Discrete Quad Neural Dynamics for Inverse-Free Control of Model-Unavailable Continuum Robots

A lot of Jacobian-based control methods for continuum robots rely on the real-time calculation of the pseudoinverse of time-varying Jacobian matrices, which; however, is not friendly to the hardware implementation of the control system and may be intractable to conventional matrix inversion methods intrinsically designed for time-invariant matrices. In this article, we propose a continuous quad neural dynamics (CQND) method for the tracking control of continuum robots. Two neural dynamic subsystems of CQND are adopted to solve the inverse kinematics problem and to estimate the Jacobian matrix whose pseudoinverse is effectively computed by another two neural dynamic subsystems. The inverse-free CQND method is able to achieve the tracking control of model-unavailable continuum robots. Furthermore, to facilitate the implementation of the control method, we propose a new 4-instant discrete quad neural dynamics (DQND4) method by leveraging discretization formulas. For the sake of comparison, we also derive and present two other methods, namely, DQND6 and DQND8, which are established by using different discretization formulas, and we performed comparative studies between proposed and existing models. Finally, simulations and experiments are conducted to verify the effectiveness, accuracy, and advantages of our method.