Tracking Error Research Articles

Distributed robust tracking control for multiple unmanned aerial vehicles: theory and experimental verification

The distributed trajectory tracking problem for multiple UAVs under unknown external disturbance is investigated. A new nonlinear robust trajectory tracking strategy for multiple UAVs is proposed. The dynamic model for the UAVs' formation is illustrated in the Tangent frame. For the trajectory tracking problem, a Robust formation tracking control strategy based on robust integral of the signum of error (RISE) is designed to compensate for the effects of unknown external disturbances, which improves the robustness of the UAVs' formation system. Based on the Lyapunov stability analysis, it is proved that the global asymptotic convergence of the coordination errors and the semi-global asymptotic convergence of the UAVs' position tracking errors are achieved. The proposed formation control strategy is validated via real-time experiments that are performed on the self-build UAVs' formation flight control testbed. Flights without wind disturbance and flights with disturbance are all performed. The performance comparison experiment with the conventional sliding mode control algorithm is performed. The experimental results show that the designed control strategy can achieve good coordinated trajectory tracking of multiple UAVs, and has better control performance compared with normal sliding mode control law.

Reduced ultimate-bound of tracking error convergence for ETV system with unknown upper-bound mismatched perturbation

The electronic throttle valve (ETV) is widely used in automobile engines to obtain efficient fuel combustion, improved fuel economy, and reduced emissions. The control of the ETV system is a challenging problem due to the unmatched structure of perturbation and its unknown upper bound. As such, deep control concerns are required. For such a system, recent control approaches could partially solve the ultimate boundedness of convergence error, but they have failed to find a solution in the presence of unknown upper-bound perturbation. The contribution of this study is to develop a novel backstepping-based barrier function integral sliding mode controller (BS-BFISMC) to find a solution for the ETV system without the pre-knowledge of the upper bound of perturbation. The proposed control scheme gets the benefits of the backstepping algorithm (BS) and barrier function integral sliding mode control (BFISMC), and the combined scheme could lead to reduced ultimate-bound convergence of tracking error and result in chattering-free control action. A rigorous stability analysis has been conducted to prove the finding reached by the proposed control approach. The efficacy and effectiveness of the proposed controller have been shown by conducting a comparison study with other existing control methods; namely, conventional backstepping controller, robust continuous backstepping (CRBS), and backstepping-based quasi-integral sliding mode controller (BS-QISMC). The numerical results showed that the proposed BS-BFISMC yields the lowest level of ultimate bound of tracking errors and the least control efforts as compared to other controllers. Also, it has been shown that the proposed controller does not require the upper bound of perturbation, which is a pre-requisition of all compared controllers.

Finite-time robust control of morphing aircraft based on time-varying observer

Morphable vehicles have strong nonlinear, strong coupling and strong time-varying characteristics in the process of variation, which brings great challenges to the design of their flight control systems. To address this problem, a time-varying gain extended state observer is proposed to accurately approximate the system coupling terms. Combining adaptive backstepping control technology and finite-time control theory, a finite-time bounded robust adaptive controller is designed. By designing the barrier Lyapunov function, the actual control law and the adaptive network update law are obtained step by step, ensuring that the system command tracking error can converge to a predetermined range within a finite time. Finally, the effectiveness of the designed control system is verified by attitude control simulation. The simulation results show that the morphable vehicle can track the command signal well in the process of variation and is basically not affected by the variation rate.

Lateral-Stability-Oriented Path-Tracking Control Design for Four-Wheel Independent Drive Autonomous Vehicles with Tire Dynamic Characteristics under Extreme Conditions

This paper proposes a lateral-stability-oriented path-tracking controller for four-wheel independent drive (4WID) autonomous vehicles. The proposed controller aims to maintain vehicle stability under extreme conditions while minimizing lateral deviation. Firstly, a tiered control framework comprising upper-level and lower-level controllers is introduced. The upper-level controller is a lateral stability path-tracking controller that incorporates tire dynamic characteristics, developed using model predictive control (MPC) theory. This controller dynamically updates the tire lateral force constraints in real time to account for variations in tire dynamics under extreme conditions. Additionally, it enhances lateral stability and reduces path-tracking errors by applying additional yaw torque based on minimum tire utilization. The lower-level controllers execute the required steering angles and yaw moments through the appropriate component equipment and torque distribution. The joint simulation results from CarSim and MATLAB/Simulink show that, compared to the traditional MPC controller with unstable sideslip, this controller can maintain vehicle lateral stability under extreme conditions. Compared to the MPC controller, which only considers lateral force constraints, this controller can significantly reduce lateral tracking errors, with an average yaw rate reduction of 31.62% and an average sideslip angle reduction of 40.21%.

