Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Cosserat-Rod Based Dynamic Modeling of Soft Slender Robot Interacting with Environment (2307.06261v1)

Published 12 Jul 2023 in cs.RO

Abstract: Soft slender robots have attracted more and more research attentions in these years due to their continuity and compliance natures. However, mechanics modeling for soft robots interacting with environment is still an academic challenge because of the non-linearity of deformation and the non-smooth property of the contacts. In this work, starting from a piece-wise local strain field assumption, we propose a nonlinear dynamic model for soft robot via Cosserat rod theory using Newtonian mechanics which handles the frictional contact with environment and transfer them into the nonlinear complementary constraint (NCP) formulation. Moreover, we smooth both the contact and friction constraints in order to convert the inequality equations of NCP to the smooth equality equations. The proposed model allows us to compute the dynamic deformation and frictional contact force under common optimization framework in real time when the soft slender robot interacts with other rigid or soft bodies. In the end, the corresponding experiments are carried out which valid our proposed dynamic model.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (57)
  1. C. Laschi, B. Mazzolai, and M. Cianchetti, “Soft robotics: Technologies and systems pushing the boundaries of robot abilities,” Science robotics, vol. 1, no. 1, p. eaah3690, 2016.
  2. D. Trivedi, C. D. Rahn, W. M. Kier, and I. D. Walker, “Soft robotics: Biological inspiration, state of the art, and future research,” Applied bionics and biomechanics, vol. 5, no. 3, pp. 99–117, 2008.
  3. D. Rus and M. T. Tolley, “Design, fabrication and control of soft robots,” Nature, vol. 521, no. 7553, pp. 467–475, 2015.
  4. G. Dogangil, B. Davies, and F. Rodriguez y Baena, “A review of medical robotics for minimally invasive soft tissue surgery,” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, vol. 224, no. 5, pp. 653–679, 2010.
  5. M. Calisti, G. Picardi, and C. Laschi, “Fundamentals of soft robot locomotion,” Journal of The Royal Society Interface, vol. 14, no. 130, p. 20170101, 2017.
  6. M. Cianchetti, C. Laschi, A. Menciassi, and P. Dario, “Biomedical applications of soft robotics,” Nature Reviews Materials, vol. 3, no. 6, pp. 143–153, 2018.
  7. T. M. Bieze, F. Largilliere, A. Kruszewski, Z. Zhang, R. Merzouki, and C. Duriez, “Finite element method-based kinematics and closed-loop control of soft, continuum manipulators,” Soft robotics, vol. 5, no. 3, pp. 348–364, 2018.
  8. G. Olson, R. L. Hatton, J. A. Adams, and Y. Mengüç, “An euler–bernoulli beam model for soft robot arms bent through self-stress and external loads,” International Journal of Solids and Structures, vol. 207, pp. 113–131, 2020.
  9. L. Lindenroth, J. Back, A. Schoisengeier, Y. Noh, H. Würdemann, K. Althoefer, and H. Liu, “Stiffness-based modelling of a hydraulically-actuated soft robotics manipulator,” in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).   IEEE, 2016, pp. 2458–2463.
  10. H. Godaba, F. Putzu, T. Abrar, J. Konstantinova, and K. Althoefer, “Payload capabilities and operational limits of eversion robots,” in Towards Autonomous Robotic Systems: 20th Annual Conference, TAROS 2019, London, UK, July 3–5, 2019, Proceedings, Part II 20.   Springer, 2019, pp. 383–394.
  11. F. Boyer, G. De Nayer, A. Leroyer, and M. Visonneau, “Geometrically exact kirchhoff beam theory: application to cable dynamics,” Journal of Computational and Nonlinear Dynamics, vol. 6, no. 4, 2011.
  12. H.-J. Su, “A pseudorigid-body 3r model for determining large deflection of cantilever beams subject to tip loads,” 2009.
  13. S. Huang, D. Meng, X. Wang, B. Liang, and W. Lu, “A 3d static modeling method and experimental verification of continuum robots based on pseudo-rigid body theory,” in 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).   IEEE, 2019, pp. 4672–4677.
  14. F. Boyer and F. Renda, “Poincare’s equations for cosserat media: Application to shells,” Journal of Nonlinear Science, vol. 27, pp. 1–44, 2017.
  15. C. B. Black, J. Till, and D. C. Rucker, “Parallel continuum robots: Modeling, analysis, and actuation-based force sensing,” IEEE Transactions on Robotics, vol. 34, no. 1, pp. 29–47, 2017.
  16. D. C. Rucker and R. J. Webster III, “Statics and dynamics of continuum robots with general tendon routing and external loading,” IEEE Transactions on Robotics, vol. 27, no. 6, pp. 1033–1044, 2011.
