TDE-Based Adaptive Super-Twisting Multivariable Fast Terminal Slide Mode Control for Cable-Driven Manipulators With Safety Constraint of Error

Abstract

An adaptive super-twisting multivariable fast terminal sliding mode control scheme based on time delay estimation (TDE) and asymmetric error constraints are proposed to guarantee high-precision trajectory tracking control of cable-driven manipulators under complicated unknown uncertainties. The control system is constrained by joint position errors, which are asymmetric and time-varying. First, the error range of the joints is designed to ensure that the deviation of the joint position from the desired profile is not too large while ensuring the safety performance of the manipulator, and the remaining set-total system dynamics are estimated and compensated using time-delay estimation. Secondly, the design analysis of the angular false expectation using safety constraint functions allows the constraints of different cross sections to be handled in a unified system architecture; the problem of robotic arm motion trajectories with output constraints and uncertainties is addressed through rigorous analysis. The super-twisting adaptive control effectively ensures fast, accurate and robust convergence of the algorithm in satisfying all constraints in operation, and the stability of the closed-loop control system is analyzed using the Lyapunov method. Finally, the effectiveness and superiority of the proposed adaptive hyper-torsional non-singular terminal sliding mode control scheme are verified by simulations and experiments in 2-DOF.INDEX TERMS Cable-diven manipulator, asymmetric error constraint, TDE scheme, adaptive supertwisting control.

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“…A high-order sliding mode observer that improves convergence speed by adding a linear term was proposed in [33] to estimate joint fault status, and Lyapunov theory was used to demonstrate the system's finite-time stability. In designing fault-tolerant controllers for robotic arms, fuzzy logic controller [34], neural network controller [35], and sliding mode controller [36][37][38][39] have been adopted to input appropriate joint torques. Among them, the sliding mode control method has been widely studied due to its advantages of a simple design process and strong robustness.…”

“…To address these issues, refs. [38,39] introduced the super-twisting method to provide additional control force, improving the system's response speed and control accuracy.…”