Skip to main content
SpringerLink
Log in

Motion and shape control of soft robots and materials

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

A continuum-based approach for simultaneously controlling the motion and shape of soft robots and materials (SRM) is proposed. This approach allows for systematically computing the actuation forces for arbitrary desired SRM motion and geometry. In order to control both motion and shape, the position and position gradients of the absolute nodal coordinate formulation (ANCF) are used to formulate rheonomic specified trajectory and shape constraint equations, used in an inverse dynamics procedure to define the actuation control forces. Unlike control of rigid-body systems which requires a number of independent actuation forces equal to the number of the joint coordinates, the SRM motion/shape control leads to generalized control forces which need to be interpreted differently in order to properly define the actuation forces. While the definition of these motion/shape control forces is demonstrated using air pressure actuation commonly used in the SRM control, the proposed procedure can be applied to other SRM actuation types. The approaches for determining the actuation pressure in the two cases of space-dependent and constant pressures are outlined. Effect of the change in the surface geometry on the actuation pressure is accounted for using Nanson’s formula. The obtained numerical results demonstrate that the motion and shape can be simultaneously controlled using the new actuation force definitions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Calderone, L.: Robots in manufacturing applications | manufacturing tomorrow, 2016. https://www.manufacturingtomorrow.com/article/2016/07/robots-in-manufacturing-applications/8333 (2016)

  2. Book, W.J.: Recursive Lagrangian dynamics of flexible manipulator arms. Int. J. Robot. Res. 3(3), 87–101 (1984)

    Article  Google Scholar 

  3. Jayaweera, N., Webb, P.: Metrology-assisted robotic processing of aerospace applications. Int. J. Comput. Integr. Manuf. 23(3), 283–296 (2010)

    Article  Google Scholar 

  4. Jafari, J., Ghazal, M., Nazemizadeh, M.: Nonlinear formulation of flexible-link robots based on finite element approach. Int. J. Basic Sci. Appl. Res. 3(11), 831–834 (2014)

    Google Scholar 

  5. Korayem, M.H., Rahimi, H.N.: Nonlinear dynamic analysis for elastic robotic arms. Front. Mech. Eng. 6, 219–228 (2008)

    Google Scholar 

  6. Korayem, M.H., Rahimi, H.N., Nikoobin, A., Nazemizadeh, M.: Maximum allowable dynamic payload for flexible mobile robotic manipulators. Latin Am. Appl. Res. 43(1), 29–35 (2013)

    Google Scholar 

  7. Kumar, R., Berkelman, P., Gupta, P., Barnes, A., Jensen, P.S., Whitcomb, L.L., Taylor, R.: Preliminary experiments in cooperative human/robot force control for robot assisted micro-surgical manipulation. Proc. IEEE Int. Conf. Robot. Autom. 1, 610–617 (2000)

    Google Scholar 

  8. Megahed, S.M., Hamza, K.T.: Modeling and simulation of planar flexible link manipulators with rigid tip connections to revolute joints. Robotica 22(3), 285–300 (2004)

    Article  Google Scholar 

  9. Meghdari, A., Fahimi, F.: On the first-order decoupling of dynamical equations of motion for elastic multibody systems as applied to a two-link flexible manipulator. Multibody Syst. Dyn. 5, 1–20 (2001)

    Article  MATH  Google Scholar 

  10. Changizi, K., Shabana, A.A.: A recursive formulation for the dynamic analysis of open loop deformable multi-body systems. ASME J. Appl. Mech. 55, 687–693 (1988)

    Article  MATH  Google Scholar 

  11. Gofron, M., Shabana, A.A.: Equivalence of driving forces in flexible multibody systems. Int. J. Numer. Methods Eng. 38, 2907–2928 (1995)

    Article  MATH  Google Scholar 

  12. Shabana, A.A., Hwang, Y.L.: Dynamic coupling between the joint and elastic coordinates in flexible mechanism systems. Int. J. Robot. Res. 12(3), 299–306 (1993)

    Article  Google Scholar 

  13. Sherif, K., Nachbagauer, K.: A detailed derivation of the velocity-dependent inertia forces in the floating frame of reference formulation. ASME J. Comput. Nonlinear Dyn. (2014). https://doi.org/10.1115/1.4026083