Adaptive interacting multiple model particle filter based on a dual-pattern bat algorithm for maneuvering target tracking

The interacting multiple model particle filter (IMM-PF) is a filtering method commonly used for nonlinear non-Gaussian radar systems. Its transfer probabilities are usually fixed and dependent on prior information. When tracking maneuvering targets, the IMM-PF may cause excessive tracking errors due to the model switching lag. In addition, the particle impoverishment caused by the resampling of the particle filter seriously affects the filtering accuracy. Therefore, the IMM-PF has difficulty meeting the accuracy and speed requirements of modern high-performance radar target tracking systems. To address these problems, an adaptive interacting multiple model particle filter based on the dual-pattern bat algorithm (ADIMM-DPBA-PF) is proposed for tracking maneuvering targets under nonlinear and non-Gaussian conditions. First, the adaptive model switching mechanism is established to adjust the transition probabilities using the model probability posterior information at consecutive times, improving the model switching efficiency. Second, a particle filter based on the dual-pattern bat algorithm (DPBA-PF) is proposed. The filter exploits global search and local search strategies to optimize the particles and intelligently move the particles to the high likelihood region. Finally, a particle filter based on the dual-pattern bat algorithm is used to form the adaptive interacting multiple model method. The experimental results show that the proposed algorithm has better comprehensive performance than the IMM-PF.

Filter‐Based Average Dwell‐Time Tuning Approach for Adaptive Prescribed‐Time Tracking of Uncertain Switched Nonlinear Systems

ABSTRACTThis paper addresses neural‐network‐based adaptive prescribed‐time (PT) tracking for uncertain switched systems with unmatched nonlinearities. A continuously switched adaptive tuning mechanism for neural network learning is developed by applying the average dwell time (ADT). First, a neural‐network‐based PT tracking control design strategy using the ADT‐based adaptive tuning mechanism is established for switched nonlinear systems in strict‐feedback form. A novel adaptive dynamic surface controller is designed recursively using a practical finite‐time scaling function and continuously switched tuning parameters. The switched adaptive tuning laws for neural networks are structured to reduce the conservatism associated with common adaptive laws. Then, a filter‐based tuning approach is employed to ensure the continuity of switched adaptive parameters with ADT in the designed controller. The practical PT stability of the closed‐loop system is demonstrated based on the boundedness of the adaptive parameters. Building upon this foundation, the proposed PT design approach is extended to control switched pure‐feedback nonlinear systems, even in cases where control directions are unspecified. The unknown sign problem encountered with switched virtual and actual control coefficient functions is resolved in the PT control framework. It is shown that the PT performance bound of the tracking error can be reduced by selecting the design parameter of the scaling function. Finally, simulation results illustrate the merits of the proposed theoretical approach.

H ∞ prescribed tracking performance-based fractional-order sliding mode control for disturbed discrete-time systems: an LMI approach

This paper presents a novel approach to the design of a discrete-time Fractional-Order Sliding Mode Control (FSMC) system for Single Input Single Output (SISO) applications, utilising the Autoregressive with exogenous input (ARX) method for system modelling. The proposed methodology emphasises the Prescribed Performance Control (PPC) to ensure minimal tracking errors through a transformation of tracking errors based on a specified performance function. A Fractional-Order Quasi-Sliding Mode Control (FQSMC) is subsequently developed to maintain the tracking error within predetermined bounds, effectively addressing the chattering phenomenon commonly associated with the traditional sliding mode control. The integration of fractional calculus enhances the smoothness of the output while ensuring accurate tracking, making it ideal for real-world applications. Additionally, a novel Linear Matrix Inequality (LMI) observer is introduced to bolster the system's resilience against uncertainties and disturbances without complicating the computational process. The effectiveness of the proposed Prescribed Performance Fractional-Order Quasi-Sliding Mode Control (PP-FQSMC) is validated through extensive MATLAB simulations and experimental studies conducted on a Tank system. Results demonstrate that the PP-FQSMC significantly outperforms traditional methods, with maximum tracking errors of 1.6 × 10−4 compared to 0.2 for the PP-QSMC and a Root Mean Square Tracking Error (RMSTE) of 1.3 × 10−3 compared to 1.2 × 10−4 for the PP-QSMC, ensuring strong tracking performance and stability. The findings indicate that the proposed controller effectively mitigates chattering in control signals while maintaining a smooth output. It showcases its potential for practical applications in environments characterised by model inaccuracies, time delays, and external disturbances.