  17. D.-Q. Cao and R. W. Tucker, “Nonlinear dynamics of elastic rods using the cosserat theory: Modelling and simulation,” International Journal of Solids and Structures, vol. 45, no. 2, pp. 460–477, 2008.
  18. Y. Haibin, K. Cheng, L. Junfeng, and Y. Guilin, “Modeling of grasping force for a soft robotic gripper with variable stiffness,” Mechanism and Machine Theory, vol. 128, pp. 254–274, 2018.
  19. J. D. Till, “On the statics, dynamics, and stability of continuum robots: Model formulations and efficient computational schemes,” 2019.
  20. J. Till, V. Aloi, and C. Rucker, “Real-time dynamics of soft and continuum robots based on cosserat rod models,” The International Journal of Robotics Research, vol. 38, no. 6, pp. 723–746, 2019.
  21. X. Zhang, F. K. Chan, T. Parthasarathy, and M. Gazzola, “Modeling and simulation of complex dynamic musculoskeletal architectures,” Nature communications, vol. 10, no. 1, p. 4825, 2019.
  22. F. Boyer, V. Lebastard, F. Candelier, and F. Renda, “Dynamics of continuum and soft robots: A strain parameterization based approach,” IEEE Transactions on Robotics, vol. 37, no. 3, pp. 847–863, 2020.
  23. F. Renda, M. Giorelli, M. Calisti, M. Cianchetti, and C. Laschi, “Dynamic model of a multibending soft robot arm driven by cables,” IEEE Transactions on Robotics, vol. 30, no. 5, pp. 1109–1122, 2014.
  24. D. E. Stewart, “Rigid-body dynamics with friction and impact,” SIAM review, vol. 42, no. 1, pp. 3–39, 2000.
  25. T. M. Wasfy and A. K. Noor, “Computational strategies for flexible multibody systems,” Appl. Mech. Rev., vol. 56, no. 6, pp. 553–613, 2003.
  26. A. Munjiza and K. Andrews, “Penalty function method for combined finite–discrete element systems comprising large number of separate bodies,” International Journal for numerical methods in engineering, vol. 49, no. 11, pp. 1377–1396, 2000.
  27. J. Spillmann, M. Becker, and M. Teschner, “Non-iterative computation of contact forces for deformable objects,” 2007.
  28. V. J. Milenkovic and H. Schmidl, “Optimization-based animation,” in Proceedings of the 28th annual conference on Computer graphics and interactive techniques, 2001, pp. 37–46.
  29. D. M. Kaufman, T. Edmunds, and D. K. Pai, “Fast frictional dynamics for rigid bodies,” in ACM SIGGRAPH 2005 Papers, 2005, pp. 946–956.
  30. D. E. Stewart and J. C. Trinkle, “An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction,” International Journal for Numerical Methods in Engineering, vol. 39, no. 15, pp. 2673–2691, 1996.
  31. K. Erleben, “Velocity-based shock propagation for multibody dynamics animation,” ACM Transactions on Graphics (TOG), vol. 26, no. 2, pp. 12–es, 2007.
  32. C. Duriez, F. Dubois, A. Kheddar, and C. Andriot, “Realistic haptic rendering of interacting deformable objects in virtual environments,” IEEE transactions on visualization and computer graphics, vol. 12, no. 1, pp. 36–47, 2005.
  33. M. A. Otaduy, R. Tamstorf, D. Steinemann, and M. Gross, “Implicit contact handling for deformable objects,” in Computer Graphics Forum, vol. 28, no. 2.   Wiley Online Library, 2009, pp. 559–568.
  34. D. Harmon, E. Vouga, B. Smith, R. Tamstorf, and E. Grinspun, “Asynchronous contact mechanics,” in ACM SIGGRAPH 2009 papers, 2009, pp. 1–12.
  35. S. Niebe and K. Erleben, “Numerical methods for linear complementarity problems in physics-based animation,” Synthesis Lectures on Computer Graphics and Animation, vol. 7, no. 1, pp. 1–159, 2015.
  36. P. Alart and A. Curnier, “A mixed formulation for frictional contact problems prone to newton like solution methods,” Computer methods in applied mechanics and engineering, vol. 92, no. 3, pp. 353–375, 1991.
  37. A. Curnier and P. Alart, “A generalized newton method for contact problems with friction,” Journal de mécanique théorique et appliquée, 1988.
  38. S. P. Dirkse and M. C. Ferris, “The path solver: a nommonotone stabilization scheme for mixed complementarity problems,” Optimization methods and software, vol. 5, no. 2, pp. 123–156, 1995.
