Authors

Enrico Franco, Tutla Ayatullah, Arif Sugiharto, Arnau Garriga-Casanovas, Vani Virdyawan

Abstract

This paper investigates the model-based nonlinear control of a class of soft continuum pneumatic manipulators that bend due to pressurization of their internal chambers and that operate in the presence of disturbances. A port-Hamiltonian formulation is employed to describe the closed loop system dynamics, which includes the pressure dynamics of the pneumatic actuation, and new nonlinear control laws are constructed with an energy-based approach. In particular, a multi-step design procedure is outlined for soft continuum manipulators operating on a plane and in 3D space. The resulting nonlinear control laws are combined with adaptive observers to compensate the effect of unknown disturbances and model uncertainties. Stability conditions are investigated with a Lyapunov approach, and the effect of the tuning parameters is discussed. For comparison purposes, a different control law constructed with a backstepping procedure is also presented. The effectiveness of the control strategy is demonstrated with simulations and with experiments on a prototype. To this end, a needle valve operated by a servo motor is employed instead of more sophisticated digital pressure regulators. The proposed controllers effectively regulate the tip rotation of the prototype, while preventing vibrations and compensating the effects of disturbances, and demonstrate improved performance compared to the backstepping alternative and to a PID algorithm.

Keywords

Nonlinear control; Underactuated systems; Soft manipulators; Pneumatic actuation

Citation

  • Journal: Nonlinear Dynamics
  • Year: 2021
  • Volume: 106
  • Issue: 1
  • Pages: 229–253
  • Publisher: Springer Science and Business Media LLC
  • DOI: 10.1007/s11071-021-06817-1

BibTeX

@article{Franco_2021,
  title={{Nonlinear energy-based control of soft continuum pneumatic manipulators}},
  volume={106},
  ISSN={1573-269X},
  DOI={10.1007/s11071-021-06817-1},
  number={1},
  journal={Nonlinear Dynamics},
  publisher={Springer Science and Business Media LLC},
  author={Franco, Enrico and Ayatullah, Tutla and Sugiharto, Arif and Garriga-Casanovas, Arnau and Virdyawan, Vani},
  year={2021},
  pages={229--253}
}

