Nonsingular recursive-structure sliding mode control for high-order nonlinear systems and an application in a wheeled mobile robot

This article presents an asymptotic tracking controller for high-order uncertain nonlinear systems. Compared to the existing results, some restrictive assumptions are relaxed and the requirement of the variables being bounded is removed. At the same time, a prescribed time tracking control strategy is constructed to make that the system has better-transient performance during operation. Specifically, a global prescribed time function is proposed and an unconstrained variable is constructed to replace the constrained tracking error. Under this framework, an appealing feature of the designed controller is that the tracking error can converge to a specified range within a prescribed time and eventually converge to zero asymptotically starting from any initial conditions, where the prescribed time and accuracy can be directly given. Finally, the simulation results validate the effectiveness of the control strategy.

In recent decades, controller design has been attracted a great deal of interest of many researchers in control community which can make the job of many other researchers in different area of research easier. The present study aims to design a finite time adaptive control input for a high-order nonlinear system in presence of a variety of mismatched uncertainties and external disturbances. Adaptive terminal sliding mode control (ATSMC) method is used to design robust controller in a finite time. Also, adaptive concept is employed in ATSMC to estimate the upper bound of mismatched uncertainties and external disturbances and their estimations are used in control input. The finite time stability proof is performed by defining a proper candidate Lyapunov function. Numerical simulation results are carried out in Simulink/MATLAB to reveal the correctness of proposed design in this research. Finally, the performance criterion, integral of the square value (ISV), is defined to provide a numerical comparison between the proposed adaptive controller and non-adaptive controller.

In this paper, the attitude control of rigid-liquid-flexible multi-body coupling spacecraft with unknown external disturbances and uncertain inertia parameters is studied, and an attitude maneuver control method based on disturbance observer and fuzzy terminal sliding mode control is proposed. The sloshing of liquid fuel in the spacecraft is equivalent to a spherical pendulum model, and the flexible appendages are assumed to be an Euler-Bernoulli beam. The coupled dynamic equation of the liquid-filled flexible spacecraft is derived by using the Lagrange method. First of all, the interference from space, the parameter uncertainty of the moment of inertia of the spacecraft, the coupling interference caused by the liquid sloshing and the vibration of flexible accessories are summed up as lumped interference. Design disturbance observer to compensate and estimate the lumped disturbance of the system. Then, based on the designed disturbance observer, a fuzzy terminal sliding mode control law is presented, and it is proved that the state of the closed-loop system is finite-time stable under the control law, and converges to the specified terminal sliding mode surface. The fuzzy terminal sliding mode control law uses fuzzy control to improve the switching gain based on the traditional terminal sliding mode control to achieve the purpose of suppressing system jitter. This optimization method can not only reduce the complexity of terminal sliding mode control method, but also reduce the difficulty of debugging parameters because it does not introduce new functions. The numerical simulation results show that the designed fuzzy terminal sliding mode control law can not only achieve the finite-time stability of the closed-loop attitude control system of the liquid-filled flexible spacecraft, but also effectively suppress the liquid sloshing and the vibration of the flexible appendages. At the same time, it has good robustness to disturbances caused by external disturbances and parameter uncertainties, and has better control performance.

This thesis suggests a control strategy based on rotation matrix for autonomous underwater vehicles (AUVs) with full actuation and input quantization regarding model uncertainties and outer interferences. First, without unwinding, the dynamics of the attitude regarding AUV will be solely and globally depicted via rotation matrix. To simplify the calculation and execution, an alternative error vector is presented. Next, a terminal sliding mode surface which includes two components is designed to guarantee the convergence in a finite time way and singularity-free character. The input quantization is considered in the controller design of AUVs, thus it reduces the relevant loads of the derived system. Then, a new adaptive law is set to ensure the information which is estimated and could appear in the form of limited values for all time. Lastly, the effectiveness of control plan is proved through abstract analysis and simulations.KeywordsAUVsRotation matrixInput quantizationTrajectory tracking control

This article studies full-state constrained control for high-order nonlinear systems with unknown multiple time-varying powers and serious parameter unknowns. Due to the simultaneous existence of unknown powers and full-state constraints, we construct a log-type quadratic barrier Lyapunov function (BLF) rather than a quadratic Lyapunov function. By skillfully combining the log-type BLF, adding a power integrator technique and adaptive technique, an adaptive state feedback controller is developed. Under feasibility conditions, which are provided as sufficient conditions for the existence of proposed full-state constrained control, it is proved that all the signals of the closed-loop system are bounded, original system states converge to zero and full-state constraints are not violated.

