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

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.