Download the bib file

References

  • Astolfi, A. & Ortega, R. Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic Control vol. 48 590–606 (2003) – 10.1109/tac.2003.809820
  • Best, C. M., Rupert, L. & Killpack, M. D. Comparing model-based control methods for simultaneous stiffness and position control of inflatable soft robots. The International Journal of Robotics Research vol. 40 470–493 (2020) – 10.1177/0278364920911960
  • Campisano, F. et al. Closed-loop control of soft continuum manipulators under tip follower actuation. The International Journal of Robotics Research vol. 40 923–938 (2021) – 10.1177/0278364921997167
  • Cao, G. et al. Observer-based continuous adaptive sliding mode control for soft actuators. Nonlinear Dynamics vol. 105 371–386 (2021) – 10.1007/s11071-021-06606-w
  • Chan, J. C. L., Lee, T. H. & Tan, C. P. A sliding mode observer for robust fault reconstruction in a class of nonlinear non-infinitely observable descriptor systems. Nonlinear Dynamics vol. 101 1023–1036 (2020) – 10.1007/s11071-020-05843-9
  • Y Chen. Chen, Y., Sun, N., Liang, D., Qin, Y., Fang, Y.: a neuroadaptive control method for pneumatic artificial muscle systems with hardware experiments. Mech. Syst. Signal Process. 146, 1–15 (2021) (2021)
  • Ching-Ping Chou & Hannaford, B. Measurement and modeling of McKibben pneumatic artificial muscles. IEEE Transactions on Robotics and Automation vol. 12 90–102 (1996) – 10.1109/70.481753
  • 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. The International Journal of Robotics Research vol. 39 490–513 (2020) – 10.1177/0278364919897292
  • Elliott, S. J., Tehrani, M. G. & Langley, R. S. Nonlinear damping and quasi-linear modelling. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences vol. 373 20140402 (2015) – 10.1098/rsta.2014.0402
  • Falkenhahn, V., Hildebrandt, A., Neumann, R. & Sawodny, O. Dynamic Control of the Bionic Handling Assistant. IEEE/ASME Transactions on Mechatronics vol. 22 6–17 (2017) – 10.1109/tmech.2016.2605820
  • Flores, G. & Rakotondrabe, M. Output Feedback Control for a Nonlinear Optical Interferometry System. IEEE Control Systems Letters vol. 5 1880–1885 (2021) – 10.1109/lcsys.2020.3045214
  • Franco, E. & Garriga-Casanovas, A. Energy-shaping control of soft continuum manipulators with in-plane disturbances. The International Journal of Robotics Research vol. 40 236–255 (2020) – 10.1177/0278364920907679
  • Franco, E., Garriga Casanovas, A. & Donaire, A. Energy shaping control with integral action for soft continuum manipulators. Mechanism and Machine Theory vol. 158 104250 (2021)10.1016/j.mechmachtheory.2021.104250
  • Franco, E., Garriga-Casanovas, A., Tang, J., Rodriguez y Baena, F. & Astolfi, A. Adaptive Energy Shaping Control of a Class of Nonlinear Soft Continuum Manipulators. IEEE/ASME Transactions on Mechatronics vol. 27 280–291 (2022)10.1109/tmech.2021.3063121
  • Franco, E., Garriga Casanovas, A., Tang, J., Rodriguez y Baena, F. & Astolfi, A. Position regulation in Cartesian space of a class of inextensible soft continuum manipulators with pneumatic actuation. Mechatronics vol. 76 102573 (2021)10.1016/j.mechatronics.2021.102573
  • Franco, E., Rodriguez y Baena, F. & Astolfi, A. Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances. International Journal of Robust and Nonlinear Control vol. 30 4112–4128 (2020) – 10.1002/rnc.4985
  • Garriga-Casanovas, A., Collison, I. & Rodriguez y Baena, F. Toward a Common Framework for the Design of Soft Robotic Manipulators with Fluidic Actuation. Soft Robotics vol. 5 622–649 (2018) – 10.1089/soro.2017.0105
  • Godage, I. S., Wirz, R., Walker, I. D. & Webster, R. J., III. Accurate and Efficient Dynamics for Variable-Length Continuum Arms: A Center of Gravity Approach. Soft Robotics vol. 2 96–106 (2015) – 10.1089/soro.2015.0006
  • Gulati, N. & Barth, E. J. A Globally Stable, Load-Independent Pressure Observer for the Servo Control of Pneumatic Actuators. IEEE/ASME Transactions on Mechatronics vol. 14 295–306 (2009) – 10.1109/tmech.2008.2009222
  • Isidori, A. Nonlinear Control Systems. Communications and Control Engineering (Springer London, 1995). doi:10.1007/978-1-84628-615-5 – 10.1007/978-1-84628-615-5
  • Kalita, B. & Dwivedy, S. K. Dynamic analysis of pneumatic artificial muscle (PAM) actuator for rehabilitation with principal parametric resonance condition. Nonlinear Dynamics vol. 97 2271–2289 (2019) – 10.1007/s11071-019-05122-2
  • Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: Nonlinear and adaptive control design. In: Adaptive and Learning Systems for Signal Processing, Communications and Control. Wiley (1995)
  • Li, J., Wang, J. & Fei, Y. Nonlinear modeling on a SMA actuated circular soft robot with closed-loop control system. Nonlinear Dynamics vol. 96 2627–2635 (2019) – 10.1007/s11071-019-04949-z