    Article  Google Scholar 

  14. Shabana, A.A.: Dynamics of Multibody Systems, 5th edn. Cambridge University Press, New York (2020)

    Book  MATH  Google Scholar 

  15. Cook, R.D.: Concepts and Applications of Finite Element Analysis. Wiley, New York (1981)

    MATH  Google Scholar 

  16. Logan, D.L.: A First Course in the Finite Element Method, 6th Edition, Chapter 15, Cengage Learning (2017)

  17. Zienkiewicz, O.C.: The Finite Element Method, 3rd edn. McGraw Hill, New York (1977)

    MATH  Google Scholar 

  18. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method, Vol 2: Solid Mechanics, vol. 5. Butterworth-Heinemann, Oxford (2000)

    MATH  Google Scholar 

  19. Farin, G.: Curves and Surfaces for CAGD, A Practical Guide, 5th edn. Morgan Kaufmann, Publishers, , San Francisco (1999)

    Google Scholar 

  20. Gallier, J.: Geometric Methods and Applications: For Computer Science and Engineering. Springer, New York (2011)

    Book  MATH  Google Scholar 

  21. Goetz, A.: Introduction to Differential Geometry. Addison Wesley, Boston (1970)

    MATH  Google Scholar 

  22. Kreyszig, E.: Differential Geometry. Dover Publications, USA (1991)

    MATH  Google Scholar 

  23. Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

  24. Rogers, D.F.: An Introduction to NURBS with Historical Perspective. Academic Press, San Diego, CA (2001)

    Google Scholar 

  25. Lee, C., Kim, M., Kim, Y.J., Hong, N., Ryu, S., Kim, J., Kim, S.: Soft robot review. Int. J. Control Autom. Syst. 15(1), 3–15 (2017)

    Article  Google Scholar 

  26. Rus, D., Tolley, M.T.: Design, fabrication and control of soft robots. Nature 521, 467–475 (2015)

    Article  Google Scholar 

  27. Boyraz, P., Runge, G., Raatz, A.: An overview of novel actuators for soft robotics. Actuators 7(3), 48–68 (2018)

    Article  Google Scholar 

  28. Kim, S., Laschi, C., Trimmer, B.: Soft robotics: a bioinspired evolution in robotics. Trends Biotechnol. 31(5), 287–294 (2013)

    Article  Google Scholar 

  29. Zolfagharian, A., Kouzani, A.Z., Khoo, S.Y., Moghadam, A.A.A., Gibson, I., Kaynak, A.: Evolution of 3D printed soft actuators. Sens. Actuators, A 250, 258–272 (2016)

    Article  Google Scholar 

  30. Galloway, K.C., Becker, K.P., Phillips, B., Licht, S., Tchernov, D., Wood, R.J., Gruber, D.F.: Soft robotic grippers for biological sampling on deep reefs. Soft Robot. 3(1), 23–33 (2016). https://doi.org/10.1089/soro.2015.0019

    Article  Google Scholar 

  31. Hod, L.: Challenges and opportunities for design, simulation, and fabrication of soft robots. Soft Robot. 1(1), 21–27 (2013)

    Google Scholar 

  32. Marchese, A.D., Onal, C.D., Rus, D.: Autonomous soft robotic fish capable of escape maneuvers using fluidic elastomer actuators. Soft Robot. 1(1), 75–87 (2014)

    Article  Google Scholar 

  33. Stokes, A.A., Sheperd, R.F., Morin, S.A., Ilievski, F., Whitesides, G.M.: A hybrid combining hard and soft robots. Soft Robot. 1(1), 70–74 (2014). https://doi.org/10.1089/soro.2013.0002

    Article  Google Scholar 

  34. Tolley, M.T., Shepherd, R.F., Mosadegh, B., Galloway, K.C., Wehner, M., Karpelson, M., Wood, R.J., Whitesides, G.M.: A resilient, untethered soft robot. Soft Robot. 1(3), 213–223 (2014). https://doi.org/10.1089/soro.2014.0008

    Article  Google Scholar 

  35. Chen, Y., Zhang, D.G., Li, L.: Dynamic analysis of rotating curved beams by using absolute nodal coordinate formulation based on radial point interpolation method. J. Sound Vib. 441, 63–83 (2019)

    Article  Google Scholar 

  36. Dmitrochenko, O.N., Pogorelov, D.Y.: Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst. Dyn. 10, 17–43 (2003)

    Article  MATH  Google Scholar 

  37. Fotland, G., Haskins, C., Rølvåg, T.: Trade study to select best alternative for cable and pulley simulation for cranes on offshore vessels. Syst. Eng. 23, 177–188 (2019). https://doi.org/10.1002/sys.21503

