Sliding Mode Control For Trajectory Tracking Research Articles

Non-singular fast terminal sliding mode trajectory tracking control of cantilever piezo-electric stack actuator based on asymmetric hysteresis compensation

Abstract Piezoelectric actuators are widely employed in micro-precision applications due to their fast response and high resolution. This paper investigates the trajectory tracking control of a cantilever piezoelectric stack actuator (CPSA) under external perturbations and hysteresis. A control scheme is proposed that effectively compensates for hysteresis by employing an asymmetric Bouc–Wen model, integrated with a non-singular fast terminal sliding mode control (NFTSMC) featuring a variable convergence law. This methodology guarantees finite-time convergence and robustness, thereby enhancing the overall control performance of the CPSA. Experimental results reveal that the proposed control algorithm significantly improves control accuracy and speed, achieving stable closed-loop system performance and maintaining bounded closed-loop signals within a finite time frame. The effectiveness and superiority of the NFTSMC method are validated through comprehensive experimental studies.

Fractional‐order fast terminal sliding mode trajectory tracking control of quadrotor UAV based on finite time disturbance observer

AbstractIn this paper, a novel trajectory tracking control problem of the quadrotor UAV is addressed, which considers the system uncertainties and unknown external disturbances meanwhile. To ensure a rapid convergence rate of the states, fast terminal sliding mode control (FTSMC) algorithm is improved combining with a fractional order method. In addition, finite‐time observer is designed to handle disturbances and enhance the robustness of the system. The closed‐loop finite‐time stability of the quadrotor UAV system is established using Lyapunov theory in accordance with the novel control law. To evaluate the effectiveness of our proposed strategy, various simulations under different scenarios are conducted respectively. These simulation results clearly demonstrate the superiority of our control scheme, which we refer to as fractional‐order fast terminal sliding mode control (FOFTSMC).

Nonlinear terminal sliding mode trajectory tracking control algorithm for industrial robots based on dung beetle optimizer

Abstract To enhance the precision of trajectory tracking control in industrial robots, a nonlinear end-to-end sliding mode trajectory tracking control algorithm for industrial robots based on the dung beetle algorithm is proposed. By employing nonlinear terminal sliding mode control to resolve the issue of inadequate trajectory tracking control performance in industrial robots, and integrating the dung beetle optimizer (DBO) algorithm for control parameter adjustment, significant enhancements are achieved in trajectory tracking accuracy.

Adaptive super-twisted sliding mode trajectory tracking control for quadrotor UAV with prescribed performance based on finite-time disturbance observer

This study proposes a finite-time disturbed observer-based prescribed performance adaptive super-twisted sliding mode trajectory tracking control scheme for quadrotor UAV. Based on the super-twisted sliding mode algorithm, adaptive control, finite-time theory, and prescribed performance control, this scheme aims to achieve stable tracking of a quadrotor UAV along a defined trajectory. This is achieved even when faced with challenges such as modeling uncertainty, external uncertainty, and complex interference environments. Firstly, the coupling between the channels and the disturbance effects are unified as the aggregate disturbance. To address the issue of the adverse impact of aggregate disturbance on system performance, a new finite-time disturbance observer is developed to estimate the overall disturbance. The observer can effectively eliminate the negative effects of the aggregate disturbance without considering the disturbed boundary conditions during the design process. Secondly, the disturbance estimation information and the adaptive super-twisted algorithm are used to construct the adaptive super-twisted sliding mode controllers for the position and attitude loops, respectively. Then, a prescribed performance control is designed to predefined the time for the position loop to effectively suppress the deleterious effects of interference. This ensures that the position system can quickly meet the prescribed tracking requirements. Finally, the stability of the designed trajectory tracking control system is demonstrated using the Lyapunov theorem. Numerical simulation results verify the effectiveness and superiority of the proposed controller.

Composite continuous fast nonsingular terminal sliding mode trajectory tracking control for Mars entry vehicle

SummaryThis paper presents a composite continuous fast nonsingular terminal sliding mode (CCFNTSM) trajectory tracking control method for Mars entry vehicle. Firstly, the trajectory tracking is transferred into the tracking of the pre‐designed drag acceleration. Secondly, the finite‐time disturbance observer (FTDO) is introduced to estimate the matched and mismatched disturbances. And then, the dynamical fast nonsingular terminal sliding mode manifold is designed based on the estimation information. Finally, the CCFNTSM controller is constructed and its continuity is guaranteed by employing the power function of sliding variable to replace the constant switching gain. Numerical simulation results validate the effectiveness of the proposed control method.