Energy-Efficient Passivity-Based Sliding Mode Controller for Small-Scale Quadrotor UAV for Trajectory Tracking

Quadrotor unmanned aerial vehicles (UAVs) have emerged as versatile platforms applicable to various fields such as surveillance, reconnaissance, and mapping. However, the limited energy capacity inherent in these vehicles poses a significant challenge. This limitation is a critical concern hindering their widespread adoption across diverse applications. Despite various proposed technological solutions addressing the energy consumption issue, the central challenge for the control community lies in developing controllers that ensure stability, robustness, and energy efficiency. In this paper, we present a passivity-based sliding mode controller (P-SMC) designed specifically for quadrotor UAVs. The suggested controller capitalizes on the robustness of the SMC and the energy efficiency of passivity-based control theory. Feedback passification is employed to create a sliding surface with passivity, ensuring stability. The inclusion of a noncontinuity term in the proposed P-SMC guarantees global asymptotic convergence to the sliding surface. To address the multi-faceted nature of the problem, a multi-objective optimization criterion is introduced. This criterion, which combines tracking error and control energy, is solved using the ant colony optimization (ACO) algorithm. The optimization process aims to identify control parameters that strike a balance between tracking accuracy and energy efficiency. Additionally, a conventional sliding mode method is developed to respond to conditions of attempted reach and sliding. Finally, the effectiveness of the proposed method is demonstrated through simulation results considering piecewise constant external disturbances. The outcomes based on the proposed control strategy indicate a notable reduction in energy consumption (ranging from [Formula: see text] to [Formula: see text]), faster reaching times (5–8 times), higher accuracy approximately ([Formula: see text]), and reduced chattering compared to the conventional sliding mode technique.

Compensation Function Observer-Based Backstepping Sliding-Mode Control of Uncertain Electro-Hydraulic Servo System

Observer-based control is the most commonly used method in the control of electro-hydraulic servo system (EHSS) with uncertainties, but it suffers from the drawback of low accuracy under the influence of large external load forces and disturbances. To address this problem, this paper proposes a novel compensation function observer-based backstepping sliding-mode control (BSMC) approach to achieve high-accuracy tracking control. In particular, the model uncertainties, including nonlinearities, parameter perturbations and external disturbances are analyzed and treated together as a lumped disturbance. Then, a fourth-order compensation function observer (CFO) is constructed, which fully utilizes the system state information to accurately estimate the lumped disturbance. On this basis, the estimate of the lumped disturbance is incorporated into the design of a backstepping sliding-mode controller, allowing the control system to compensate for the disturbance effect. The stability of the closed-loop control system under the CFO and BSMC is rigorously proven through the use of the Lyapunov theory, which guarantees that all the tracking error signals converge exponentially to the origin. Comparative simulations are carried out to show the effectiveness and efficiency of the proposed approach, i.e., compared with PID and ESO-based BSMC methods, the tracking accuracy is respectively improved by 94.86% and 88.19% under the influence of large external load forces and disturbances.

