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Geometric Mechanics of Contact-Switching Systems (2306.10276v2)

Published 17 Jun 2023 in cs.RO, cs.SY, and eess.SY

Abstract: Discrete and periodic contact switching is a key characteristic of steady-state legged locomotion. This paper introduces a framework for modeling and analyzing this contact-switching behavior through the framework of geometric mechanics on a toy robot model that can make continuous limb swings and discrete contact switches. The kinematics of this model form a hybrid shape-space and by extending the generalized Stokes' theorem to compute discrete curvature functions called \textit{stratified panels}, we determine average locomotion generated by gaits spanning multiple contact modes. Using this tool, we also demonstrate the ability to optimize gaits based on the system's locomotion constraints and perform gait reduction on a complex gait spanning multiple contact modes to highlight the method's scalability to multilegged systems.

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References (34)
  1. S. D. Kelly and R. M. Murray, “Geometric phases and robotic locomotion,” Journal of Robotic Systems, vol. 12, no. 6, pp. 417–431, 1995.
  2. R. L. Hatton and H. Choset, “Nonconservativity and noncommutativity in locomotion,” European Phy. J. Special Topics, vol. 224, no. 17, pp. 3141–3174, 2015.
  3. B. Bittner, R. L. Hatton, and S. Revzen, “Geometrically optimal gaits: a data-driven approach,” Nonlinear Dynamics, vol. 94, pp. 1933–1948, 2018.
  4. H. C. Astley, J. R. Mendelson III, J. Dai, C. Gong, B. Chong, J. M. Rieser, P. E. Schiebel, S. S. Sharpe, R. L. Hatton, H. Choset, et al., “Surprising simplicities and syntheses in limbless self-propulsion in sand,” J. Exp. Biology, vol. 223, no. 5, p. jeb103564, 2020.
  5. B. Chong, T. Wang, E. Erickson, P. J. Bergmann, and D. I. Goldman, “Coordinating tiny limbs and long bodies: Geometric mechanics of lizard terrestrial swimming,” Proc. of the Nat. Acad. of Sci., vol. 119, no. 27, p. e2118456119, 2022.
  6. H. O. Jacobs, “Geometric descriptions of couplings in fluids and circuits,” Ph.D. dissertation, California Institute of Technology, 2012.
  7. R. L. Hatton and H. Choset, “Geometric swimming at low and high reynolds numbers,” IEEE Trans. on Robotics, vol. 29, no. 3, pp. 615–624, 2013.
  8. J. Dai, H. Faraji, C. Gong, R. L. Hatton, D. I. Goldman, and H. Choset, “Geometric swimming on a granular surface.” in Robotics: Science and Systems, 2016, pp. 1–7.
  9. D. Zhao, B. Bittner, G. Clifton, N. Gravish, and S. Revzen, “Walking is like slithering: A unifying, data-driven view of locomotion,” Proc. of the Nat. Acad. of Sci., vol. 119, no. 37, p. e2113222119, 2022.
  10. B. Chong, Y. O. Aydin, C. Gong, G. Sartoretti, Y. Wu, J. M. Rieser, H. Xing, P. E. Schiebel, J. W. Rankin, K. B. Michel, et al., “Coordination of lateral body bending and leg movements for sprawled posture quadrupedal locomotion,” Int. J. of Robotics Research, vol. 40, no. 4-5, pp. 747–763, 2021.
  11. B. Chong, J. He, S. Li, E. Erickson, K. Diaz, T. Wang, D. Soto, and D. I. Goldman, “Self-propulsion via slipping: Frictional swimming in multilegged locomotors,” Proc. of the Nat. Acad. of Sci., vol. 120, no. 11, p. e2213698120, 2023.
  12. B. Chong, Y. Ozkan Aydin, G. Sartoretti, J. M. Rieser, C. Gong, H. Xing, H. Choset, and D. I. Goldman, “A hierarchical geometric framework to design locomotive gaits for highly articulated robots,” in Robotics: science and systems, 2019.
  13. B. Chong, Y. O. Aydin, J. M. Rieser, G. Sartoretti, T. Wang, J. Whitman, A. Kaba, E. Aydin, C. McFarland, K. D. Cruz, et al., “A general locomotion control framework for multi-legged locomotors,” Bioinspiration & Biomimetics, vol. 17, no. 4, p. 046015, 2022.
  14. B. Chong, T. Wang, B. Lin, S. Li, H. Choset, G. Blekherman, and D. Goldman, “Moving sidewinding forward: optimizing contact patterns for limbless robots via geometric mechanics,” in Robotics: science and systems, vol. 17, 2021.