Fixed-time sliding mode trajectory tracking control for marine surface vessels with input saturation and prescribed performance constraints

Fixed-time sliding mode trajectory tracking control for marine surface vessels with input saturation and prescribed performance constraints

Backstepping and Novel Sliding Mode Trajectory Tracking Controller for Wheeled Mobile Robots

A novel variable structure controller based on sliding mode is developed for addressing the trajectory tracking challenge encountered by wheeled mobile robots. Firstly, the trajectory tracking error model under the global coordinate system is established according to the kinematic model of the wheeled mobile robot. Secondly, the novel sliding mode algorithm and backstepping method are introduced to design the motion controller of the system, respectively. Different sliding mode surfaces are formulated to guarantee rapid and stable convergence of the system’s trajectory tracking error to zero. Ultimately, comparative simulation trials validate the controller’s ability to swiftly and consistently follow the reference trajectory. In contrast to traditional controllers, this controller shows rapid convergence, minimal error, and robustness.

Adaptive Terminal Sliding Mode Trajectory Tracking Control for Autonomous Vehicles Considering Completely Unknown Parameters and Unknown Perturbation Conditions

In the actual implementation of autonomous vehicle controller and related applications, it is difficult to obtain all the actual parameters of the vehicle. Considering factors such as uneven pavement and different pavement conditions, it is difficult to accurately establish the vehicle dynamic system model. Based on the non-singular terminal sliding mode and adaptive control theory, this paper establishes a trajectory tracking control strategy for an autonomous vehicle with unknown parameters and unknown disturbances. Firstly, the complex trajectory tracking problem is decoupled from the position and heading angle tracking problem, and the preview error equation is established. Secondly, a non-singular terminal sliding mode (NTSM) controller is established to stabilize the trajectory tracking error to the origin in a finite time, and adaptive laws are proposed to estimate the unknown vehicle parameters to adapt to environmental changes. Through the CarSim–Matlab platform, typical working conditions are implemented to verify the proposed controller. Our experimental outcomes affirm that the NTSM controller effectively guarantees the autonomous vehicle’s accurate following of the reference path, ensuring smooth control inputs throughout the entire process.

Fixed‐time sliding mode trajectory tracking control for marine surface vessels under mismatched conditions and input saturation

SummaryThis paper addresses a trajectory tracking control problem for marine surface vessels (MSVs) in the presence of mismatched conditions and input saturation. Firstly, an MSV model under mismatched conditions is established to solve the problem of unreasonable modeling methods in the existing literature. Secondly, fixed‐time disturbance observers (FXDOs) are designed, where the designed FXDOs not only avoid selecting complicated parameters but also has simple structures, and the disturbance estimation errors can converge to the origin within a setting time. Thirdly, based on the FXDOs and an anti–saturation auxiliary dynamic system, a trajectory tracking control scheme in the presence of mismatched conditions and input saturation is constructed by virtue of fixed‐time integral sliding mode control (SMC), and the actual tracking error signals are uniformly fixed‐time bounded rather than finite‐time one. Fourthly, in order to decrease theoretical calculation values of the original setting time in fixed‐time control, the new setting time under three different parameter conditions is derived, and thus reducing the conservatism. Finally, the simulation results are provided to show the effectiveness and superiority of the designed tracking control scheme.

Adaptive terminal sliding mode trajectory tracking control with fixed‐time prescribed performance considering rollover stability of autonomous vehicles

SummaryIn the face of external disturbances, the autonomous vehicle with a high center of gravity is exposed to the risk of roll instability during trajectory tracking. To this end, this paper aims to propose a vector‐extended‐state‐observer (VESO)‐based adaptive fixed‐time terminal sliding mode prescribed performance control strategy, which coordinates the front wheel steering angle and external roll moment to ensure the roll stability of the high center of gravity autonomous vehicle while improving the tracking dynamic and steady state performances. The VESO for estimating the external disturbance is designed to enhance the robustness outside the sliding mode surface, based on which the adaptive updating laws compensate the estimation errors to provide the control system's dynamic performance. A fixed‐time sliding mode control with prescribed performance is proposed, which combines a fixed‐time prescribed performance control method to further improve the transient performance and steady‐state accuracy. The double lane‐changing reference trajectory tracking conditions under different vehicle driving speeds and initial errors settings are verified by simulation in MATLAB/Simulink environment, and the results show that the proposed control strategy can ensure the rolling stability of the vehicle, can track the reference trajectory accurately and quickly, and has strong robustness.

