Observer Error Research Articles

Attitude Tracking of Rigid-Liquid-Flexible Coupling Spacecraft by Active Disturbance Rejection Control

Considering the complex attitude dynamics of Rigid-Liquid-Flexible Coupling Spacecraft, especially when the large amplitude sloshing of liquid exists in rapid attitude maneuver, the conventional control design method based on the linearized model is not suitable for the significant coupling and strong nonlinearity. By contrast, Active Disturbance Rejection Control is model-independent and easy to design and implement. In this paper, the three main components of Active Disturbance Rejection Control, Tracking Differentiator, Extended State Observer and Nonlinear State Error Feedback are comprehensively applied to the attitude tracking control of Rigid-Liquid-Flexible Coupling Spacecraft. Firstly, two cascaded Tracking Differentiators are used to arrange the transition process of the attitude command, which not only reduces overshoot and oscillation of the tracking process, but also obtains the angular acceleration information of attitude trajectory for feed-forward compensation. Secondly, the total disturbance caused by liquid sloshing and flexible vibration is observed by Extended State Observer and compensated synchronously. Finally, the Nonlinear State Error Feedback is used to further improve the transient behavior and steady-state quality of the control system. The simulation results show that the tracking accuracy of the attitude and angular velocity using the Active Disturbance Rejection Control are about 3 to 27 times and 6 to 115 times that of the PID control, respectively. The convergence time, overshooting are also significantly less than the PID control.

Similarities and differences between exosystem-model-based disturbance observer and model error compensator

Similarities and differences between exosystem-model-based disturbance observer and model error compensator

Event-triggered fixed-time distributed observers for general linear systems

This paper delves into the implementation of a distributed fixed-time state estimation approach for linear systems, utilizing an event-triggered strategy. Particularly, the output data from the linear systems are strategically distributed across various observers. A novel fixed-time distributed observer is proposed to reconstruct full states of the linear system cooperatively with the observer error converges to zero within fixed time. Based on the event-triggered strategy, the communication times among observers are reduced by intermittent communication. Simultaneously, Zeno-behavior is ruled out completely. Finally, the proposed results are verified by a simulation example.

Human-in-the-Loop Consensus Control for Multiagent Systems With External Disturbances.

In this article, the human-in-the-loop leader-follower consensus control problem is addressed for multiagent systems (MASs) with unknown external disturbances. A human operator is deployed to monitor the MASs' team by transmitting an execution signal to a nonautonomous leader in response to any hazard detected, with the control input of the leader unknown to all followers. For each follower, a full-order observer, in which the observer error dynamic system decouples the unknown disturbance input, is designed for asymptotic state estimation. Then, an interval observer is constructed for the consensus error dynamic system, where the unknown disturbances and control inputs of its neighbors and its disturbance are treated as unknown inputs (UIs). To process the UIs, a new asymptotic algebraic UI reconstruction (UIR) scheme is proposed based on the interval observer, and one of the significant features of the UIR is the capacity to decouple the control input of the follower. The subsequent human-in-the-loop asymptotic convergence consensus protocol is developed by applying an observer-based distributed control strategy. Finally, the proposed control scheme is validated through two simulation examples.

Distributed finite-time attack detection and estimation of intelligent connected vehicle platoon

ABSTRACT This paper presents a distributed finite-time observer design approach for the problem of intelligent connected vehicles (ICVs) containing both attack signals and unknown disturbances. Firstly, an analysis is conducted on the two types of network attacks that ICVs may encounter, followed by the construction of a dynamic vehicle model and its transformation into a state space equation. Secondly, an intermediate variable is introduced to design a distributed attack estimation observer, which both ensures accurate estimation of the vehicle safety state and attack signal within a limited time and overcomes the constraints of traditional observers. Additionally, sufficient conditions for the finite-time boundedness of the observer error system with H ∞ performance are provided in the form of linear matrix inequalities. Furthermore, an adaptive threshold attack detection method is designed. Finally, the simulation results validate the efficiency of the design methods.

Osteon shape variation in the femoral diaphysis: A geometric-morphometric approach on human cortical bone microstructure in an elderly sample.

