Fractional Differential Equations

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Humanoid robots, unmanned rovers, entertainment pets, drones, and so on are great examples of mobile robots. They can be distinguished from other robots by their ability to move autonomously, with ...

https://journals.sagepub.com/doi/pdf/10.1177/1729881419839596

A review of mobile robots: Concepts, methods, theoretical framework, and applications

This paper develops a novel control methodology for tracking control of robot manipulators based on a novel adaptive backstepping nonsingular fast terminal sliding mode control (ABNFTSMC). In this approach, a novel backstepping nonsingular fast terminal sliding mode controller (BNFTSMC) is developed based on an integration of integral nonsingular fast terminal sliding mode surface and a backstepping control strategy. The benefits of this approach are that the proposed controller can preserve the merits of the integral nonsingular fast terminal sliding mode control (NFTSMC) in terms of high robustness, fast transient response, and finite-time convergence, as well as backstepping control strategy in terms of globally asymptotic stability based on Lyapunov criterion. However, the major limitation of the proposed BNFTSMC is that its design procedure is dependent on the prior knowledge of the bound value of the disturbance and uncertainties. In order to overcome this limitation, an adaptive technique is employed to approximate the upper bound value; yielding an ABNFTSMC is recommended. The proposed controller is then applied for tracking control of a PUMA560 robot and compared with other state-of-the-art controllers, such as computed torque controller, PID controller, conventional PID-based sliding mode controller, and NFTSMC. The comparison results demonstrate the superior performance of the proposed approach.

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An Adaptive Backstepping Nonsingular Fast Terminal Sliding Mode Control for Robust Fault Tolerant Control of Robot Manipulators

This paper studies practical tracking control design of robot manipulators with continuous fractional-order nonsingular terminal sliding mode (CFONTSM) based on time-delay estimation (TDE). The proposed control design requires no detailed information about the robot dynamics, leading to an attractive model-free nature thanks to TDE, and ensures fast convergence and high tracking precision under heavy lumped uncertainties due to the FONTSM surface and fast-TSM-type reaching law. Stability of the closed-loop system and finite-time convergence are analyzed using Lyapunov stability theory. Comparative 2-DOF (degree of freedom) simulation and experiment results show that the proposed control design can ensure higher tracking precision and faster convergence compared with TDE-based continuous integer-order NTSM (CIONTSM) design in a wide range of speed; meanwhile, better performance is also observed compared with TDE-based IONTSM and FONTSM control designs using a boundary layer technique.

Practical Tracking Control of Robot Manipulators With Continuous Fractional-Order Nonsingular Terminal Sliding Mode

This paper proposes a new adaptive time-delay control (ATDC) scheme for cable-driven manipulators. The proposed ATDC scheme contains three elements, i.e., time-delay estimation (TDE), injected dynamics, and adaptive laws. The TDE utilizes intentionally time-delayed signals to estimate the unknown system dynamics and brings a fascinating model-free nature. The injected dynamics employ a fractional-order nonsingular terminal sliding mode (FONTSM) manifold and a fast-TSM-type reaching law, thus it can ensure fast dynamical response and high tracking accuracy in both sliding mode and reaching phases. The adaptive laws are utilized to obtain good robustness and effective suppression of the chatters simultaneously. Moreover, the continuous and chatter-free adaptive gains are used to enhance the control performance under time-varying disturbances. The tracking error is proved to be uniformly ultimately bounded (UUB) using Lyapunov approach. Finally, the superiorities of the proposed ATDC scheme are demonstrated by three experiments using a cable-driven manipulator.

A New Adaptive Time-Delay Control Scheme for Cable-Driven Manipulators

This paper proposes a novel adaptive super-twisting fractional-order nonsingular terminal sliding mode (AST-FONTSM) control scheme using time delay estimation (TDE) for the cable-driven manipulators. The designed control scheme utilizes TDE to obtain the estimation of system dynamics, and therefore no system dynamic model information will be required. Afterwards, AST and FONTSM schemes are applied to ensure good control performance in both reaching and sliding mode phases. Due to the adoption of AST scheme, good robustness and high control precision are obtained in the reaching phase, while the boundary information of the lumped uncertainties will be no longer required. Thanks to the utilization of FONTSM error dynamics, fast convergence and accurate tracking and strong robustness can be simultaneously ensured in the sliding mode phase. Corresponding comparative simulation and experimental results demonstrate the effectiveness and superiorities of our proposed method over the existing control methods.

Adaptive super-twisting fractional-order nonsingular terminal sliding mode control of cable-driven manipulators.

Practical adaptive fractional‐order nonsingular terminal sliding mode control for a cable‐driven manipulator

This work proposes a model-free robust control for cable-driven manipulators with disturbance. To achieve accurate, singularity-free and fast dynamical control performance, we design a new NFTSM surface utilizing a new continuous TSM-type switch element. By replacing the integral power with fractional one for the error dynamics, the designed TSM-type switch element can effectively enhance the dynamical performance of the NFTSM surface. Time-delay estimation (TDE) technique is applied to cancel out complicated nonlinear dynamics guaranteeing an excellent model-free scheme. Thanks to the designed NFTSM surface, adopted reaching law and TDE, our control can provide good comprehensive control performance effectively. Stability and comparisons of control precision and convergence speed have been theoretically analyzed. Finally, comparative experiments were conducted to prove the superiorities of our control.

Yaoyao Wang

Papers

Practical Tracking Control of Robot Manipulators With Continuous Fractional-Order Nonsingular Terminal Sliding Mode

A New Adaptive Time-Delay Control Scheme for Cable-Driven Manipulators

Adaptive super-twisting fractional-order nonsingular terminal sliding mode control of cable-driven manipulators.

Practical adaptive fractional‐order nonsingular terminal sliding mode control for a cable‐driven manipulator

Model-free continuous nonsingular fast terminal sliding mode control for cable-driven manipulators.