Adaptive asymptotic tracking control design for high-order uncertain nonlinear systems

This article investigates the attitude tracking control problem of a rigid spacecraft under the modeling inaccuracy, environmental disturbance, and input magnitude and rate saturations. A robust controller is proposed based on several nonlinear control methods, including the integral terminal sliding mode control, adaptive control, backstepping control, auxiliary system, and nonlinear observer methods. Within the control framework, a new integral terminal sliding mode surface (ITSMS) is first designed which integrates the fast nonsingular terminal sliding mode surface (FNTSMS) with a first-order filter to achieve the finite time stability without the input singularity problem. And adaptive laws are employed to compensate for the modeling inaccuracy and environmental disturbance with no prior knowledge. To satisfy the input magnitude and rate saturation constraints, a dynamic model in the form of a first-order filter is built up to restrict the dynamics of the actuators, which is then associated with the auxiliary system. Meanwhile, a nonlinear observer is used to avoid calculating the derivative of the expected virtual control signal. Semi-globally uniformly ultimate bounded stability is proved for the closed-loop system, and the tracking errors can converge to small regions around the expected equilibrium in finite time. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed controller.

This paper deals with the development of a new strategy for the tracking control for Wheeled Mobile Robots (WMR). Mobile robots constitute a typical example of non-holonomic systems. They become progressively important in industries as a means of transport, detection and operation because of their effectiveness and flexibility. Some distinct applications of such system include instance order pick and place robots in manufacturing zone, post delivery robots in office buildings and deep see discovery robots. Wide area of research has been carried out on the tracking control problems of WMR. The kinematic tracking control schemes do not consider the dynamics of the mobile robot, so the tracking performance may not attain satisfactory. In this development a robust control law which is called backstepping sliding mode control is proposed for asymptotically stabilizing the mobile robot to a desired trajectory. First and foremost the dynamic model of wheeled mobile robot is done by using Euler-Lagrange approach. Following the controller is designed to find an acceptable control law so that the tracking error asymptotically moves to zero as the time approaches infinity with an initial error. The simulation result shows the effectiveness of the proposed scheme.

This paper addresses the challenge of bidirectional trajectory tracking, for the first time in literature, in wheeled mobile robots (WMRs) powered by renewable energy by thoroughly considering all involved subsystems. A comprehensive robust multilevel average controller is developed, utilizing the mathematical models of the WMR's mechanical structure, actuators, and power stage. At the mechanical-level, a kinematic control is implemented to ensure precise trajectory tracking. The actuator-level control incorporates two controllers based on differential flatness theory, managing the dynamic behavior of the actuators to achieve smooth and efficient motion. Finally, the power-stage-level employs two additional controllers, also based on flatness theory, dedicated to the power stage subsystem. The effectiveness of the proposed robust controller is experimentally validated using: A differential WMR prototype and a BK Precision PVS60085MR for replicating the characteristics of a commercial photovoltaic (PV) panel. System integration is facilitated by the DS1104 control board and implemented using MATLAB/Simulink software for real-time operation. The experimental results demonstrate the multilevel average controller's robustness and reliability, highlighting its capacity to maintain precise bidirectional trajectory tracking even in the presence of sudden changes in system parameters. • Bidirectional trajectory tracking in solar WMRs, considering all subsystems. • Use of full-bridge Buck inverters in the power stage to drive the actuator subsystem. • Validation on a WMR using Bézier polynomial-based bidirectional trajectories. • Experimental verification of the controller under disturbances in WMR's parameters. • Controller evaluation against a three-level strategy reported in the literature.

In this brief, a novel prescribed-time output feedback control strategy is developed for high-order nonlinear systems. To begin with, a new coordinate transformation method is proposed, under which a time-varying gain that goes to infinity towards the terminal time and a constant scaling gain are simultaneously introduced into the system. Then, the reduced-order observer and output feedback controller are successfully constructed by using the homogeneous domination approach. Unlike many existing results, our proposed control strategy can ensure that the convergence time is independent of both the initial conditions and design parameters, and the convergence rate of the system is adjustable. Moreover, the design process is simplified and the control scheme can operate even after the prescribed-time. Finally, a simulation example is used to verify the validity of the proposed control strategy.