  15. B. Chong, T. Wang, L. Bo, S. Li, P. C. Muthukrishnan, J. He, D. Irvine, H. Choset, G. Blekherman, and D. I. Goldman, “Optimizing contact patterns for robot locomotion via geometric mechanics,” The International Journal of Robotics Research, p. 02783649231188387, 2023.
  16. R. L. Hatton, Z. Brock, S. Chen, H. Choset, H. Faraji, R. Fu, N. Justus, and S. Ramasamy, “The geometry of optimal gaits for inertia-dominated kinematic systems,” IEEE Transactions on Robotics, vol. 38, no. 5, pp. 3279–3299, 2022.
  17. B. Goodwine and J. Burdick, “Motion planning for kinematic stratified systems with application to quasi-static legged locomotion and finger gaiting,” IEEE Trans. on Rob. & Automation, vol. 18, no. 2, pp. 209–222, 2002.
  18. S. D. De Rivaz, B. Goldberg, N. Doshi, K. Jayaram, J. Zhou, and R. J. Wood, “Inverted and vertical climbing of a quadrupedal microrobot using electroadhesion,” Science Robotics, vol. 3, no. 25, p. eaau3038, 2018.
  19. A. Ruina, “Nonholonomic stability aspects of piecewise holonomic systems,” Reports on mathematical physics, vol. 42, no. 1-2, pp. 91–100, 1998.
  20. R. J. Full and D. E. Koditschek, “Templates and anchors: neuromechanical hypotheses of legged locomotion on land,” Journal of experimental biology, vol. 202, no. 23, pp. 3325–3332, 1999.
  21. R. L. Hatton, T. Dear, and H. Choset, “Kinematic cartography and the efficiency of viscous swimming,” IEEE Trans. on Robotics, vol. 33, no. 3, pp. 523–535, 2017.
  22. R. L. Hatton, Y. Ding, H. Choset, and D. I. Goldman, “Geometric visualization of self-propulsion in a complex medium,” Physical review letters, vol. 110, no. 7, p. 078101, 2013.
  23. J. Gray and G. Hancock, “The propulsion of sea-urchin spermatozoa,” Journal of Experimental Biology, vol. 32, no. 4, pp. 802–814, 1955.
  24. D. Zhao, “Locomotion of low-dof multi-legged robots,” Ph.D. dissertation, Ph. D. dissertation, University of Michigan, 2021.
  25. Z. Wu, D. Zhao, and S. Revzen, “Coulomb friction crawling model yields linear force–velocity profile,” Journal of Applied Mechanics, vol. 86, no. 5, p. 054501, 2019.
  26. T. Zhang and D. I. Goldman, “The effectiveness of resistive force theory in granular locomotion,” Physics of Fluids, vol. 26, no. 10, 2014.
  27. S. Ramasamy and R. L. Hatton, “The geometry of optimal gaits for drag-dominated kinematic systems,” IEEE Trans. on Robotics, vol. 35, no. 4, pp. 1014–1033, 2019.
  28. R. L. Hatton and H. Choset, “Geometric motion planning: The local connection, stokes’ theorem, and the importance of coordinate choice,” Int. J. of Robotics Research, vol. 30, no. 8, pp. 988–1014, 2011.
  29. J. Lee, J. Hwangbo, L. Wellhausen, V. Koltun, and M. Hutter, “Learning quadrupedal locomotion over challenging terrain,” Science robotics, vol. 5, no. 47, p. eabc5986, 2020.
  30. K. Jayaram, J. Shum, S. Castellanos, E. F. Helbling, and R. J. Wood, “Scaling down an insect-size microrobot, hamr-vi into hamr-jr,” in 2020 IEEE International Conference on Robotics and Automation (ICRA).   IEEE, 2020, pp. 10 305–10 311.
  31. N. Doshi, K. Jayaram, S. Castellanos, S. Kuindersma, and R. J. Wood, “Effective locomotion at multiple stride frequencies using proprioceptive feedback on a legged microrobot,” Bioinspiration & biomimetics, vol. 14, no. 5, p. 056001, 2019.
  32. S. Choi, G. Ji, J. Park, H. Kim, J. Mun, J. H. Lee, and J. Hwangbo, “Learning quadrupedal locomotion on deformable terrain,” Science Robotics, vol. 8, no. 74, p. eade2256, 2023.
  33. K. Jayaram, N. T. Jafferis, N. Doshi, B. Goldberg, and R. J. Wood, “Concomitant sensing and actuation for piezoelectric microrobots,” Smart Materials and Structures, vol. 27, no. 6, p. 065028, 2018.
  34. H. Kabutz and K. Jayaram, “Design of clari: A miniature modular origami passive shape-morphing robot,” Advanced Intelligent Systems, vol. n/a, no. n/a, p. 2300181, 2023. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/aisy.202300181
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