Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T05:14:07.313Z Has data issue: false hasContentIssue false
  • English
  • Français

Energetics of constant height level bounding in quadruped robots

Published online by Cambridge University Press:  24 June 2014

Murali Krishna P.  and
Prasanth Kumar R.
Murali Krishna P.
Affiliation:
Department of Mechanical & Aerospace Engineering, Indian Institute of Technology Hyderabad, Yeddumailaram, Medak 502 205, Andhra Pradesh, India CAIR, DRDO, Bangalore 560 093, Karnataka, India
Prasanth Kumar R.*
Affiliation:
Department of Mechanical & Aerospace Engineering, Indian Institute of Technology Hyderabad, Yeddumailaram, Medak 502 205, Andhra Pradesh, India
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, we investigate the energetics of constant height level bounding gaits in quadruped robots with asymmetric body-mass distribution along the longitudinal axis. Analytical expressions for mechanical specific resistance for two cases of bounding are derived: bounding with equal front and rear leg step lengths, and bounding with unequal front and rear leg step lengths. Specific resistance is found to be independent of mass distribution in the first case, and dependent in the second case. The quadruped robot has average nonzero acceleration/deceleration due to unsymmetric distribution of mass when front and rear leg step lengths are equal. Results show that lower body lengths, lower step lengths, and higher heights from the ground level give lower specific resistance. The effect of body-mass asymmetry is to accelerate in the first case, and to reduce specific resistance in the second case. This result provides some insight into why certain quadrupedal animals in nature evolved to have body-mass asymmetry.