Practical Tracking Control for High-order Nonlinear Systems With Dynamic Uncertainties and Unknown Powers via Event-triggered Mechanism

In this article, an adaptive tracking control method is proposed for wheeled mobile robots (WMR). In the trajectory tracking control of WMR, skidding and slipping are taken into account, and the slip degree parameters are introduced. The disturbance observer is designed to estimate the total disturbances. Then, we design the adaptive controller to guarantee that the tracking errors asymptotically converge to zero, the stability of the system is proved by Lyapunov theory. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed scheme.

Wheeled mobile robots (WMRs) have been a focus of research for several decades, particularly concerning navigation strategies in static and dynamic environments. This review article carefully examines the extensive academic efforts spanning several decades addressing navigational complexities in the context of WMR route analysis. Several approaches have been explored by various researchers, with a notable emphasis on the inclusion of stability and intelligent capabilities in WMR controllers attracting the attention of the academic community. This study traces historical and contemporary WMR research, including the establishment of kinetic stability and the construction of intelligent WMR controllers. WMRs have gained prominence in various applications, with precise navigation and efficient control forming the basic prerequisites for their effective performance. The review presents a comprehensive overview of stability analysis and navigation techniques tailored for WMRs. Initially, the exposition covers the basic principles of WMR dynamics and kinematics, explaining the different wheel types and their associated constraints. Subsequently, various stability analysis approaches, such as Lyapunov stability analysis and passivation-based control, are discussed in depth in the context of WMRs. Starting an exploration of navigation techniques, the review highlights important aspects including path planning and obstacle avoidance, localization and mapping, and trajectory tracking. These techniques are carefully examined in both indoor and outdoor settings, revealing their benefits and limitations. Finally, the review ends with a comprehensive discussion of the current challenges and possible routes in the field of WMR. The discourse includes the fusion of advanced sensors and state-of-the-art control algorithms, the cultivation of more robust and reliable navigation strategies, and the continued exploration of novel WMR applications. This article also looks at the progress of mobile robotics during the previous three decades. Motion planning and path analysis techniques that work with single and multiple mobile robots have been discussed extensively. One common theme in this research is the use of soft computing methods to give mobile robot controllers cognitive behaviors, such as artificial neural networks (ANNs), fuzzy logic control (FLC), and genetic algorithms (GAs). Nevertheless, there is still a dearth of applications for mobile robot navigation that leverage nature-inspired algorithms, such as firefly and ant colony algorithms. Remarkably, most studies have focused on kinematics analysis, with a small number also addressing dynamics analysis.

This article presents the development of a Computed Torque Control (CTC) scheme for Cartesian velocity control of Wheeled Mobile Robots (WMRs). The literature presents extensive study on the need and suitability of the CTC scheme for robot arms. Many researchers have identified the benefits of using a CTC scheme for mobile robots. There is however very little information on CTC schemes for controlling mobile robots. The need for the CTC scheme stems from the fact that mobile robots (industrial AGVs) employing conventional velocity control schemes experience side slip due to suspended loads while negotiating curves, and the controller gains and accelerations need to be modified for changes in the dynamics. The structure of the proposed control scheme can be employed to control any mobile robot for which an inverse dynamic model exists, as a CTC scheme requires an inverse dynamic model to compute unique values for the motor current for a given trajectory. It is demonstrated that the existence of the inverse dynamic model is guaranteed for all differentially driven WMRs for all operating conditions, and is not affected by the number of castor wheels in the WMR. In the proposed CTC scheme, the linear and angular velocities of the WMR are controlled by adjusting the WMR accelerations, which are computed based on the motor torques required to follow a given trajectory. The motor torque is pre-computed based on a dynamic model of the mobile robotic system. The simulation and experimental results presented for a differentially driven WMR demonstrate that a computed-torque control scheme provides adaptive cruising and steering control for nominally tuned controller gains compared to a conventional velocity controller to achieve proper road following in the presence of changes in the dynamics. © 1997 John Wiley & Sons, Inc.

A visual servo controller is developed for a monocular camera system mounted on a wheeled mobile robot (WMR), which simultaneously solves the tracking and regulation control problems. A prerecorded image sequence (e.g., a video) or single image of four target points is used to define a desired trajectory or desired fixed position and orientation for the WMR. By comparing the target points from a stationary reference image with the corresponding target points in the live image and the prerecorded sequence of images, projective geometric relationships are exploited to construct Euclidean homographies. The information obtained by decomposing the Euclidean homographies is then used to derive a standard WMR form. The proposed result is the first visual servo control result that solves the unified tracking and regulation problem.