Recover a moving rotor UAV without ground–air communications: System and control of a dual-stage tracking device

Recovering a moving rotor unmanned aerial vehicle (UAV) using a single-stage dynamic tracking device poses a significant challenge, particularly without real-time communication between the two systems. This study presents a dual-stage tracking system comprising an unmanned ground vehicle (UGV) and a Stewart platform, aimed at dynamically tracking and recovering the UAV. Firstly, an observation algorithm combining Kalman filtering (KF) and curve fitting is designed to estimate and complete the drone’s states and predict its trajectory. Subsequently, a decoupled dual-stage tracking control structure is introduced, integrating two independent controlled subsystems. Specifically, in the UGV controller, the model predictive control (MPC) is employed to enhance dynamic tracking capabilities using absolute kinematics. A motion tracking algorithm based on relative kinematics was developed for the Stewart recovery platform to compensate for UGV tracking errors and improve tracking accuracy. Dynamic recovery simulations and experiments have been conducted to validate the feasibility and effectiveness of the proposed dual-stage tracking system. The results demonstrate the system’s capability to dynamically track and recover the drone without real-time communication in complex environments characterized by detection noise and target trajectory disturbances.

High dynamic performance based by sliding mod control of quadrotor MAV

The paper focuses on strong control of high dynamic performance based on the sliding mode in order to control the quadrotor MAV. The model used in the simulation is the Newton-Euler model, and also choose the Mambo Parrot quadrotor parameters, to improve the latter's performance in terms of accuracy and robustness in case the impedance control chosen by the manufacturer needs to be changed. The results of which gave effectiveness and efficiency compared to classical controls PID and sliding mode. High dynamic performance control (HDP) is a type of control system designed to provide the highest level of performance over a wide range of operating conditions. This control is not a regulator but an organizing technique. It uses a prediction-based approach to anticipate rapid variations in system states and disturbances and to generate real-time commands to correct tracking errors and maintain system stability. This approach allows HDP control to achieve high performance while maintaining system stability, even under harsh operating conditions.

Integrated Motion Control Strategy Considering Parameter Robustness for Distributed Vehicle by Wire

<div>To address the issues of functional conflicts in execution subsystems and the deterioration of control performance due to model parameter uncertainties in the motion control of distributed vehicle by wire, this article proposes an integrated control strategy considering parameter robustness. This strategy aims to compensate for model mismatch, resolve functional conflicts, and achieve motion coordination. Based on the over-actuation characteristics of distributed vehicle by wire, this article constructs the dynamic model and utilizes the tire cornering properties along with phase portraits to delineate the working regions of the execution subsystems. To deal with model parameter uncertainties and mismatch, tube-based model predictive control (tube-based MPC) is applied to the control strategy design, which compensates for model deviations through state feedback and constructs a robust positively invariant set (RPI) to constrain the system state. Correspondingly, the weights of control inputs are adjusted adaptively, according to the working regions, to optimize the coordination logic of integrated control. In order to verify the effectiveness and feasibility of the strategy, extreme driving condition tests are executed on hardware-in-the-loop (HIL) and real vehicle test platforms. The test results indicate that the strategy proposed in this article is able to reduce the sideslip angle and tracking error of yaw rate, improve driving stability under extreme conditions through integrated control, and especially, it can still maintain precise stability control performance under severe model mismatch, exhibiting strong robustness facing parameter uncertainties.</div>

System modeling and fuzzy adaptive PI sliding-mode control of a novel ship-mounted cable-based bulkhead cleaning robot

Ship cleaning poses significant risks and consumes considerable time, primarily due to the irregular hull surface geometry and the unpredictable ship motion induced by wave excitation. To address this challenge and achieve efficient, autonomous cleaning, a spatial variable structure cable-based bulkhead cleaning robot (SC-R) is proposed. Unlike traditional cable-driven parallel mechanisms (CDPMs), SC-R operates in a non-inertial frame, whereby its motion is subject to continuous and unpredictable ship motion. Consequently, SC-R exhibits intricate dynamic characteristics, posing a significant hurdle for controller design. To solve this problem, a sliding-mode controller is proposed for SC-R. Specifically, the dynamic model of SC-R, which includes ship motion and various disturbing forces, is systematically established using the Newton-Euler method. Furthermore, a fuzzy adaptive PI sliding-mode controller (FAPI-SMC) is specifically proposed to enhance the convergence speed and robustness of SC-R. The stability of the closed-loop system is analyzed using Lyapunov theory, and the tracking error is proved to be eventually bounded. Finally, the availability of this theory is confirmed by simulation and experiment. It is shown that FAPI-SMC can achieve a satisfactory control effect in practice.

