Trajectory Tracking of Underactuated Surface Vessels Based on Hierarchical Sliding Mode

In this paper, the swing-up problem of the Furuta pendulum has been solved by introducing a new combined method based on the frequency response, and the sliding mode method. Furthermore, a trajectory tracking controller has been introduced and applied to the Furuta pendulum; which the pendulum remained regulated at the upward position, while the arm tracks a desired time-varying trajectory. The hierarchical sliding mode control (HSMC) approach has been employed to achieve the mentioned goals. The Furuta system is made up of two subsystems. Based on this physical structure, the hierarchical structure of the sliding surfaces is designed as follows: first, the sliding surface of each subsystem is defined. Then the sliding surface of one subsystem is established as the first layer sliding surface. Eventually, this layer is used to construct the second layer sliding surface with the sliding surface of the other subsystem. According to the hierarchical structure, the total control law is deduced, and stability of the closed-loop system has been proved by the Lyapunov theorem. Simulation results have been shown the validity of the proposed method. Finally, the tracking performance of the mentioned method has been compared with the feedback linearization controller and superiority of the HSMC has been revealed.

Robust integral backstepping hierarchical sliding mode controller for a ballbot system

To address non-linear disturbances and uncertainties in complex marine environments, this paper proposes a disturbance-resistant controller for deep-sea cranes. The controller integrates hierarchical sliding mode control, adaptive control, and neural network compensation techniques. By designing a global sliding mode surface, the dynamic coordination between the driving and non-driving subsystems is achieved, ensuring overall system stability. The subsystem surfaces reduce oscillations and enhance tracking accuracy. Adaptive control dynamically adjusts system parameters, enhancing robustness against external uncertainties, while the neural network compensates for time-varying disturbances through real-time learning. The stability of the control scheme is verified on the basis of Lyapunov theory. The simulation results demonstrate that, compared to traditional PID control, the proposed controller exhibits significant advantages in trajectory tracking accuracy, response speed, and disturbance rejection.

2D Ballbot is an actual under-actuated system with second-order nonholonomic velocity constraints and input coupling case where only control input is employed to control two outputs of the system. Controlling such a system is not easy because it faces many changelings including nonlinearities, external disturbances, and uncertainties. This study proposed a robust control system for a Ballbot mobile robot. The proposed control scheme is constructed using the hierarchical sliding mode control technique. The kinematics and dynamics of the Ballbot are derived. A Lyapunov function is used to prove the stability of the closed-loop control system. The stabilizing and transferring problems are investigated through several simulations and experiments by using the actual Ballbot platform.

The development of the spherical robot to meet the requirements of high-speed and high-precision tasks is of great importance. In this study, a fractional-order adaptive integral hierarchical sliding mode controller (F-AIHSMC) is proposed. F-AIHSMC enables the spherical robot to have better controlled performance when facing unknown disturbances and system chattering, which can seriously affect the high-speed and high-precision motion of the spherical robot. We establish the standard dynamic model of the spherical robot for high-speed linear motion first, and then use the feedforward compensation method to compensate the controllable influencing factors in the motion process. According to the standard dynamic model, the integral term and fractional calculus methods are integrated into the hierarchical sliding mode controller, and the adaptive method is used to evaluate and compensate unknown disturbances in the high-speed motion process. In order to verify the efficiency of the proposed F-AIHSMC, we test its control effect using the BYQ-GS spherical robot. The experimental results demonstrate that, compared with the classical hierarchical sliding mode controller and the adaptive hierarchical sliding mode controller, the F-AIHSMC has obvious advantages in response speed, convergence speed, stability and robustness when being applied to the control of high-speed linear motion of spherical robot. Moreover, the advantages of its control performance are more highlighted with the increase of the speed of the spherical robot.

The robotic airship is a unique and promising light-than-air platform, which has attracted worldwide developing interests for its broad applications. This article addresses the control problem of trajectory tracking for robotic airships. A neural network fuzzy sliding mode controller is proposed to steer a robotic airship along a referenced trajectory precisely. First, the dynamics model of a robotic airship is presented, and the problem of trajectory tracking is formulated. Second, a sliding mode controller is designed to track a time-varying trajectory. The neural network is employed to approximate the uncertain model of the airship, with the tracking error and its derivatives and the trajectory and its derivatives as neural network inputs and the approximation of the uncertain model as neural network output. And a fuzzy logic system is adopted to reduce the chattering results from the sliding mode controller. The control gains are tuned synchronously with the sliding surface according to fuzzy rules, with switching sliding surface as fuzzy logic inputs and control gains as fuzzy logic outputs. The stability and convergence of the closed-loop controller are proven using the Lyapunov stability theorem. Finally, the effectiveness and robustness of the proposed controller are demonstrated via simulation results. Contrasting simulation results indicate that the neural network fuzzy sliding mode controller reduces the chattering effectively and has better performance against the sliding mode controller.

