This article centers around investigating the event-triggered nonsingular fixed-time tracking issue for an $n$ -link rigid robot manipulator with full-state constraints, external disturbances, and model uncertainties. We propose the definition of the constrainedly practically fixed-time stability (CPFTS) and provide a sufficient condition for CPFTS. A novel auxiliary function is developed to address the singularity issue caused by repeated differentiation in achieving the fixed-time tracking control. The uncertain parameters are approximated using the radial basis function neural network (RBFNN). This study proposes the model-based and the neutral network-based tracking control approaches, designed using the scaling function technique and the barrier Lyapunov function, respectively, to ensure that the tracking error systems are CPFTS and the full-state constraints comply. Moreover, the communication transmission load is reduced using the relative threshold event-triggered control strategy. Simulation results demonstrate the effectiveness of the proposed tracking control algorithms.

The purpose of crane control is to transport the payload precisely to the desired destination while minimizing rope swing. Aiming at such an objective, this work thoroughly analyzes the dynamic system of the overhead crane with double-pendulum effects. The findings indicate that, despite being physically underactuated, the overhead crane can retain a fully actuated form mathematically. This form guides the natural transition of the controlled plant from the underactuated system to a fully actuated system (FAS). Within the FAS framework, the behaviors of both the original actuated and unactuated variables are interpreted as indirect outcomes of the control actions applied to the FAS. Consequently, the challenges of trolley positioning and swing elimination are reduced to control issues of FAS. Furthermore, a well-designed dynamical term is integrated into the system space of FAS to enhance swing suppression. The integration further leads to the control scheme for precise positioning and anti-swing, offering a fresh perspective on crane system control. Extensions to the cases with uncertainties and input saturation have also been discussed. Finally, we compare several representative methods for crane control and demonstrate that the proposed scheme outperforms them.

This article considers the control issue for chained nonholonomic systems in the presence of disturbances and model uncertainties. The original system is a cascaded form with two subsystems. In the proposed algorithm, the first subsystem is designed to be exponentially stable, while the second is reformulated into a fully actuated system (FAS) with some states remaining unavailable. Consequently, state feedback control of the original system is transformed into output feedback control of FAS. An effective observer based on Fourier transform technique is presented to simultaneously estimate states and disturbances. Then, output feedback control and relay-switching-based control are proposed to achieve exponential or asymptotical convergence of the states. Finally, simulation and experiment results are presented to illustrate the efficacy of the proposed strategy. Note to Practitioners —Nonholonomic systems, exemplified by wheeled robots, are ubiquitous in engineering applications. This paper is motivated by the practical requirements of the stabilization control tailored to such systems. Nonholonomic systems often face complex scenarios with disturbances. For example, when a wheeled robot is parking in the snow fields, skidding and slipping may occur. Handling uncertainty and disturbance increases the challenge to the control task. Furthermore, onboard computers typically have limited computing power, thereby requiring straightforward and concise control algorithms. To meet these requirements, this paper introduces the framework of FAS, which eliminates the need for conventional recursive design procedures. Consequently, two controllers are presented: the output-feedback-based controller and the state-feedback-based controller. Both two controllers offer robustness, low complexity, and strong ability in disturbance rejection, making them suitable for practical applications. On the other hand, the controllers can not only be deployed independently to meet specific requirements, but can also be combined into a relay-switching-based strategy. This strategy is a two-stage control scheme. In the first stage, accurate parameter identification is performed while the output feedback controller maintains primary control performance. Once precise parameters are obtained, the output feedback controller seamlessly transitions to the state feedback controller, achieving higher control accuracy. Overall, this approach balances the control effectiveness with the computational efficiency, addressing the practical needs of stabilization control in nonholonomic systems.

This work centers around investigating the fixed-time tracking issue for an underactuated crane system with full-state constraints, disturbance, and measurement noise. A two-module design strategy consisting of state estimation stage and fixed-time tracking control design stage is proposed. Specifically, the composite disturbance filtering (CDF) approach is introduced to estimate states while rejecting and attenuating disturbance. Then by using fuzzy-based variables separation technique and integral barrier Lyapunov function (iBLF), the constrainedly practically fixed-time stability (CPFTS) is implemented to the studied crane system in the second stage. In the end, simulation and experiment results are presented to illustrate the efficacy of the proposed strategy.