    Article  Google Scholar 

  38. Hewlett, J.: Methods for Real-Time Simulation of Systems of Rigid and Flexible Bodies with Unilateral Contact and Friction, Ph.D. Thesis, Department of Mechanical Engineering, McGill University (2019)

  39. Hewlett, J., Arbatani, S., Kovecses, J.: A fast and stable first-order method for simulation of flexible beams and cables. Nonlinear Dyn. 99, 1211–1226 (2020)

    Article  Google Scholar 

  40. Htun, T.Z., Suzuki, H., Garcia-Vallejo, D.: Dynamic modeling of a radially multilayered tether cable for a remotely-operated underwater vehicle (ROV) based on the absolute nodal coordinate formulation (ANCF). Mech. Mach. Theory 153, 103961 (2020). https://doi.org/10.1016/j.mechmachtheory.2020.103961

    Article  Google Scholar 

  41. Shabana, A.A., Eldeeb, A.E.: Relative orientation constraints in the nonlinear large displacement analysis: application to soft materials. Nonlinear Dyn. 101, 2551–2575 (2020)

    Article  Google Scholar 

  42. Kłodowski, A., Rantalainen, T., Mikkola, A., Heinonen, A., Sievänen, H.: Flexible multibody approach in forward dynamic simulation of locomotive strains in human skeleton with flexible lower body bones. Multibody Syst. Dyn. 25(4), 395–409 (2011)

    Article  MATH  Google Scholar 

  43. Laflin, J.J., Anderson, K.S., Khan, I.M., Poursina, M.: New and extended applications of the divide-and-conquer algorithm for multibody dynamics. ASME J. Comput. Nonlinear Dyn. 9(4), 0410041–0410048 (2014)

    Google Scholar 

  44. Lee, J.H., Park, T.W.: Dynamic analysis model for the current collection performance of high-speed trains using the absolute nodal coordinate formulation. Trans. Kor. Soc. Mech. Eng. A 36, 339–346 (2012)

    Article  Google Scholar 

  45. Li, S., Wang, Y., Ma, X., Wang, S.: Modeling and simulation of a moving yarn segment: based on the absolute nodal coordinate formulation. Math. Probl. Eng. 2019, 1–15 (2019). https://doi.org/10.1155/2019/6567802

    Article  Google Scholar 

  46. Nachbagauer, K.: Development of shear and cross section deformable beam finite elements applied to large deformation and dynamics problems, Ph.D. dissertation, Johannes Kepler University, Linz, Austria (2013)

  47. Nachbagauer, K.: State of the art of ANCF elements regarding geometric description, interpolation strategies, definition of elastic forces, validation and locking phenomenon in comparison with proposed beam finite elements. Arch. Comput. Methods Eng. 21(3), 293–319 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  48. Nachbagauer, K., Pechstein, A.S., Irschik, H., Gerstmayr, J.: A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation. Multibody Syst. Dyn. 26(3), 245–263 (2011)

    Article  MATH  Google Scholar 

  49. Olshevskiy, A., Dmitrochenko, O., Kim, C.W.: Three-dimensional solid brick element using slopes in the absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 9(2), 021001-1-021001–10 (2014)

    Google Scholar 

  50. Orzechowski, G.: Analysis of beam elements of circular cross section using the absolute nodal coordinate formulation. Arch. Mech. Eng. 59(3), 283–296 (2012)

    Article  MathSciNet  Google Scholar 

  51. Orzechowski, G., Frączek, J.: Integration of the equations of motion of multibody systems using absolute nodal coordinate formulation. Acta Mech. Autom. 6(2), 75–83 (2012)

    Google Scholar 

  52. Orzechowski, G., Fraczek, J.: Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF. Nonlinear Dyn. 82(1), 451–464 (2015)

    Article  MathSciNet  Google Scholar 

  53. Pan, K., Cao, D.: Absolute nodal coordinate finite element approach to the two-dimensional liquid sloshing problems. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 234(2), 322–346 (2020). https://doi.org/10.1177/1464419320907785

    Article  Google Scholar 

  54. Shabana, A.A.: Computational Continuum Mechanics, 3rd edn. Wiley, Chichester, UK (2018)

    Book  MATH  Google Scholar 

  55. Shen, Z., Liu, C., Li, H.: Viscoelastic analysis of bistable composite shells via absolute nodal coordinate formulation. Compos. Struct. (2020). https://doi.org/10.1016/j.compstruct.2020.112537

