PDE Cosserat rod modelling of a pneumatic soft arm and position control in extending mode

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

2 New Technologies Research Center, Amirkabir University of Technology, Tehran, Iran

3 Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran.

4 Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran.

Abstract

Accurate modelling and control of a soft arm has enormous importance because of the inherent softness and shape adaptability. The goal of this work is to represent an exact position control approach based on the precise Cosserat rod modelling method. To this aim, a compact Cosserat model of the pneumatically-actuated soft arm is extracted owing to the viscoelastic behaviour of the constructing material and the pneumatic pressure effects that appear as external loads. To address high nonlinearity, a PID sliding controller is suggested and formulated. The PDE equation set is solved by a recursive numerical method satisfying both boundary and domain requirements. Experimental results represented good behaviour of the proposed model, and the effectiveness of the control approach is demonstrated by simulation in both continuous and set-point positioning.

Keywords

Main Subjects

References

[1] C. Majidi, “Soft robotics: a perspective—current trends and prospects for the future,” Soft Robotics, vol. 1, no. 1, pp. 5-11, 2014.
[2] D. Rus and M. T. Tolley, “Design, fabrication and control of soft robots,” Nature, vol. 521, no. 7553, p. 467, 2015.
[3] M. Rolf and J. J. Steil, “Efficient exploratory learning of inverse kinematics on a bionic elephant trunk,” IEEE transactions on neural networks and learning systems, vol. 25, no. 6, pp. 1147-1160, 2013.
[4] C. Laschi, M. Cianchetti, B. Mazzolai, L. Margheri, M. Follador, and P. Dario, “Soft robot arm inspired by the octopus,” Advanced Robotics, vol. 26, no. 7, pp. 709- 727, 2012.
[5] H. Li, L. Xun, and G. Zheng, “Piecewise linear strain Cosserat model for soft slender manipulator,” IEEE Transactions on Robotics, 2023.
[6] M. Wehner, B. Quinlivan, P. M. Aubin, E. Martinez[1]Villalpando, M. Bauman, L. Stirling, K. Holt, R. Wood, C. Walsh, “Design and evaluation of lightweight soft exosuit for gait assistance”, ,” in 2013 IEEE International Conference on Robotics and Automation, 2013: IEEE.
[7] M. D. Gilbertson, G. McDonald, G. Korinek, J. D. Van de Ven, and T. M. Kowalewski, “Serially actuated locomotion for soft robots in tube-like environments,” IEEE Robotics and Automation Letters, vol ,2 .pp. 1140- 1147, 2017.
[8] M. T. Tolley, R. F. Shepherd, M. Karpelson, N. W. Bartlett, K. C. Galloway, M. Wehner, et al., “An untethered jumping soft robot,” in Intelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on, 2014.
[9] S. Kennedy, N. Vlajic, and E. Perkins, “Cosserat modeling for deformation configuration of shape memory alloy unimorph actuators,” Journal of Intelligent Material Systems and Structures, vol. 34, no. 6, pp. 642- 652, 2023.
[10] A. Ahmadjou, S. Sadeghi, M. Zareinejad, H. A. Talebi, “A compact valveless pressure control source for soft rehabilitation glove”, Journal of Medical Robotics and Computer Assisted Surgery, vol. 17, 2021.
[11] B. A. Jones and I. D. Walker, “Kinematics for multisection continuum robots,” IEEE Transactions on Robotics, vol. 22, no. 1, pp. 43-55, 2006.
[12] 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.
[13] F. Renda, F. Giorgio-Serchi, F. Boyer, and C. Laschi, “Locomotion and elastodynamics model of an underwater shell-like soft robot,” in 2015 IEEE International Conference on Robotics and Automation (ICRA), 2015: IEEE, pp. 1158-1165.
[14] J. Till, V. Aloi, and C. Rucker, “Real-Time Dynamics of Soft and Continuum Robots based on Cosserat-Rod Models,” 2018.
[15] M. Wiese, R. Berthold, M. Wangenheim, and A. Raatz, “Describing and Analyzing Mechanical Contact for Continuum Robots Using a Shooting-Based Cosserat Rod Implementation,” IEEE Robotics and Automation Letters, 2023.
[16] M. Dehghani and S. A. A. Moosavian, “Compact modeling of spatial continuum robotic arms towards real-time control,” Advanced Robotics, vol. 28, no. 1, pp. 15-26, 2014.
[17] M. Gerdts, G. Greif, H. J. Pesch, “Numerical optimal control of the wave equation: optimal boundary control of a string to rest in finite time”, Mathematics and Computers in Simulation, vol. 79, pp. 1020-1032, 2008.
[18] O. Axelsson, M. Beres, R. Blaheta, “Computational methods for boundary optimal control and identification problems”, Mathematics and Computers in Simulation, vol. 189, pp. 276-290, 2021.
[19] S. S. Antman, Problems in nonlinear elasticity (Nonlinear Problems of elasticity, no. 107). Springer, 2005, pp. XVIII, 838.
AUT Journal of Modeling and Simulation
Volume 56, Issue 1
2024
Pages 87-102

Files

Share

How to cite

Statistics