Disturbance observer–based fixed-time sliding mode trajectory tracking control for marine surface vehicles with uncertain dynamics

In this paper, a fixed-time sliding mode control scheme is developed to fulfill the trajectory tracking task of a marine surface vehicle with unknown dynamics. To restrain the adverse effects of the unknown dynamics including the parameter inaccuracy and exogenous disturbances, a fixed-time disturbance observer is designed to estimate the lumped uncertainties using the bi-limit homogeneous theory without requiring any knowledge of the model uncertainties. Then, a nominal tracking controller is proposed to stabilize the error dynamic model in the sense of fixed-time Lyapunov stability, based on which a novel integral-type sliding mode manifold with bi-limit homogeneity is constructed to drive tracking error convergence in fixed time. To enhance the robustness of the vessel control system, a disturbance observer–based fixed-time integral sliding mode tracking controller is finally proposed, and the chattering phenomenon is effectively alleviated by direct estimation compensations. The analysis of Lyapunov stability indicates that the closed-loop system is fixed-time stable. Numerical simulations on a model vessel are carried out to validate theoretical results of the proposed control scheme.

Finite-time sliding mode trajectory tracking control of an autonomous surface vehicle with prescribed performance

This paper investigates the finite-time sliding mode trajectory tracking control problem for the autonomous surface vehicle (ASV). A prescribed performance function is introduced to improve the transient and steady-state tracking performance simultaneously. Two PID-type sliding surfaces are constructed such that the closed-loop system can reach the sliding surface with good performance, on which the developed sliding mode controllers can make the system error go to zero. In order to demonstrate the effectiveness of the proposed algorithms, an application example of the surface vehicle CyberShip II is borrowed from Skjetne et al., (2005), for which detailed comparisons are made between finite-time second-order sliding mode control (2-SMC) and finite-time first-order sliding mode control (1-SMC). A large number of simulations show that the proposed 2-SMC algorithm can achieve better control accuracy in comparison with 1-SMC algorithm and existing results.

Highly Robust Adaptive Sliding Mode Trajectory Tracking Control of Autonomous Vehicles

Autonomous driving technology has not yet been widely adopted, in part due to the challenge of achieving high-accuracy trajectory tracking in complex and hazardous driving scenarios. To this end, we proposed an adaptive sliding mode controller optimized by an improved particle swarm optimization (PSO) algorithm. Based on the improved PSO, we also proposed an enhanced grey wolf optimization (GWO) algorithm to optimize the controller. Taking the expected trajectory and vehicle speed as inputs, the proposed control scheme calculates the tracking error based on an expanded vector field guidance law and obtains the control values, including the vehicle's orientation angle and velocity on the basis of sliding mode control (SMC). To improve PSO, we proposed a three-stage update function for the inertial weight and a dynamic update law for the learning rates to avoid the local optimum dilemma. For the improvement in GWO, we were inspired by PSO and added speed and memory mechanisms to the GWO algorithm. Using the improved optimization algorithm, the control performance was successfully optimized. Moreover, Lyapunov's approach is adopted to prove the stability of the proposed control schemes. Finally, the simulation shows that the proposed control scheme is able to provide more precise response, faster convergence, and better robustness in comparison with the other widely used controllers.

Adaptive fractional order non-singular terminal sliding mode controller for underwater soft crawling robots with parameter uncertainties and unknown disturbances

Unknown disturbances and nonlinear properties of materials bring challenges to the precise trajectory tracking control of underwater soft robots. An underwater soft crawling robot with high adaptability and mobility in a disturbed underwater environment is proposed. A dynamic model that can characterize asymmetric hysteresis, creep and rate-dependent hysteresis behaviours is presented to solve the problem of electromechanical nonlinear coupling and viscoelasticity affecting the modelling accuracy. Moreover, an adaptive fractional order non-singular terminal sliding mode trajectory tracking controller is proposed to eliminate the influence of underwater uncertain disturbance. The adaptive trajectory tracking controller can achieve fast switching gain and avoid over-tuning, which can effectively improve the accuracy and robustness of the controller. Finally, the stability of the controller is verified according to Lyapunov theory, and the superiority and effectiveness of the control method proposed are proven by numerical simulation and experiment.