    Article  Google Scholar 

  56. Shen, Z., Tian, Q., Liu, X., Hu, G.: Thermally induced vibrations of flexible beams using absolute nodal coordinate formulation. Aerosp. Sci. Technol. 29(1), 386–393 (2013)

    Article  Google Scholar 

  57. Sheng, F., Zhong, Z., Wang, K.: Theory and model implementation for analyzing line structures subject to dynamic motions of large deformation and elongation using the absolute nodal coordinate formulation (ANCF) approach. Nonlinear Dyn. 101(1), 333–359 (2020). https://doi.org/10.1007/s11071-020-05783-4

    Article  Google Scholar 

  58. Skrinjar, L., Slavic, J., Boltežar, M.: Absolute nodal coordinate formulation in a pre-stressed large-displacements dynamical system. J. Mech. Eng. 63, 417–425 (2017). https://doi.org/10.5545/sv-jme.2017.4561

    Article  Google Scholar 

  59. Takahashi, Y., Shimizu, N., Suzuki, K.: Study on the frame structure modeling of the beam element formulated by absolute coordinate approach. J. Mech. Sci. Technol. 19, 283–291 (2005)

    Article  Google Scholar 

  60. Tian, Q., Chen, L.P., Zhang, Y.Q., Yang, J.Z.: An efficient hybrid method for multibody dynamics simulation based on absolute nodal coordinate formulation. ASME J. Comput. Nonlinear Dyn. 4(2), 021009-1-021009–14 (2009)

    Google Scholar 

  61. Wang, J., Wang, T.: Buckling analysis of beam structure with absolute nodal coordinate formulation. IMechE J. Mech. Eng. Sci. (2020). https://doi.org/10.1177/0954406220947117

    Article  Google Scholar 

  62. Yamano, A., Shintani, A., Ito, T., Nakagawa, C., Ijima, H.: Influence of boundary conditions on a flutter-mill. J. Sound Vib. 478, 115359 (2020)

    Article  Google Scholar 

  63. Yoo, W.S., Lee, J.H., Park, S.J., Sohn, J.H., Pogolev, D., Dmitrochenko, O.: Large deflection analysis of a thin plate: computer simulation and experiment. Multibody Syst. Dyn. 11, 185–208 (2004)

    Article  MATH  Google Scholar 

  64. Yu, L., Zhao, Z., Tang, J., Ren, G.: Integration of absolute nodal elements into multibody system. Nonlinear Dyn. 62, 931–943 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  65. Yuan, T., Liu, Z., Zhou, Y., Liu, J.: Dynamic modeling for foldable origami space membrane structure with contact-impact during deployment. Multibody Syst. Dyn. 50, 1–24 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  66. Zhang, W., Zhu, W., Zhang, S.: Deployment dynamics for a flexible solar array composed of composite-laminated plates. ASCE J. Aerosp. Eng. 33, 04020071-1-04020071–21 (2020)

    Article  Google Scholar 

  67. Marchese, A.D, Katzshmann, R.K, Rus, D.: Whole arm planning for a soft and highly compliant 2d robotic manipulator. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Chicago, IL, pp. 554–560 (2014)

  68. Calisti, M., Gioelli, M., Levy, G., Mazzolai, B., Hochner, B., Laschi, C., Dario, P.: An octopus-bioinspired solution to movement and manipulation for soft robots. Bioinsp. Biomimetics 6(3), 036002 (2011)

    Article  Google Scholar 

  69. Laschi, C., Cianchetti, M., Mazzolai, B., Margheri, L., Follador, M., Dario, P.: Soft robot arm inspired by the octopus. Adv. Robot. 26(7), 709–727 (2012)

    Article  Google Scholar 

  70. Goldberg, N.N., Huang, X., Majidi, C., Novelia, A., O’Reilly, O.M., Paley, D.A., Scott, W.L.: On planar discrete elastic rod models for the locomotion of soft robots. Soft Robot. 6(5), 595–610 (2019)

    Article  Google Scholar 

  71. Guo, H., Zhang, J., Wang, T., Li, Y., Hong, J., Li, Y.: Design and control of an inchworm-inspired soft robot with omega-arching locomotion. In: 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, pp. 4154–4159 (2017)

  72. Huang, W., Huang, X., Majidi, C., Jawed, M.K.: Dynamics simulation of articulated soft robots. Nat. Commun. 11(1), 2233 (2020)