  39. F. Bertails-Descoubes, F. Cadoux, G. Daviet, and V. Acary, “A nonsmooth newton solver for capturing exact coulomb friction in fiber assemblies,” ACM Transactions on Graphics (TOG), vol. 30, no. 1, pp. 1–14, 2011.
  40. G. Daviet, F. Bertails-Descoubes, and L. Boissieux, “A hybrid iterative solver for robustly capturing coulomb friction in hair dynamics,” in Proceedings of the 2011 SIGGRAPH Asia Conference, 2011, pp. 1–12.
  41. D. M. Kaufman, R. Tamstorf, B. Smith, J.-M. Aubry, and E. Grinspun, “Adaptive nonlinearity for collisions in complex rod assemblies,” ACM Transactions on Graphics (TOG), vol. 33, no. 4, pp. 1–12, 2014.
  42. C. Armanini, F. Boyer, A. T. Mathew, C. Duriez, and F. Renda, “Soft robots modeling: A structured overview,” IEEE Transactions on Robotics, 2023.
  43. H. Li, L. Xun, and G. Zheng, “Piecewise linear strain cosserat model for soft slender manipulator,” IEEE Transactions on Robotics, pp. 1–18, 2023.
  44. C. Armanini, I. Hussain, M. Z. Iqbal, D. Gan, D. Prattichizzo, and F. Renda, “Discrete cosserat approach for closed-chain soft robots: Application to the fin-ray finger,” IEEE Transactions on Robotics, vol. 37, no. 6, pp. 2083–2098, 2021.
  45. E. Drumwright and D. A. Shell, “Modeling contact friction and joint friction in dynamic robotic simulation using the principle of maximum dissipation,” in Algorithmic Foundations of Robotics IX: Selected Contributions of the Ninth International Workshop on the Algorithmic Foundations of Robotics.   Springer, 2011, pp. 249–266.
  46. O. L. Mangasarian, “Equivalence of the complementarity problem to a system of nonlinear equations,” SIAM Journal on Applied Mathematics, vol. 31, no. 1, pp. 89–92, 1976.
  47. O. Mangasarian and C. Chen, “A class of smoothing functions for nonlinear and mixed complementarity problems,” Tech. Rep., 1994.
  48. F. Renda, F. Boyer, J. Dias, and L. Seneviratne, “Discrete cosserat approach for multisection soft manipulator dynamics,” IEEE Transactions on Robotics, vol. 34, no. 6, pp. 1518–1533, 2018.
  49. Y. H. Cheng and J. Wang, “A motion image detection method based on the inter-frame difference method,” in Applied Mechanics and Materials, vol. 490.   Trans Tech Publ, 2014, pp. 1283–1286.
  50. F. Boyer, V. Lebastard, F. Candelier, and F. Renda, “Dynamics of continuum and soft robots: A strain parameterization based approach,” IEEE Transactions on Robotics, vol. 37, no. 3, pp. 847–863, 2021.
  51. Z. Zhu and K. Zhang, “A superlinearly convergent sqp algorithm for mathematical programs with linear complementarity constraints,” Applied mathematics and computation, vol. 172, no. 1, pp. 222–244, 2006.
  52. F. Facchinei and J. Soares, “A new merit function for nonlinear complementarity problems and a related algorithm,” SIAM Journal on Optimization, vol. 7, no. 1, pp. 225–247, 1997.
  53. E. Todorov, “Implicit nonlinear complementarity: A new approach to contact dynamics,” in 2010 IEEE international conference on robotics and automation.   IEEE, 2010, pp. 2322–2329.
  54. T. S. Munson, F. Facchinei, M. C. Ferris, A. Fischer, and C. Kanzow, “The semismooth algorithm for large scale complementarity problems,” INFORMS Journal on Computing, vol. 13, no. 4, pp. 294–311, 2001.
  55. D. M. Kaufman, S. Sueda, D. L. James, and D. K. Pai, “Staggered projections for frictional contact in multibody systems,” in ACM SIGGRAPH Asia 2008 papers, 2008, pp. 1–11.
  56. M. Macklin, K. Erleben, M. Müller, N. Chentanez, S. Jeschke, and V. Makoviychuk, “Non-smooth newton methods for deformable multi-body dynamics,” ACM Transactions on Graphics (TOG), vol. 38, no. 5, pp. 1–20, 2019.
  57. F. Boyer, V. Lebastard, F. Candelier, and F. Renda, “Extended hamilton’s principle applied to geometrically exact kirchhoff sliding rods,” Journal of Sound and Vibration, vol. 516, p. 116511, 2022.
Citations (5)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now