Adaptive performance optimal control for flexible-joint robots with random noises: Design and experiment

This study developes a flexible performance optimal control scheme via reinforcement learning strategy and event-triggered mechanism for flexible-joint robots with random noise and non-affine input. It is notable that an event-triggered optimization mechanism is developed, which meets the optimality principle and saves communication resources. Nevertheless, the existing event-triggered strategy is unable to handle non-affine input, which limits the applicability of this method. To overcome the above problems, a modified event-triggered mechanism is proposed. At the same time, the optimal solution of the system is given by an optimized control algorithm based on the improved performance index function. In the controller design, neural network is used to deal with random disturbances and uncertainties, and an adaptive law is designed to replace the identifier structure. Besides, a flexible prescribed performance function is constructed to yield multiple prescribed performance behaviors by adjusting the key parameters, while the tracking error is stayed within a prescribed boundary. Finally, the effectiveness of the proposed control scheme is further demonstrated by simulation and the experiment of the 2-link flexible-joint robot on the Quanser platform.

Adaptive Matching of Discrete Antenna Tuning Units of High Frequency Band to Varying Load Impedance

The issue of matching the antenna with thetransmitter-receiverplays a primary role in radio communications. The matching problem is relevant for different ranges and is solved in many ways. In the high frequency wave range, matching has a number of features when using an antenna coupler based on discrete elements consisting of capacitance and inductance boxes. The article discusses the concept of fast matching of high-frequency amplifying paths ofdecametric wavestransceivers with non-stationary loads using discrete antenna couplers. An innovative approach has been developed to the tuning process when changing the operating frequency and ensuring self-adaptation of the antenna coupler when changing the impedance, based on methods for quickly searching for the geometric proximity of points. A quick method for configuring the antenna coupler is proposed, eliminating the procedure for recalculating the input impedance based on the results of measuring the input impedance of the antenna coupler. When using it, the speed of setting the antenna coupler at the current operating frequency is limited only by the time of a single state change of the discrete power circuit, which in the case of electromagnetic relays is numerically equal to their switching time. The configuration of the antenna coupler using the method of fast search for the geometric proximity of points is based on a set of frequency cards with settings options. Such cards can be recalculated for the reference plane between the generator and the antenna coupler input for all combinations of discrete elements in accordance with the known matrix model of a discrete power circuit. This eliminates the complicated procedure of recalculating the input impedance of the antenna using complex numbers. The technical result of the proposed innovative method of antenna coupler configuringis simplification, tracking of systematic errors of the impedance meter, elimination of time-consuming calculations with complex numbers, expansion of the method functionality, reduction of the tuning duration and improvement its quality. The practical significance lies in the fact that the implementation of the proposed technical solutions in the high frequency range communications means can significantly (about 100 times) limit the duration of preparation for a radio communication session, eliminate the procedure for recalculating the antenna input impedance and reduce the resource requirements of switching elements.

In vivo Multi-perspective 3D + t Ultrasound Imaging and Motion Estimation of Abdominal Aortic Aneurysms.

Time-resolved three-dimensional ultrasound (3D + t US) is a promising imaging modality for monitoring abdominal aortic aneurysms (AAAs), providing their 3D geometry and motion. The lateral contrast of US is poor, a well-documented drawback which multi-perspective (MP) imaging could resolve. This study aims to show the feasibility of in vivo multi-perspective 3D + t ultrasound imaging of AAAs for improving the image contrast and displacement accuracy. To achieve this, single-perspective (SP) aortic ultrasound images from three different angles were spatiotemporally registered and fused, and the displacements were compounded. The fused MP had a significantly higher wall-lumen contrast than the SP images, for both patients and volunteers (P < .001). MP radial displacements patterns are smoother than SP patterns in 67% of volunteers and 92% of patients. The MP images from three angles have a decreased tracking error (P < .001 for all participants), and an improved SNRe compared to two out of three SP images (P < .05). This study has shown the added value of MP 3D + t US, improving both image contrast and displacement accuracy in AAA imaging. This is a step toward using multiple or large transducers in the clinic to capture the 3D geometry and strain more accurately, for patient-specific characterization of AAAs.

Fully planar solar-pumped fiber laser with 0.1% slope efficiency.