Keywords

Biomimetic robotsLegged robotsService robotsDesignMotion planning
Type
Articles
Information
Robotica , Volume 34 , Issue 2 , February 2016 , pp. 403 - 422
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Raibert, M., Blankespoor, K., Nelson, G., Playter, R. and the BigDog Team, “BigDog, the Rough-Terrain Quadruped Robot,” Proceedings of the 17th World Congress of the International Federation of Automatic Control, Seoul, South Korea (2008) pp. 10823–10825.Google Scholar
2.Song, S. M. and Waldron, K. J., Machines That Walk: The Adaptive Suspension Vehicle (MIT Press, Cambridge, MA, 1989).Google Scholar
3.Jayes, A. S. and Alexander, R., “Mechanics of locomotion of dogs (Canis Familiaris) and sheep (Ovis Aries),” J. Zool. 185 (3), 289–308 (1978).CrossRefGoogle ScholarPubMed
4.Raibert, M. H., “Trotting, pacing, and bounding by a quadruped robot,” J. Biomech. 23, 79–98 (1990).CrossRefGoogle ScholarPubMed
5.Shkolnik, A., Levashov, M., Manchester, I. R. and Tedrake, R., “Bounding on rough terrain with the LittleDog robot,” Int. J. Robot. Res. 30 (2), 192–215 (2011).CrossRefGoogle Scholar
6.Kazemi, H., Majd, V. J. and Moghaddam, M. M., “Modeling and robust backstepping control of an underactuated quadruped robot in bounding motion,” Robotica 31 (3), 423–439 (2013).Google Scholar
7.Minetti, A. E., Ardigo, L. P., Reinach, E. and Saibene, F., “The relationship between mechanical work and energy expenditure of locomotion in horses,” J. Exp. Biol. 202 (17), 2329–2338 (1999).CrossRefGoogle ScholarPubMed
8.Song, S. M., Vohnout, V. J., Waldron, K. J. and Kinzel, G. L., “Computer-aided design of a leg for an energy efficient walking machine,” Mech. Mach. Theory 19, 17–24 (1994).CrossRefGoogle Scholar
9.Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive dynamic walkers,” Sci. Mag. 307, 1082–1085 (2005).Google ScholarPubMed
10.Mettin, U., La Hera, P. X., Freidovich, L. B. and Shiriaev, A. S., “Parallel elastic actuators as a control tool for preplanned trajectories of underactuated mechanical systems,” Int. J. Robot. Res. 29 (9), 1186–1198 (2010).CrossRefGoogle Scholar
11.Haeufle, D. B., Taylor, M. D., Schmitt, S. and Geyer, H., “A Clutched Parallel Elastic Actuator Concept: Towards Energy Efficient Powered Legs in Prosthetics and Robotics,” Proceedings of the IEEE International Conference on Biomedical Robotics and Biomechatronics, Roma, Italy (2012) pp. 1614–1619.Google Scholar
12.Ortega, J. D. and Farley, C. T., “Minimizing center of mass vertical movement increases metabolic cost in walking,” J. Appl. Physiol. 99, 2099–2107 (2005).CrossRefGoogle Scholar
13.Estremera, J. and Waldron, K. J., “Thrust control, stabilization and energetics of a quadruped running robot,” Int. J. Robot. Res. 27 (10), 1135–1151 (2008).CrossRefGoogle Scholar
14.Talebi, S., Poulakakis, I., Papadopoulos, E. and Buehler, M., “Quadruped Robot Running with a Bounding Gait,” In: Experimental Robotics VII (Rus, D. and Singh, S., eds.) (Springer-Verlag, Berlin, Germany, 2001) pp. 281–289.CrossRefGoogle Scholar
15.Poulakakis, I., Smith, J. A. and Buehler, M., “Modeling and experiments of untethered quadrupedal running with a bounding gait: The Scout II robot,” Int. J. Robot. Res. 24 (4), 239–256 (2005).CrossRefGoogle Scholar
16.Krishna, P. M., Kumar, R. P. and Srivastava, S., “Energetics of Level Walking Trot Gaits in Quadruped Robots,” In: Proceedings of the IEEE International Conference on Robotics and Biomimetics-2012, Guangzhou, China (2012) pp. 61–65.CrossRefGoogle Scholar
17.Krishna, P. M., Kumar, R. P. and Srivastava, S., “Level Trot Gait in Quadruped Robots,” Proceedings of Conference on Advances in Robotics, India (2013) pp. 1–5.Google Scholar
18.Lee, D. V., Stakebake, E. F., Walter, R. M. and Carrier, D. R., “Effects of mass distribution on the mechanics of level trotting in dogs,” J. Exp. Biol. 207, 1715–1728 (2004).CrossRefGoogle ScholarPubMed
19.Zou, H. and Schmiedeler, J. P., “The effect of asymmetrical body-mass distribution on the stability and dynamics of quadruped bounding,” IEEE Trans. Robot. 22 (4), 711–723 (2006).Google Scholar
20.Von Karman, T. and Gabrielli, G., “What price speed? Specific power required for propulsion of vehicles,” Mech. Eng. 72, 775–781 (1950).Google Scholar
21.Hiroshi, K., Isao, S. and Hirofumi, M., “Dynamics in the dynamic walk of a quadruped robot,” Adv. Robot. 4 (3), 283–301 (1989).Google Scholar
22.Bertram, J. E. A. and Gutmann, A., “Motions of the running horse and cheetah revisited: Fundamental mechanics of the transverse and rotary gallop,” J. R. Soc. Interface 35 (6), 549–559 (2009).CrossRefGoogle Scholar
23.Srinivasan, M., “Why Walk and Run: Energetic Costs and Energetic Optimality in Simple Mechanics-Based Models of a Bipedal Animal,” Ph.D. Dissertation (Cornell University, Ithaca, NY, 2006).Google Scholar
24.Bryant, J. D., Bennett, M. B., Brust, J. and Alexander, R., “Forces exerted on the ground by galloping dogs (Canis Familiaris),” J. Zool., 213 (2), 193–203 (1987).CrossRefGoogle Scholar
25.Walter, R. M. and Carrier, D. R., “Ground forces applied by galloping dogs,” J. Exp. Biol. 210 (2), 208–216 (2007).CrossRefGoogle ScholarPubMed
26.Walter, R. M. and Carrier, D. R., “Effects of fore-aft body mass distribution on acceleration in dogs,” J. Exp. Biol. 214 (10), 1763–1772 (2011).CrossRefGoogle ScholarPubMed
27.Williams, S. B., Tan, H., Usherwood, J. R. and Wilson, A. M., “Pitch then power: Limitations to acceleration in quadrupeds,” Biol. Lett. 5 (5), 610–613 (2009).CrossRefGoogle ScholarPubMed
28.Hudson, P. E., Corr, S. A. and Wilson, A. M., “High speed galloping in the cheetah (Acinonyx Jubatus) and the racing greyhound (Canis Familiaris): Spatio-temporal and kinetic characteristics,” J. Exp. Biol. 215 (14), 2425–2434 (2012).CrossRefGoogle ScholarPubMed
29.Strang, K. T. and Steudel, K., “Explaining the scaling of transport costs: The role of stride frequency and stride length,” J. Zool. 221 (3), 343–358 (1990).CrossRefGoogle Scholar