Abstract
As robot bodies become more capable, the motivation grows to better coordinate them–whether multiple limbs attached to a body or multiple bodies assigned to a task. This paper introduces a new formalism for coordination of periodic tasks, with specific application to gait transitions for legged platforms. Specifically, we make modest use of classical group theory to replace combinatorial search and optimization with a computationally simpler and conceptually more straightforward appeal to elementary algebra.
We decompose the space of all periodic legged gaits into a cellular complex indexed using “Young Tableaux”, making transparent the proximity to steady state orbits and the neighborhood structure. We encounter the simple task of transitioning between these gaits while locomoting over level ground. Toward that end, we arrange a family of dynamical reference generators over the “Gait Complex” and construct automated coordination controllers to force the legged system to converge to a specified cell’s gait, while assessing the relative static stability of gaits by approximating their stability margin via transit through a “Stance Complex”. To integrate these two different constructs–the Gait Complex describing possible gaits, the Stance Complex defining safe locomotion–we utilize our compositional lexicon to plan switching policies for a hybrid control approach. Results include automated gait transitions for a variety of useful gaits, shown via tests on a hexapedal robot.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bretl, T., Lall, S.: Testing static equilibrium for legged robots. IEEE Transactions on Robotics 24(4), 794–807 (2008)
Cohen, F., Koditschek, D.E.: Hybrid control over the coordination complex (2009) (in preparation)
Cohen, F.R.: On Configuration Spaces (2008) (in preparation)
Farley, C., Taylor, C.: A mechanical trigger for the trot-gallop transition in horses. Science 253, 306–308 (1991)
Griffin, T., Kram, R., Wickler, S., Hoyt, D.: Biomechanical and energetic determinants of the walk-trot transition in horses. Journal of Experimental Biology 207, 4215–4223 (2004)
Hatcher, A.: Algebraic topology. Cambridge University Press, Cambridge (2002)
Haynes, G.C.: Gait regulation control techniques for robust legged locomotion. Ph.D. thesis, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA (2008)
Haynes, G.C., Khripin, A., Lynch, G., Amory, J., Saunders, A., Rizzi, A.A., Koditschek, D.E.: Rapid pole climbing with a quadrupedal robot. In: Proc. IEEE International Conference on Robotics and Automation (2009)
Haynes, G.C., Rizzi, A.A.: Gait regulation and feedback on a robotic climbing hexapod. In: Proceedings of Robotics: Science and Systems, Philadelphia, USA (2006)
Haynes, G.C., Rizzi, A.A.: Gaits and gait transitions for legged robots. In: ICRA, Orlando, FL, USA, pp. 1117–1122 (2006)
Hildebrand, M.: Symmetrical gaits of horses. Science 150, 701–708 (1965)
Klavins, E., Koditschek, D.E.: Phase regulation of decentralized cyclic robotic systems. International Journal of Robotics Research 21(3) (2002)
McMordie, D., Buehler: Towards pronking with a hexapod robot. In: Proc. 4th Intl. Conf. on Climbing and Walking Robots, Storming Media, Karlsruhe, Germany, pp. 659–666 (2001)
Moore, E.Z., Campbell, D., Grimminger, F., Buehler, M.: Reliable stair climbing in the simple hexapod ’rhex’. In: IEEE International Conference on Proceedings Robotics and Automation 2002 (ICRA 2002), vol. 3 (2002)
Muybridge, E.: Animals in Motion. Dover Publications, New York (1899)
Sagan, B.: The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions. Wadsworth and Brooks/Cole, Mathematics Series (1991)
Saranli, U., Buehler, M., Koditschek, D.E.: RHex: A Simple and Highly Mobile Hexapod Robot. The International Journal of Robotics Research 20(7), 616–631 (2001), doi:10.1177/02783640122067570
Saranli, U., Buehler, M., Koditschek, D.E.: Rhex: A simple and highly mobile hexapod robot. The International Journal of Robotics Research 20, 616 (2001)
Spenko, M.A., Haynes, G.C., Saunders, A., Rizzi, A.A., Cutkosky, M., Full, R.J., Koditschek, D.E.: Biologically inspired climbing with a hexapedal robot. Journal of Field Robotics 25(4-5) (2008)
Weingarten, J.D., Groff, R.E., Koditschek, D.E.: A framework for the coordination of legged robot gaits. In: IEEE Conference on Robotics, Automation and Mechatronics (2004)
Wickler, S., Hoyt, D., Cogger, E., Myers, G.: The energetics of the trot-gallop transition. Journal of Experimental Biology 206, 1557–1564 (2003)
Wilson, D.M.: Insect walking. Annual Review of Entomology 11, 103–122 (1966)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haynes, G.C., Cohen, F.R., Koditschek, D.E. (2011). Gait Transitions for Quasi-static Hexapedal Locomotion on Level Ground. In: Pradalier, C., Siegwart, R., Hirzinger, G. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19457-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-19457-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19456-6
Online ISBN: 978-3-642-19457-3
eBook Packages: EngineeringEngineering (R0)