    Article  Google Scholar 

  73. Huang, X., Kumar, K., Jawed, M.K., Nasab, A.M., Ye, Z., Shan, W., Majidi, C.: Highly dynamic shape memory alloy actuator for fast moving soft robots. Adv. Mater. Technol. 4(4), 1–9 (2019)

    Article  Google Scholar 

  74. Huang, X., Kumar, K., Jawed, M.K., Ye, Z., Majidi, C.: Soft electrically actuated quadruped (SESQ)—integrating a flex circuit board and elastomeric limbs for versatile mobility. IEEE Robot. Autom. Lett. 4(3), 2415–2422 (2019)

    Article  Google Scholar 

  75. Lin, H., Leisk, G.G., Trimmer, B.: GoQBot: a caterpillar-inspired soft-bodied rolling robot. Bioinsp. Biomimetics 6(2), 026007 (2011)

    Article  Google Scholar 

  76. Tian, Q., Zhang, P., Luo, K.: Dynamics of soft mechanical systems actuated by dielectric elastomers. Mech. Syst. Signal Process. 151, 107392 (2021)

    Article  Google Scholar 

  77. Branyan, C., Fleming, C., Remaley, J., Kothari, A., Tumer, K., Hatton, R.L., Mengüç Y.: Soft snake robots: mechanical design and geometric gait implementation. In: IEEE International Conference on Robotics and Biomimetics (ROBIO), Macau, pp. 282–289 (2017)

  78. De Payrebrune, K.M., O’Reilly, O.M.: On the development of rod-based models for pneumatically actuated soft robot arms: a five-parameter constitutive relation. Int. J. Solids Struct. 120, 1339–1351 (2017)

    Article  Google Scholar 

  79. De Payrebrune, K.M., O’Reilly, O.M.: On constitutive relations for a rod-based model of a pneu-net bending actuator. Extreme Mech. Lett. 8, 38–46 (2016)

    Article  Google Scholar 

  80. Alici, G., Canty, T., Mutlu, R., Hu, W., Sencadas, V.: Modeling and experimental evaluation of bending behavior of soft pneumatic actuators made of discrete actuation chambers’. Soft Robot. 5(1), 24–35 (2018)

    Article  Google Scholar 

  81. Gasoto, R., Macklin, M., Liu, X., Sun, Y., Erleben, K., Onal, C., Fu, J.: A validated physical model for real-time simulation of soft robotic snakes. In: International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada, pp. 6272–6279 (2019)

  82. Homberg, B.S., Katzschmann, R.K., Dogar, M.R., Rus, D.: Haptic identification of object using a modular soft robotic gripper. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, pp. 1698–1705 (2015)

  83. Hu, W., Mutlu, R., Li, W., Alici, G.: A structural optimisation method for a soft pneumatic actuator. Robotics 7(2), 1–16 (2018)

    Article  Google Scholar 

  84. Katzschmann, R.K., Marchese, A.D., Rus, D.: Hydraulic autonomous soft robotic fish for 3d swimming. Exp. Robot. 109, 405–420 (2016)

    Article  Google Scholar 

  85. Luo, M., Yan, R., Wan, Z., Qin, Y., Santoso, J., Skorina, E.H., Onal, C.D.: OriSnake: design, fabrication and experimental analysis of a 3-d origami snake robot. IEEE Robot. Autom. Lett. 3(3), 1993–1999 (2018)

    Article  Google Scholar 

  86. Manns, M., Morales, J., Frohn, P.: Additive manufacturing of silicon based pneunets as soft robotic actuators. Proc. CIRP 72, 328–333 (2018)

    Article  Google Scholar 

  87. Mosadegh, B., Polygerinos, P., Keplinger, C., Wennstedt, S., Shepard, R.F., Gupta, U., Shim, J., Bertoldi, K., Walsh, C.J., Whitesides, G.M.: Pneumatic networks for soft robotics that actuate rapidly. Adv. Funct. Mater. 24(15), 2163–2170 (2014)

    Article  Google Scholar 

  88. Onal, C.D., Rus, D.: Autonomous undulatory serpentine locomotion utilizing body dynamics of a fluidic soft robot. Bioinsp. Biomimetics 8(2), 1–10 (2013)

    Article  Google Scholar 

  89. Polygerinos, P., Lyne, S., Wang, Z., Nicolini, L.F., Mosadegh, B., Whitesides, G.M., Walsh, C.J.: Towards a soft pneumatic glove for hand rehabilitation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, pp. 1512–1517 (2013)

