Authors

Brandon Caasenbrood, Alexander Pogromsky, Henk Nijmeijer

Abstract

In this work, we discuss the application of energy-based controller design for under-actuated soft robot manipulators. The continuous dynamics of the soft robot are modeled through the differential geometry of Cosserat beams. Using a finite-dimensional truncation, the system can be written as a reduced port-Hamiltonian model that preserves the passivity condition. Then, a model-based controller is introduced that produces a local minimizer of closed-loop potential energy for the desired end-effector configuration. The stabilizing control utilizes an energy-based approach and exploits the passivity of the soft robotic system. The effectiveness of the energy-based controller is demonstrated through extensive simulations of various soft robotic systems that share a resemblance with biology. All software and numerical studies are provided in an open-access SOROTOKI toolkit written in Matlab.

Keywords

Soft robotics; Port-Hamiltonian; Energy-based control

Citation

  • Journal: SN Computer Science
  • Year: 2022
  • Volume: 3
  • Issue: 6
  • Pages:
  • Publisher: Springer Science and Business Media LLC
  • DOI: 10.1007/s42979-022-01373-w

BibTeX

@article{Caasenbrood_2022,
  title={{Energy-Shaping Controllers for Soft Robot Manipulators Through Port-Hamiltonian Cosserat Models}},
  volume={3},
  ISSN={2661-8907},
  DOI={10.1007/s42979-022-01373-w},
  number={6},
  journal={SN Computer Science},
  publisher={Springer Science and Business Media LLC},
  author={Caasenbrood, Brandon and Pogromsky, Alexander and Nijmeijer, Henk},
  year={2022}
}

