Impedance Iterative Learning Backstepping Control for Output-Constrained Multisection Continuum Arms Based on PMA

Background: Pneumatic muscle actuator (PMA) actuated multisection continuum arms are widely applied in various fields with high flexibility and bionic properties. Nonetheless, their kinematic modeling and control strategy proves to be extremely challenging tasks. Methods: The relationship expression between the deformation parameters and the length of PMA with the geometric method is obtained under the assumption of piecewise constant curvature. Then, the kinematic model is established based on the improved D-H method. Considering the limitation of PMA telescopic length, an impedance iterative learning backstepping control strategy is investigated. For one thing, the impedance control is utilized to ensure that the ideal static balance force is maintained constant in the Cartesian space. For another, the iterative learning backstepping control is applied to guarantee that the desired trajectory of each PMA can be accurately tracked with the output-constrained requirement. Moreover, iterative learning control (ILC) is implemented to dynamically estimate the unknown model parameters and the precondition of zero initial error in ILC is released by the trajectory reconstruction. To further ensure the constraint requirement of the PMA tracking error, a log-type barrier Lyapunov function is employed in the backstepping control, whose convergence is demonstrated by the composite energy function. Results: The tracking error of PMA converges to 0.004 m and does not exceed the time-varying constraint function through cosimulation. Conclusion: From the cosimulation results, the superiority and validity of the proposed theory are verified.