  90. Qin, Y., Wan, Z., Sun, Y., Skorina, E.H., Luo, M., Onal, C.D.: Design, fabrication and experimental analysis of a 3-D robotic snake. In: 2018 IEEE International Conference on Soft Robotics (RoboSoft), Livorno, pp. 77–82 (2018)

  91. Souhail. A., Vessakosol, P.: PneuNets bending actuator design and fabrication using low cost silicones. In: The 9th TSME International Conference on Mechanical Engineering, pp. 1–7 (2018)

  92. Sun, Y., Song, Y.S., Paik, J.: Characterization of silicone rubber based soft pneumatic actuators. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, pp. 4446–4453 (2013)

  93. Sun, Y., Zhang, Q., Chen, X., Chen, H.: An optimum design method of pneu-net actuators for trajectory matching utilizing a bending model and GA. Math. Probl. Eng. 2019, 1–12 (2019)

    Google Scholar 

  94. Della Santina, C., Katzschmann, R.K., Bicchi, A., Rus, D.: Model-based dynamic feedback control of a planar soft robot: Trajectory tracking and interaction with the environment. Int. J. Robot. Res. 39(4), 490–513 (2020)

    Article  Google Scholar 

  95. Sadati, S.M.H., Naghibi, S.E., Shiva, A., Michael, B., Renson, L., Howard, M., Rucker, C.D., Althoefer, K., Nanayakkara, T., Zschaler, S., Bergeles, C.: TMTDyn: a matlab package for modeling and control of hybrid rigid-continuum robots based on discretized lumped systems and reduced-order models. Int. J. Robot. Res. (2019). https://doi.org/10.1177/0278364919881685

    Article  Google Scholar 

  96. Du Pasquier, C., Chen, T., Tibbits, S., Shea, K.: Design and computational modeling of a 3D printed pneumatic toolkit for soft robotics’. Soft Robot. 6(5), 657–663 (2019)

    Article  Google Scholar 

  97. Nguyen, P.H., Zhang, W.: Design and computational modeling of fabric soft pneumatic actuators for wearable assistive devices. Sci. Rep. 10(1), 1–13 (2020)

    Google Scholar 

  98. Grossi, E., Shabana, A.A.: ‘Analysis of high-frequency ANCF modes: Navier–Stokes physical damping and implicit numerical integration. Acta Mech. 230, 2581–2605 (2019)

    Article  MathSciNet  Google Scholar 

  99. Lipińska, M., Soszka, K.: Viscoelastic behavior, curing and reinforcement mechanism of various silica and POSS filled methyl-vinyl polysiloxane MVQ rubber. Silicon 11, 2293–2305 (2019)

    Article  Google Scholar 

  100. Zhao, J., Jiang, N., Zhang, D., He, B., Chen, X.: Study on optimization of damping performance and damping temperature range of silicone rubber by polyborosiloxane gel. Polymers 12, 1196 (2020)

    Article  Google Scholar 

  101. Di Lallo, A., Catalano, M.G., Garabini, M., Grioli, G., Gabiccini, M., Bicchi, A.: Dynamic morphological computation through damping design of soft continuum robots. Front. Robot. AI 6, 1–19 (2019)

    Article  Google Scholar 

  102. Adami, M., Seibel, A.: On-board pneumatic pressure generation methods for soft robotics applications. Actuators, ol. 8(1) (2019)

  103. Shabana, A.A.: Continuum-based geometry/analysis approach for flexible and soft robotic systems (FSRS). Soft Rob. 5(5), 613–621 (2018). https://doi.org/10.1089/soro.2018.0007

    Article  Google Scholar 

  104. SOFA (Simulation Open Framework Architecture) Software, https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.sofa-framework.org%2F&data=04%7C01%7Cshabana%40uic.edu%7C79e4c8fb5bcd4c80af3208d8a88f9c14%7Ce202cd477a564baa99e3e3b71a7c77dd%7C0%7C0%7C637444682071332605%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=t5fm2yU%2FqHfw39GtKbKI1fVKXwh%2BAOazmKMRoeKKXE0%3D&reserved=0

Download references

Acknowledgements

This research was supported by the National Science Foundation (Projects # 1852510).

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Ahmed A. Shabana & Ahmed E. Eldeeb

Authors
  1. Ahmed A. Shabana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed E. Eldeeb
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmed A. Shabana.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shabana, A.A., Eldeeb, A.E. Motion and shape control of soft robots and materials. Nonlinear Dyn 104, 165–189 (2021). https://doi.org/10.1007/s11071-021-06272-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06272-y

Keywords

Search

Navigation