Discrete-time adaptive predictive sliding mode trajectory tracking control for dynamic positioning ship with input magnitude and rate saturations

This paper investigates the discrete-time adaptive predictive sliding mode trajectory tracking control problem based on a reference sliding mode trajectory for the dynamic positioning ship with model uncertainty, environmental disturbances and input magnitude and rate saturations. Initially, a two-step delay discrete-time disturbance observer is designed to estimate the model uncertainty and environmental disturbances, and the input constraints are processed by quadratic programming. Then, an adaptive expected heading is proposed to ensure faster trajectory tracking and more stable heading changes simultaneously. Furthermore, using a double closed-loop control strategy, a new discrete-time virtual velocity controller is designed in the outer loop based on Euler discretization to convert trajectory tracking into velocity tracking. In the inner loop, a discrete-time adaptive predictive sliding mode velocity controller is designed based on a new adaptive reference sliding mode trajectory and an integral terminal sliding mode surface with disturbance estimation error. The proposed strategy can adaptively adjust the sliding mode bandwidth and convergence speed, which not only ensures the system’s rapid convergence but also reduces the tracking error and weakens the chattering. Finally, the stability analysis proves that the closed-loop system is uniformly bounded stable. Comparative simulation results verify the effectiveness of the proposed control scheme.

Event-triggered sliding mode trajectory tracking control for underactuated unmanned surface vessel

This article considers the trajectory tracking control for underactuated unmanned surface vessel and actuator loss caused by frequent updating of the controller. An event-triggered sliding mode trajectory tracking control algorithm is proposed for the problems. A sliding mode tracking controller is designed by the integral sliding surface at the beginning to guarantee global asymptotic tracking of the desired trajectory. Based on the tracking controller, the event-triggered condition is designed in the channel of the controller to actuator, which effectively reduces the update frequency of the controller. Theoretical analysis proves that the states of underactuated unmanned surface vessel are uniformly stable, while the Zeno behavior is prevented. The results of the numerical simulation are presented to demonstrate the effectiveness of the proposed algorithm.

Digital Twin for a Multifunctional Technology of Flexible Assembly on a Mechatronics Line with Integrated Robotic Systems and Mobile Visual Sensor-Challenges towards Industry 5.0.

A digital twin for a multifunctional technology for flexible manufacturing on an assembly, disassembly, and repair mechatronics line (A/D/RML), assisted by a complex autonomous system (CAS), is presented in the paper. The hardware architecture consists of the A/D/RML and a six-workstation (WS) mechatronics line (ML) connected to a flexible cell (FC) and equipped with a six-degree of freedom (DOF) industrial robotic manipulator (IRM). The CAS has in its structure two driving wheels and one free wheel (2DW/1FW)-wheeled mobile robot (WMR) equipped with a 7-DOF robotic manipulator (RM). On the end effector of the RM, a mobile visual servoing system (eye-in-hand MVSS) is mounted. The multifunctionality is provided by the three actions, assembly, disassembly, and repair, while the flexibility is due to the assembly of different products. After disassembly or repair, CAS picks up the disassembled components and transports them to the appropriate storage depots for reuse. Disassembling or repairing starts after assembling, and the final assembled product fails the quality test. The virtual world that serves as the digital counterpart consists of tasks assignment, planning and synchronization of A/D/RML with integrated robotic systems, IRM, and CAS. Additionally, the virtual world includes hybrid modeling with synchronized hybrid Petri nets (SHPN), simulation of the SHPN models, modeling of the MVSS, and simulation of the trajectory-tracking sliding-mode control (TTSMC) of the CAS. The real world, as counterpart of the digital twin, consists of communication, synchronization, and control of A/D/RML and CAS. In addition, the real world includes control of the MVSS, the inverse kinematic control (IKC) of the RM and graphic user interface (GUI) for monitoring and real-time control of the whole system. The "Digital twin" approach has been designed to meet all the requirements and attributes of Industry 4.0 and beyond towards Industry 5.0, the target being a closer collaboration between the human operator and the production line.

