetics of jump landing in agility dogs. Vet. J. 190(2), 278–283 (2011)CrossRef Pfau, T., Garland de Rivaz, A., Brighton, S., Weller, R.: Kinetics of jump landing in agility dogs. Vet. J. 190(2), 278–283 (2011)CrossRef
25.
go back to reference Walker, J.A.: Does a rigid body limit maneuverability? J. Exp. Biol. 203(22), 3391–3396 (2000) Walker, J.A.: Does a rigid body limit maneuverability? J. Exp. Biol. 203(22), 3391–3396 (2000)
26.
go back to reference Williams, S.B., Tan, H., Usherwood, J.R., Wilson, A.M.: Pitch then power: limitations to acceleration in quadrupeds. Biol. Lett. 5(5), 610–613 (2009)CrossRef Williams, S.B., Tan, H., Usherwood, J.R., Wilson, A.M.: Pitch then power: limitations to acceleration in quadrupeds. Biol. Lett. 5(5), 610–613 (2009)CrossRef
27.
go back to reference Roberts, T.J., Scales, J.A.: Mechanical power output during running accelerations in wild turkeys. J. Exp. Biol. 205(10), 1485–1494 (2002) Roberts, T.J., Scales, J.A.: Mechanical power output during running accelerations in wild turkeys. J. Exp. Biol. 205(10), 1485–1494 (2002)
28.
go back to reference McGowan, C.P., Baudinette, R.V., Usherwood, J.R., Biewener, A.A.: The mechanics of jumping versus steady hopping in yellow-footed rock wallabies. J. Exp. Biol. 208(14), 2741–2751 (2005)CrossRef McGowan, C.P., Baudinette, R.V., Usherwood, J.R., Biewener, A.A.: The mechanics of jumping versus steady hopping in yellow-footed rock wallabies. J. Exp. Biol. 208(14), 2741–2751 (2005)CrossRef
29.
go back to reference Hoover, A.M., Burden, S., Fu, X., Sastry, S.S., Fearing, R.S.: Bio-inspired design and dynamic maneuverability of a minimally actuated six-legged robot. In: 2010 3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics, BioRob 2010, (2010), pp. 869–876 Hoover, A.M., Burden, S., Fu, X., Sastry, S.S., Fearing, R.S.: Bio-inspired design and dynamic maneuverability of a minimally actuated six-legged robot. In: 2010 3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics, BioRob 2010, (2010), pp. 869–876
30.
go back to reference Jindrich, D.L., Smith, N.C., Jespers, K., Wilson, A.M.: Mechanics of cutting maneuvers by ostriches (struthio camelus). J. Exp. Biol. 210(8), 1378–1390 (2007)CrossRef Jindrich, D.L., Smith, N.C., Jespers, K., Wilson, A.M.: Mechanics of cutting maneuvers by ostriches (struthio camelus). J. Exp. Biol. 210(8), 1378–1390 (2007)CrossRef
31.
go back to reference Jindrich, D.L., Full, R.J.: Many-legged maneuverability: dynamics of turning in hexapods. J. Exp. Biol. 202(12), 1603–1623 (1999) Jindrich, D.L., Full, R.J.: Many-legged maneuverability: dynamics of turning in hexapods. J. Exp. Biol. 202(12), 1603–1623 (1999)
32.
go back to reference Jindrich, D.L., Besier, T.F., Lloyd, D.G.: A hypothesis for the function of braking forces during running turns. J. Biomech. 39(9), 1611–1620 (2006)CrossRef Jindrich, D.L., Besier, T.F., Lloyd, D.G.: A hypothesis for the function of braking forces during running turns. J. Biomech. 39(9), 1611–1620 (2006)CrossRef
33.
go back to reference Astley, H.C., Roberts, T.J.: Evidence for a vertebrate catapult: elastic energy storage in the plantaris tendon during frog jumping. Biol. Lett. 8(3), 386–389 (2012)CrossRef Astley, H.C., Roberts, T.J.: Evidence for a vertebrate catapult: elastic energy storage in the plantaris tendon during frog jumping. Biol. Lett. 8(3), 386–389 (2012)CrossRef
34.
go back to reference Webb, P.W.: Maneuverability-general issues. IEEE J. Oceanic Eng. 29(3), 547–555 (2004)CrossRef Webb, P.W.: Maneuverability-general issues. IEEE J. Oceanic Eng. 29(3), 547–555 (2004)CrossRef
35.
go back to reference Schmidt-Nielsen, K.: Scaling: Why is Animal Size so Important?. Cambridge University Press, Cambridge, (1984) Schmidt-Nielsen, K.: Scaling: Why is Animal Size so Important?. Cambridge University Press, Cambridge, (1984)
36.
go back to reference d’Arcy, W.T.: On Growth and Form. Cambridge Univ Press, Cambridge (1963) d’Arcy, W.T.: On Growth and Form. Cambridge Univ Press, Cambridge (1963)
37.
go back to reference Burridge, R.R., Rizzi, A.A., Koditschek, D.E.: Sequential composition of dynamically dexterous robot behaviors. Int. J. Robot. Res. 18(6), 534555 (1999)CrossRef Burridge, R.R., Rizzi, A.A., Koditschek, D.E.: Sequential composition of dynamically dexterous robot behaviors. Int. J. Robot. Res. 18(6), 534555 (1999)CrossRef
38.