In this chapter an adaptive sliding mode controller for the Furuta pendulum is proposed. The Furuta pendulum is a class of underactuated mechanical systems commonly used in many control systems laboratories due to its complex stabilization which allows the analysis and design of different nonlinear and multivariable controllers that are useful in some fields such as aerospace and robotics. Sliding mode control has been extensively used in the control of mechanical systems as an alternative to other nonlinear control strategies such as backstepping, passivity based control etc. The design and implementation of an adaptive sliding mode controller for this kind of system is explained in this chapter, along with other sliding mode controller variations such as second order sliding mode (SOSMC) and PD plus sliding mode control (PD \(+\) SMC) in order to compare their performance under different system conditions. These control techniques are developed using the Lyapunov stability theorem and the variable structure design procedure to obtain asymptotically stable system trajectories. In this chapter the adaptive sliding mode consist of a sliding mode control law with an adaptive gain that makes the controller more flexible and reliable than other sliding mode control (SMC) algorithms and nonlinear control strategies. The adaptive sliding mode control (ASMC) of the Furuta pendulum, and the other SMC strategies shown in this chapter, are derived according to the Furuta’s pendulum dynamic equations making the sliding variables, position errors and velocity errors reach the zero value in a specified reaching time. The main reason of deriving two well known sliding mode control strategy apart from the proposed control strategy of this chapter (adaptive sliding mode control) is for comparison purposes and to evince the advantages and disadvantages of adaptive sliding mode control over other sliding mode control strategies for the stabilization of the Furuta pendulum. A chattering analysis of the three SMC variations is done, to examine the response of the system, and to test the performance of the ASMC in comparison with the other control strategies explained in this chapter.

The quadrotor control as nonlinear and underactuated systems is a huge challenge in getting a fine stabilization and trajectory tracking. The present work seeks to introduce a novel hybrid control structure composed of an Internal Model Control-based Proportional-Integral (IMC-PI) controller, with the integration of a Sliding Mode Controller (SMC) and an Extended State Observer (ESO). The main purpose is to achieve improvement of stability and tracking performance under dynamic flight operations. A six degrees of freedom (6-DoF) dynamic model is developed under rigid body structure and proportional thrust-drag assumptions. An IMC-PI controller is initially employed to stabilize the Euler angles and vertical position but is not able to control the lateral positions (x and y). For this, a hybrid SMC-ESO method is incorporated for enhanced robustness along with precise path tracking. Simulation results reveal that while the stand-alone IMC-PI controller can stabilize altitude and orientation within 3 seconds, it cannot converge to the complete position. Nevertheless, the hybrid controller achieves very precise moving in complex trajectories (helical and figure-eight) within 25 seconds, which outperforms the stand-alone solution. The results confirm the viability of the hybrid controller in autonomous UAV operations where stability and precision are of particular importance.

Rehabilitation is a process that aims to restore individuals to full functionality following an injury or illness that has compromised their ability to perform daily activities. A significant challenge in addressing these needs is the selection of robotic devices that can adequately respond to the complex requirements of rehabilitation. This study presents a simulation study for the position control of the wrist and fingers using Hierarchical Sliding Mode Control (HSMC) that is optimized via metaheuristic algorithms. A novel hierarchical approach is applied that is optimized with Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms. The model was simulated under disturbances to track the desired trajectory. Simulation results are compared with Hierarchical PID controller results. The findings demonstrate that HSMC-based control effectively improve trajectory tracking, reducing mean absolute and normalized root mean square (NRMS) errors compared to HPID controllers. The proposed approach shows promising potential for real implementation, enhancing the efficiency of rehabilitation devices.

A spherical robot is a nonlinear, nonholonomic, and unstable system which increases the difficulty of the direction and trajectory tracking problem. In this study, we propose a new direction controller Hierarchical Terminal Sliding Mode Controller (HTSMC), an instruction planning controller called Model Prediction Control-based Planner (MPCBP), and a trajectory tracking framework named MPCBP-HTSMC-HSMC (MHH). The HTSMC is designed by integrating a fast terminal algorithm, a hierarchical method, the motion features of a spherical robot, and its dynamics. In addition, the new direction controller has an excellent control effect with a quick response speed and strong stability. MPCBP can obtain optimal commands that are then transmitted to the velocity and direction controller. Since the two torque controllers in MHH are all Lyapunov-based sliding mode controllers, the MHH framework may achieve optimal control performance while assuring stability. Finally, the two controllers eliminate the requirement for MPCBP's stability and dynamic constraints. Finally, hardware experiments demonstrate the efficacy of the HTSMC, MPCBP, and MHH.