  • Liu, F., Wu, W., Hu, J. & Yuan, S. Design of multi-range hydro-mechanical transmission using modular method. Mechanical Systems and Signal Processing vol. 126 1–20 (2019) – 10.1016/j.ymssp.2019.01.061
  • Loría, A. & de León Morales, J. On persistently exciting observers and a non-linear separation principle: Application to the stabilization of a generator. International Journal of Control vol. 76 607–617 (2003) – 10.1080/0020717031000104482
  • Luo, K., Tian, Q. & Hu, H. Dynamic modeling, simulation and design of smart membrane systems driven by soft actuators of multilayer dielectric elastomers. Nonlinear Dynamics vol. 102 1463–1483 (2020) – 10.1007/s11071-020-06001-x
  • Morales Bieze, T., Kruszewski, A., Carrez, B. & Duriez, C. Design, implementation, and control of a deformable manipulator robot based on a compliant spine. The International Journal of Robotics Research vol. 39 1604–1619 (2020) – 10.1177/0278364920910487
  • Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control vol. 47 1218–1233 (2002) – 10.1109/tac.2002.800770
  • Petit, F., Daasch, A. & Albu-Schaffer, A. Backstepping Control of Variable Stiffness Robots. IEEE Transactions on Control Systems Technology vol. 23 2195–2202 (2015) – 10.1109/tcst.2015.2404894
  • Richer, E. & Hurmuzlu, Y. A High Performance Pneumatic Force Actuator System: Part I—Nonlinear Mathematical Model. Journal of Dynamic Systems, Measurement, and Control vol. 122 416–425 (1999) – 10.1115/1.1286336
  • Ross, D., Nemitz, M. P. & Stokes, A. A. Controlling and Simulating Soft Robotic Systems: Insights from a Thermodynamic Perspective. Soft Robotics vol. 3 170–176 (2016)10.1089/soro.2016.0010
  • Runciman, M., Avery, J., Zhao, M., Darzi, A. & Mylonas, G. P. Deployable, Variable Stiffness, Cable Driven Robot for Minimally Invasive Surgery. Frontiers in Robotics and AI vol. 6 (2020) – 10.3389/frobt.2019.00141
  • Runciman, M., Darzi, A. & Mylonas, G. P. Soft Robotics in Minimally Invasive Surgery. Soft Robotics vol. 6 423–443 (2019) – 10.1089/soro.2018.0136
  • Rus, D. & Tolley, M. T. Design, fabrication and control of soft robots. Nature vol. 521 467–475 (2015) – 10.1038/nature14543
  • Sadati, S. M. H., Naghibi, S. E., Walker, I. D., Althoefer, K. & Nanayakkara, T. Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz–Galerkin Methods. IEEE Robotics and Automation Letters vol. 3 328–335 (2018) – 10.1109/lra.2017.2743100
  • Shabana, A. A. & Eldeeb, A. E. Motion and shape control of soft robots and materials. Nonlinear Dynamics vol. 104 165–189 (2021) – 10.1007/s11071-021-06272-y
  • Suzumori, K., Iikura, S., Tanaka, H.: Development of flexible microactuator and its applications to robotic mechanisms. In: Proceedings. 1991 IEEE International Conference on Robotics and Automation, pp. 1622–1627. IEEE Computer Society Press (1991)
  • Suzumori, K. Elastic materials producing compliant robots. Robotics and Autonomous Systems vol. 18 135–140 (1996) – 10.1016/0921-8890(95)00078-x
  • George Thuruthel, T., Ansari, Y., Falotico, E. & Laschi, C. Control Strategies for Soft Robotic Manipulators: A Survey. Soft Robotics vol. 5 149–163 (2018) – 10.1089/soro.2017.0007
  • Wang, C., Frazelle, C. G., Wagner, J. R. & Walker, I. D. Dynamic Control of Multisection Three-Dimensional Continuum Manipulators Based on Virtual Discrete-Jointed Robot Models. IEEE/ASME Transactions on Mechatronics vol. 26 777–788 (2021) – 10.1109/tmech.2020.2999847
  • Wang, J., Min, J., Fei, Y. & Pang, W. Study on nonlinear crawling locomotion of modular differential drive soft robot. Nonlinear Dynamics vol. 97 1107–1123 (2019) – 10.1007/s11071-019-05035-0
  • Yang, C. et al. Geometric constraint-based modeling and analysis of a novel continuum robot with Shape Memory Alloy initiated variable stiffness. The International Journal of Robotics Research vol. 39 1620–1634 (2020) – 10.1177/0278364920913929
  • Yang, C., Kang, R., Branson, D. T., Chen, L. & Dai, J. S. Kinematics and statics of eccentric soft bending actuators with external payloads. Mechanism and Machine Theory vol. 139 526–541 (2019) – 10.1016/j.mechmachtheory.2019.05.015
  • Yu, Y.-Q., Howell, L. L., Lusk, C., Yue, Y. & He, M.-G. Dynamic Modeling of Compliant Mechanisms Based on the Pseudo-Rigid-Body Model. Journal of Mechanical Design vol. 127 760–765 (2005) – 10.1115/1.1900750
  • Zhang, J. & Chen, H. Voltage-induced beating vibration of a dielectric elastomer membrane. Nonlinear Dynamics vol. 100 2225–2239 (2020) – 10.1007/s11071-020-05678-4
  • L Zhao. Zhao, L., Cheng, H., Zhang, J., Xia, Y.: Adaptive control for a motion mechanism with pneumatic artificial muscles subject to dead-zones. Mech. Syst. Signal Process. 148, 1–14 (2021) (2021)
  • Zhao, L., Liu, X. & Wang, T. Trajectory tracking control for double-joint manipulator systems driven by pneumatic artificial muscles based on a nonlinear extended state observer. Mechanical Systems and Signal Processing vol. 122 307–320 (2019) – 10.1016/j.ymssp.2018.12.016