Trajectory Tracking Control Method Based on Adaptive Higher Order Sliding Mode

To resolve the problem of high-precision trajectory tracking control under interference conditions in a missile’s mid-guidance phase, according to the constructed nominal trajectory, an improved adaptive high-order sliding mode trajectory tracking controller (AHSTC) is proposed. In this method, the open-loop nominal trajectories are established according to the nonlinear programming and Gaussian pseudospectra method. A high-precision trajectory tracking controller is developed by designing a nonlinear sliding mode surface and an adaptive high-order sliding mode approaching law combined with the trajectory tracking nonlinear error model. To verify the effectiveness and superiority of the proposed method, analysis and simulation are carried out through the example of a missile mid-guidance phase tracking control. Compared to the linear quadratic regulator (LQR) and active disturbance rejection controller (ADRC) method, the simulation results show that the proposed AHSTC method shows faster convergence and improved tracking effect. Therefore, the proposed AHSTC method has a good results and engineering application value.

Mobile Visual Servoing Based Control of a Complex Autonomous System Assisting a Manufacturing Technology on a Mechatronics Line

The main contribution of this paper is the modeling and control for a complex autonomous system (CAS). It is equipped with a visual sensor to operate precision positioning in a technology executed on a laboratory mechatronics line. The technology allows the retrieval of workpieces which do not completely pass the quality test. Another objective of this paper is the implementation of an assisting technology for a laboratory processing/reprocessing mechatronics line (P/RML) containing four workstations, assisted by the following components: a complex autonomous system that consists of an autonomous robotic system (ARS), a wheeled mobile robot (WMR) PeopleBot, a robotic manipulator (RM) Cyton 1500 with seven degrees of freedom (7 DOF), and a mobile visual servoing system (MVS) with a Logitech camera as visual sensor used in the process of picking, transporting and placing the workpieces. The purpose of the MVS is to increase the precision of the RM by utilizing the look and move principle, since the initial and final positions of the CAS can slightly deviate from their trajectory, thus increasing the possibility of errors to appear during the process of catching and releasing the pieces. If the processed piece did not pass the quality test and has been rendered as defective, it is retrieved from the last station of the P/RML and transported to the first station for reprocessing. The control of the WMR is done using the trajectory-tracking sliding-mode control (TTSMC). The RM control is based on inverse kinematics model, and the MVS control is implemented with the image moments method.

Communication and Control of an Assembly, Disassembly and Repair Flexible Manufacturing Technology on a Mechatronics Line Assisted by an Autonomous Robotic System

This paper aims to describe modeling and control in what concerns advanced manufacturing technology running on a flexible assembly, disassembly and repair on a mechatronic line (A/D/RML) assisted by an Autonomous Robotic System (ARS), two robotic manipulators (RM) and visual servoing system (VSS). The A/D/RML consists of a six workstations (WS) mechatronics line (ML) connected to a flexible cell (FC) equipped with a 6-DOF ABB industrial robotic manipulator (IRM) and an ARS used for manipulation and transport. A hybrid communication and control based on programmable logic controller (PLC) architecture is used, which consists of two interconnected systems that feature both distributed and centralized topology, with specific tasks for all the manufacturing stages. Profinet communication link is used to interconnect and control FC and A/D/RML. The paper also discusses how to synchronize data between different field equipment used in the industry and the control systems. Synchronization signals between the master PLC and ARS is performed by means of Modbus TCP protocol and OPC UA. The structure of the ARS consists of a wheeled mobile robot (WMR) with two driving wheels and one free wheel (2DW/1FW) equipped with a 7-DOF RM. Trajectory tracking sliding-mode control (TTSMC) is used to control WMR. The end effector of the ARS RM is equipped with a mobile eye-in-hand VSS technology for the precise positioning of RM to pick and place the workparts in the desired location. Technology operates synchronously with signals from sensors and from the VSS HD camera. If the workpiece does not pass the quality test, the process handles it by transporting back from the end storage unit to the flexible cell where it will be considered for reprocessing, repair or disassembling with the recovery of the dismantled parts. The recovered or replaced components are taken over by the ARS from disassembling location and transported back to the dedicated storage warehouses to be reused in the further assembly processes.