Tracking control of tendon-driven manipulators has become a prevalent research area. However, the existence of flexible elastic tendons generates substantial residual vibrations, resulting in difficulties for trajectory tracking control of the manipulator. This paper proposes the radial basis function neural network adaptive hierarchical sliding mode control (RBFNNA-HSMC) method, which combines the dynamic model of the elastic tendon-driven manipulator (ETDM) with radial basis neural network adaptive control and hierarchical sliding mode control technology. The aim is to achieve trajectory tracking control of ETDM even under conditions of model inaccuracy and disturbance. The Lyapunov stability theory demonstrates the stability of the proposed RBFNNA-HSM controller. In order to assess the effectiveness and adaptability of the proposed control method, simulations and experiments were performed on a two-DOF ETDM. The RBFNNA-HSM method shows superior tracking accuracy compared to traditional model-based HSM control. The experiment shows that the maximum tracking error for ETDM double-joint trajectory tracking is below 2.593×10-3 rad and 1.624×10-3 rad, respectively.

This paper investigates the precise trajectory tracking of unmanned aerial vehicles (UAV) capable of vertical take-off and landing (VTOL) subjected to external disturbances. For this reason, a robust higher-order-observer-based dynamic sliding mode controller (HOB-DSMC) is developed and optimized using the fractional-order firefly algorithm (FOFA). In the proposed scheme, the sliding surface is defined as a function of output variables, and the higher-order observer is utilized to estimate the unmeasured variables, which effectively alleviate the undesirable effects of the chattering phenomenon. A neighboring point close to the sliding surface is considered, and as the tracking error approaches this point, the second control is activated to reduce the control input. The stability analysis of the closed-loop system is studied based on Lyapunov stability theorem. For a better study of the proposed scheme, various trajectory tracking tests are provided, where accurate tracking and strong robustness can be simultaneously ensured. Comparative simulation results validate the proposed control strategy’s effectiveness and its superiorities over conventional sliding mode controller (SMC) and integral SMC approaches.

This paper presents a control design technique which enables approximate reference trajectory tracking for a class of underactuated mechanical systems. The control law comprises two terms. The first involves feedback of the trajectory tracking error in the actuated coordinates. Building on the concept of vibrational control, the second term imposes high-frequency periodic inputs that are modulated by the tracking error in the unactuated coordinates. Under appropriate conditions on the system structure and the commanded trajectory, and with sufficient separation between the time scales of the vibrational forcing and the commanded trajectory, the approach provides convergence in both the actuated and unactuated coordinates. The procedure is first described for a two degree-of-freedom (DOF) system with one input. Generalizing to higher-dimensional, underactuated systems, the approach is then applied to a 4DOF system with two inputs. A final example involves control of a rigid plate that is flapping in a uniform flow, a 3DOF system with one input. More general applications include biomimetic locomotion systems, such as underwater vehicles with articulating fins and flapping wing micro-air vehicles.

Stabilization of underactuated mechanical systems is one of the fundamental benchmark problem in the field of control theory. In this article, a hierarchical sliding mode control based on state-dependent switching gain is proposed for stabilization of underactuated mechanical systems. This controller is based on the so called first-level and second-level sliding surfaces. The asymptotic stability of these surfaces is proved by the Lyapunov stability theory. The proposed control technique is applied to two nonlinear underactuated mechanical systems and its feasibility is verified by numerical simulation. The proposed controller efficiently tackles the bounded external disturbance and shows robust performance. The convergence rate of the proposed controller is much faster as compared with the conventional decoupled sliding mode control and the integral sliding mode control.

This article proposed a novel control approach for trajectory tracking of robotic airships. First, the nonlinear dynamics model of a robotic airship is derived and formulated. Second, a sliding mode controller is designed to track the commanded trajectory for its robustness against parametric variations and external disturbances. To address the chattering problem results from the sliding mode controller, a radial basis function neural network is adopted to construct the neural network self-gain-scheduling sliding mode controller in which the control gains are scheduled synchronously with the sliding surface via radial basis function neural network according to the learning algorithm, with switching sliding surface and its differential as radial basis function neural network inputs and control gains as radial basis function neural network outputs. In addition, the stability and convergence of the closed-loop controller are proven using the Lyapunov stability theorem. Finally, the effectiveness and robustness of the proposed controller are demonstrated via numerical simulations. Contrasting simulation results indicate that the neural network self-gain-scheduling sliding mode controller attenuates the chattering effectively and has better performance against the sliding mode controller.