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

Document Type : Research Article

Authors

1 New Technologies Research Center,Amirkabir University of Technoloy

2 Department of Mechanical Engineering, 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 an 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 modeling method. To this aim, a compact Cosserat model of the pneumatically-actuated soft arm is extracted owing to the viscoelastic behavior 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 behavior of the proposed model, and the effectiveness of the control approach is demonstrated by simulation in both continuous and set-point positioning.
To achieve precise position control for a soft arm, we proposed a PID sliding mode controller based on the Cosserat rod theory. The model is comprehensively represented, with an explicit determination of pneumatic pressure effects as control elements. The control law is established for achieving the straight-line motion of the end-tip in the linear dynamic regime. The solution to the PDE is implemented using the recursive "Shooting Method" in Python programming. Simulation results demonstrate the controller's capability to track both continuous trajectories and set-point positioning accurately. Efficient behavior of the cosserat model is presented via experimental results.

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AUT Journal of Modeling and Simulation
Volume 56, Issue 1
2024
Pages 87-102

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