A slope efficiency of 0.1% has been achieved for a fully planar solar-pumped fiber laser (SPFL) with a diameter of 30 cm and an output power of 34 mW. The fiber length is constrained to 400 m, but numerical simulations indicate that the maximum laser output power can be elevated to 113 mW by simply extending the length of the fiber and housing it in the same body. The tolerance to the solar tracking error was quantified, and the results demonstrated that more than 80% of the maximum output power can be sustained up to a ±23° tracking error. This study demonstrates the capability of the fully planar SPFL to operate without solar tracking.

Electronic brake system-based hierarchical motion control of commercial vehicle for autonomous obstacle avoidance

As a high-level autonomous driving technology, efficient and safe automatic obstacle avoidance on highway is one of the critical and ongoing topics that requires in-depth research for commercial vehicles. Electronic control air pressure brake system, owing to its fast response and active braking ability, is an effective active-chassis technology to function path tracking and stability control in such condition. Yaw motion stability control problem of autonomous driving commercial vehicle based on active braking control with electronic air brake system for automatic obstacle avoidance is investigated. First, a hierarchical yaw motion dynamics control architecture is introduced after vehicle and brake system modeling. The quintic polynomial curve-based trajectory planning method and a Model Predictive Control based trajectory tracking control strategy are formulated. Second, to evade the possible stability losing issue in this circumstance, Cubature Kalman Filter (CKF) is utilized to estimate the vehicle motion states, and a fuzzy PID control-based differential brake stability control strategy is designed for the electronic brake system composed of front-and-rear two sets of dual-channel pressure regulator and ABS solenoid valve. Finally, the proposed hierarchical yaw stability control strategy for a commercial vehicle in typical obstacle avoidance conditions is comparatively verified based on the joint simulation tools. After the yaw stability control, the peak value of the lateral displacement error of trajectory tracking can be reduced by 44.7%. The yaw stability control strategy based on fuzzy PID control can reduce the yaw rate by 46%–57% and the sideslip angle by 60%–73% under different conditions. The results show that the proposed control strategy can effectively improve the yaw stability of the vehicle while avoiding obstacles at high speed.

Unified Fault-Tolerant Control and Adaptive Velocity Planning for 4WID-4WIS Vehicles under Multi-Fault Scenarios

Four-wheel independent drive and four-wheel independent steering (4WID-4WIS) vehicles provide increased redundancy in fault-tolerant control (FTC) schemes, enhancing heterogeneous fault-tolerant capabilities. This paper addresses the challenge of maintaining vehicle safety and maneuverability in the presence of actuator faults in autonomous vehicles, focusing on 4WID-4WIS systems. A novel unified hierarchical active FTC strategy is proposed to handle various actuator failures. The strategy includes an upper-layer motion controller that determines resultant force requirements based on trajectory tracking errors and a middle-layer allocation system that redistributes tire forces to fault-free actuators using fault information. This study, for the first time, considers multi-fault scenarios involving longitudinal and lateral coupling, calculating FTC boundaries for each fault type. Additionally, a fault tolerance index is introduced for 256 fault scenarios, using singular value decomposition to linearly represent the vehicle attainable force domain. Based on this, an adaptive velocity planning strategy is developed to balance safety and maneuverability under fault conditions. Matlab 2021a/Simulink and Carsim 2019 co-simulation results validate the proposed strategies, demonstrating significant improvements in fault-tolerant performance, particularly in complex and emergency scenarios.

Adaptive visual servoing control for uncalibrated robot manipulator with uncertain dead-zone constraint

This paper addresses the adaptive visual tracking control problem of an uncalibrated camera robot system with unknown dead-zone inputs. The uncertainties include camera extrinsic and intrinsic parameters, robot dynamic parameters, and feature depth parameters. The control achieves a better performance by establishing a smooth inverse model of the dead-zone input, which eliminates the nonlinear effect of the actuator constraint. A novel adaptive control scheme is presented which does not require a priori knowledge of the parameter intervals of dead-zone model, to update the parameter values online. Furthermore, adaptive laws are provided to estimate the uncertainties that exist both in robot and in camera models. Meanwhile, in order to avoid the singularity of the image Jacobian matrix, a projection algorithm is also introduced. Subsequently, a novel robust adaptive controller together with dead-zone compensation is established so that the tracking error image space converges to the origin. Simulations and experimental studies are conducted to verify the effectiveness of the proposed method.