Download the bib file

References

  • Astrid, P., Weiland, S., Willcox, K. & Backx, T. Missing Point Estimation in Models Described by Proper Orthogonal Decomposition. IEEE Trans. Automat. Contr. 53, 2237–2251 (2008) – 10.1109/tac.2008.2006102
  • Borja, P., Dabiri, A. & Santina, C. D. Energy-based shape regulation of soft robots with unactuated dynamics dominated by elasticity. 2022 IEEE 5th International Conference on Soft Robotics (RoboSoft) (2022) doi:10.1109/robosoft54090.2022.9762071 – 10.1109/robosoft54090.2022.9762071
  • F Boyer, Appl Robot. (2010)
  • Boyer, F., Lebastard, V., Candelier, F. & Renda, F. Dynamics of Continuum and Soft Robots: A Strain Parameterization Based Approach. IEEE Trans. Robot. 37, 847–863 (2021) – 10.1109/tro.2020.3036618
  • Bruder, D., Fu, X., Gillespie, R. B., Remy, C. D. & Vasudevan, R. Data-Driven Control of Soft Robots Using Koopman Operator Theory. IEEE Trans. Robot. 37, 948–961 (2021) – 10.1109/tro.2020.3038693
  • Caasenbrood, B. J., Pogromsky, A. Y. & Nijmeijer, H. Dynamic modeling of hyper-elastic soft robots using spatial curves. IFAC-PapersOnLine 53, 9238–9243 (2020) – 10.1016/j.ifacol.2020.12.2209
  • Caasenbrood, B., Pogromsky, A. & Nijmeijer, H. Energy-based Control for Soft Manipulators using Cosserat-beam Models. Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics 311–319 (2021) doi:10.5220/0010581503110319 – 10.5220/0010581503110319
  • Caasenbrood, B., Pogromsky, A. & Nijmeijer, H. Control-Oriented Models for Hyperelastic Soft Robots Through Differential Geometry of Curves. Soft Robotics 10, 129–148 (2023) – 10.1089/soro.2021.0035
  • Chang, H.-S. et al. Energy Shaping Control of a CyberOctopus Soft Arm. 2020 59th IEEE Conference on Decision and Control (CDC) 3913–3920 (2020) doi:10.1109/cdc42340.2020.9304408 – 10.1109/cdc42340.2020.9304408
  • Shepherd, R. F. et al. Multigait soft robot. Proc. Natl. Acad. Sci. U.S.A. 108, 20400–20403 (2011) – 10.1073/pnas.1116564108
  • Santina, C. D. & Rus, D. Control Oriented Modeling of Soft Robots: The Polynomial Curvature Case. IEEE Robot. Autom. Lett. 5, 290–298 (2020) – 10.1109/lra.2019.2955936
  • Duriez, C. Control of elastic soft robots based on real-time finite element method. 2013 IEEE International Conference on Robotics and Automation (2013) doi:10.1109/icra.2013.6631138 – 10.1109/icra.2013.6631138
  • Falkenhahn, V., Mahl, T., Hildebrandt, A., Neumann, R. & Sawodny, O. Dynamic Modeling of Bellows-Actuated Continuum Robots Using the Euler–Lagrange Formalism. IEEE Trans. Robot. 31, 1483–1496 (2015) – 10.1109/tro.2015.2496826
  • Franco, E. & Garriga-Casanovas, A. Energy-shaping control of soft continuum manipulators with in-plane disturbances. The International Journal of Robotics Research 40, 236–255 (2020) – 10.1177/0278364920907679
  • Katzschmann, R. K., Santina, C. D., Toshimitsu, Y., Bicchi, A. & Rus, D. Dynamic Motion Control of Multi-Segment Soft Robots Using Piecewise Constant Curvature Matched with an Augmented Rigid Body Model. 2019 2nd IEEE International Conference on Soft Robotics (RoboSoft) 454–461 (2019) doi:10.1109/robosoft.2019.8722799 – 10.1109/robosoft.2019.8722799
  • Kim, N.-H. Erratum to: Introduction to Nonlinear Finite Element Analysis. Introduction to Nonlinear Finite Element Analysis E1–E1 (2018) doi:10.1007/978-1-4419-1746-1_6 – 10.1007/978-1-4419-1746-1_6
  • Largilliere, F. et al. Real-time control of soft-robots using asynchronous finite element modeling. 2015 IEEE International Conference on Robotics and Automation (ICRA) (2015) doi:10.1109/icra.2015.7139541 – 10.1109/icra.2015.7139541
  • Marchese, A. D., Onal, C. D. & Rus, D. Autonomous Soft Robotic Fish Capable of Escape Maneuvers Using Fluidic Elastomer Actuators. Soft Robotics 1, 75–87 (2014) – 10.1089/soro.2013.0009
  • RM Murray, A mathematical introduction to robotic manipulation (1994)
  • Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
  • Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
  • Renaud, C., Cros, J.-M., Feng, Z.-Q. & Yang, B. The Yeoh model applied to the modeling of large deformation contact/impact problems. International Journal of Impact Engineering 36, 659–666 (2009) – 10.1016/j.ijimpeng.2008.09.008
  • Renda, F., Boyer, F., Dias, J. & Seneviratne, L. Discrete Cosserat Approach for Multisection Soft Manipulator Dynamics. IEEE Trans. Robot. 34, 1518–1533 (2018) – 10.1109/tro.2018.2868815
  • Renda, F., Armanini, C., Lebastard, V., Candelier, F. & Boyer, F. A Geometric Variable-Strain Approach for Static Modeling of Soft Manipulators With Tendon and Fluidic Actuation. IEEE Robot. Autom. Lett. 5, 4006–4013 (2020) – 10.1109/lra.2020.2985620
  • Schaft, A. J. Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems. Advanced Dynamics and Control of Structures and Machines 127–167 (2004) doi:10.1007/978-3-7091-2774-2_9 – 10.1007/978-3-7091-2774-2_9
  • Simo, J. C. & Vu-Quoc, L. A three-dimensional finite-strain rod model. part II: Computational aspects. Computer Methods in Applied Mechanics and Engineering 58, 79–116 (1986) – 10.1016/0045-7825(86)90079-4
  • Sonneville, V., Cardona, A. & Brüls, O. Geometrically exact beam finite element formulated on the special Euclidean group. Computer Methods in Applied Mechanics and Engineering 268, 451–474 (2014) – 10.1016/j.cma.2013.10.008
  • MW Spong, Robot modeling and control (2006)
  • Till, J., Aloi, V. & Rucker, C. Real-time dynamics of soft and continuum robots based on Cosserat rod models. The International Journal of Robotics Research 38, 723–746 (2019) – 10.1177/0278364919842269
  • Wu, K. & Zheng, G. FEM-Based Gain-Scheduling Control of a Soft Trunk Robot. IEEE Robot. Autom. Lett. 6, 3081–3088 (2021) – 10.1109/lra.2021.3061311
  • Zhang, Z., Bieze, T. M., Dequidt, J., Kruszewski, A. & Duriez, C. Visual servoing control of soft robots based on finite element model. 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2895–2901 (2017) doi:10.1109/iros.2017.8206121 – 10.1109/iros.2017.8206121