go back to reference Ghigliazza, R.M., Altendorfer, R., Holmes, P., Koditschek, D.: A simply stabilized running model. SIAM J. Appl. Dyn. Syst. 2(2), 187218 (2003)MathSciNetCrossRefMATH Ghigliazza, R.M., Altendorfer, R., Holmes, P., Koditschek, D.: A simply stabilized running model. SIAM J. Appl. Dyn. Syst. 2(2), 187218 (2003)MathSciNetCrossRefMATH
39.
go back to reference Johnson, A.M., Koditschek, D.E.: Parametric Jumping Dataset on the Rhex Robot. University of Pennsylvania, Tech. Rep. (2012) Johnson, A.M., Koditschek, D.E.: Parametric Jumping Dataset on the Rhex Robot. University of Pennsylvania, Tech. Rep. (2012)
40.
go back to reference Paranjape, A.A., Ananthkrishnan, N.: Combat aircraft agility metrics-a review. J. Aerosp. Sci. Technol. 58(2), 143–154 (2006) Paranjape, A.A., Ananthkrishnan, N.: Combat aircraft agility metrics-a review. J. Aerosp. Sci. Technol. 58(2), 143–154 (2006)
41.
go back to reference Cho, W., Choi, J., Kim, C., Choi, S., Yi, K.: Unified chassis control for the improvement of agility, maneuverability, and lateral stability. IEEE Trans. Veh. Technol. 61(3), 1008–1020 (2012)CrossRef Cho, W., Choi, J., Kim, C., Choi, S., Yi, K.: Unified chassis control for the improvement of agility, maneuverability, and lateral stability. IEEE Trans. Veh. Technol. 61(3), 1008–1020 (2012)CrossRef
42.
go back to reference Yi, J., Li, J., Lu, J., Liu, Z.: On the stability and agility of aggressive vehicle maneuvers: a pendulum-turn maneuver example. IEEE Trans. Control Syst. Technol. 20(3), 663–676 (2012)CrossRef Yi, J., Li, J., Lu, J., Liu, Z.: On the stability and agility of aggressive vehicle maneuvers: a pendulum-turn maneuver example. IEEE Trans. Control Syst. Technol. 20(3), 663–676 (2012)CrossRef
43.
go back to reference Nie, C., Van Dooren, S.C., Shah, J., Spenko, M.: “Increasing agility in unmanned ground vehicles using variable internal mass and inertial properties,” in. Proc. SPIE 7332, 733218 (2009)CrossRef Nie, C., Van Dooren, S.C., Shah, J., Spenko, M.: “Increasing agility in unmanned ground vehicles using variable internal mass and inertial properties,” in. Proc. SPIE 7332, 733218 (2009)CrossRef
44.
go back to reference Paranjape, A.A., Chung, S.-J., Selig, M.S.: Flight mechanics of a tailless articulated wing aircraft. Bioinspiration Biomimetics 6(2), 026005 (2011)CrossRef Paranjape, A.A., Chung, S.-J., Selig, M.S.: Flight mechanics of a tailless articulated wing aircraft. Bioinspiration Biomimetics 6(2), 026005 (2011)CrossRef
45.
go back to reference Wise, K.A., Roy, D.J.B.: Agile missile dynamics and control. J. Guidance, Control, Dyn. 21(3), 441–449 (1998)CrossRef Wise, K.A., Roy, D.J.B.: Agile missile dynamics and control. J. Guidance, Control, Dyn. 21(3), 441–449 (1998)CrossRef
47.
go back to reference Bitten, R.: Qualitative and quantitative comparison of government and industry agility metrics. J. Aircr. 27(3), 276–282 (1990)CrossRef Bitten, R.: Qualitative and quantitative comparison of government and industry agility metrics. J. Aircr. 27(3), 276–282 (1990)CrossRef
48.
go back to reference Galloway, K.C., Haynes, G.C., Ilhan, B.D., Johnson, A.M., Knopf, R., Lynch, G., Plotnick, B., White, M., Koditschek, D.E.: X-rhex: A Highly Mobile Hexapedal Robot for Sensorimotor Tasks. University of Pennsylvania, Tech. Rep. (2010) Galloway, K.C., Haynes, G.C., Ilhan, B.D., Johnson, A.M., Knopf, R., Lynch, G., Plotnick, B., White, M., Koditschek, D.E.: X-rhex: A Highly Mobile Hexapedal Robot for Sensorimotor Tasks. University of Pennsylvania, Tech. Rep. (2010)
49.
go back to reference Lynch, G.A., Clark, J.E., Lin, P.-C., Koditschek, D.E.: A bioinspired dynamical vertical climbing robot. Int. J. Robot. Res. 31(8), 974–996 (2012)CrossRef Lynch, G.A., Clark, J.E., Lin, P.-C., Koditschek, D.E.: A bioinspired dynamical vertical climbing robot. Int. J. Robot. Res. 31(8), 974–996 (2012)CrossRef
50.
go back to reference Goldman, D.I., Chen, T.S., Dudek, D.M., Full, R.J.: Dynamics of rapid vertical climbing in cockroaches reveals a template. J. Exp. Biol. 209(15), 29903000 (2006)CrossRef Goldman, D.I., Chen, T.S., Dudek, D.M., Full, R.J.: Dynamics of rapid vertical climbing in cockroaches reveals a template. J. Exp. Biol. 209(15), 29903000 (2006)CrossRef
Metadata
Title
Towards a Comparative Measure of Legged Agility
Authors
J. M. Duperret
G. D. Kenneally
J. L. Pusey
D. E. Koditschek
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-23778-7_1