Geometric morphometrics (GMM) have been applied to understand morphological variation in biological structures. However, research studying cortical bone through geometric histomorphometrics (GHMM) is scarce. This research aims to develop a landmark-based GHMM protocol to depict osteonal shape variation in the femoral diaphysis, exploring the role of age and biomechanics in bone microstructure. Proximal, midshaft, and distal anatomical segments from the femoral diaphysis of six individuals were assessed, with 864 secondary intact osteons from eight periosteal sampling areas being manually landmarked. Observer error was tested using Procrustes ANOVA. Average osteonal shape and anatomical segment-specific variation were explored using principal component analysis. Osteon shape differences between segments were examined using canonical variate analysis (CVA). Sex differences were assessed through Procrustes ANOVA and discriminant function analysis (DFA). The impact of osteonal size on osteonal shape was investigated. High repeatability and reproducibility in osteon shape landmarking were reported. The average osteon shape captured was an elliptical structure, with PC1 reflecting more circular osteons. Significant differences in osteon shape were observed between proximal and distal segments according to CVA. Osteon shape differed between males and females, with DFA showing 52% cross-validation accuracies. No effect of size on shape was reported. Osteonal shape variation observed in this study might be explained by the elderly nature of the sample as well as biomechanical and physiological mechanisms playing different roles along the femoral diaphysis. Although a larger sample is needed to corroborate these findings, this study contributes to the best of our knowledge on human microanatomy, proposing a novel GHMM approach.

Distributed State Observer for Systems with Multiple Sensors under Time-Delay Information Exchange.

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Distributed event‐triggered fixed‐time formation tracking control for multi‐spacecraft systems based on adaptive immersion and invariance technique

AbstractIn this study, the problem of fixed‐time formation tracking for multi‐spacecraft systems without internal collisions was investigated. Aiming to ensure that the formation members can accurately realize and maintain the required configuration within the user‐given time, we designed a novel adaptive immersion and invariance (I&I)‐based control protocol. The novelty here lies in two aspects. First and foremost, this study was based on the adaptive I&I technique, combined with a new artificial potential function, to achieve the desired formation tracking without internal collision. Second, unlike the asymptotic convergence of the traditional I&I‐related works, to guarantee the fixed‐time stability, the proposed protocol introduced the prescribed performance control, which can also alleviate the possible system performance degradation caused by the non‐periodic control signal update of the event‐triggered mechanism. Further, the introduction of the event‐triggered mechanism can reduce the unnecessary information interaction. Lyapunov stability analysis shows that this proposed protocol can enable the defined implicit manifold to converge to the origin for the most initial conditions. Also, benefiting from the prescribed performance techniques, the convergence time can eliminate the dependence of the system on designed controller parameters or initial system conditions, relying only on the actual mission requirements. In addition, we adopted a linear extended state observer to deal with the parameter uncertainties and external disturbances, and used the I&I adaption to estimate the observer errors, thus further improving the system performance. Moreover, a new exponential‐type artificial potential function was designed to avoid close proximity between formation members and prevent internal collisions. Finally, numerical simulations were conducted to verify the theoretical results.

A spatiotemporal comparison of interobserver error in vegetation sampling

AbstractQuestionsWe asked how interobserver error in sampling vegetation (excluding trees) varied over time, space and habitat type; determined whether there were any obvious correlates of observer error; and evaluated evidence of bias among observers.LocationNine national park units in the Midwestern USA.MethodsWe quantified observer error in the context of a long‐term monitoring program employing three observers, evaluating interobserver error across 11 locations in the Midwestern USA over five years. The vegetation (excluding trees) was sampled independently by two teams of observers at prairie and woodland locations (n = 94 plots total).ResultsTotal pseudoturnover ranged between 20.2% and 22.1% at prairie locations, and between 16.8% and 28.6% at woodland locations. The overlooking component of pseudoturnover accounted for 75% or more of total pseudoturnover, with misidentification and cautious components each contributing 19% or less of the total, depending on location. The percentage of comparisons in which both observers recorded the same cover class ranged from 71.3% to 78.5% at the prairie locations and 56.9% to 85.6% at woodland locations. When observers did not agree on cover class, they were off by more than one class less than 6% of the time. Overlooking error was more likely to occur for species with less cover, while estimation error was more likely to occur for species with greater cover. A bias existed among observers, as the least experienced observer recorded 6.2%–11.8% more species than the other two observers. Interobserver bias also existed for rates of estimation error, as one observer consistently recorded higher cover classes.ConclusionsObserver error is a pervasive aspect of vegetation sampling. Continued training and experience yielded limited increases in precision. Elements of the sampling design probably reduced observer error to a certain degree, although some level of interobserver error in vegetation surveys is unavoidable.

Differentiation of petro-sourced plastic microfilaments from organic microfilaments by SEM-EDX in environmental samples

Quantifying microplastics (MPs) in marine environments is challenging due to the complexities of differentiation from other materials. This study aims to distinguish petro-sourced plastic microfilaments from organic ones in environmental samples using scanning electron microscope coupled with energy dispersive X-ray (SEM-EDX) analysis. Therefore, 38 particles resembling MPs (PRMPs) from sediments and organisms in Madagascar were analyzed. MPs identification thresholds were determined from SEM-EDX analysis of macroplastics and seaweed, the primary sources of microfilaments. SEM-EDX results of the 38 PRMPs were compared with identification/misidentification made by five MPs observation experts. Results indicated that a carbon/oxygen (C/O) ratio >1 distinguished macroplastics and MPs from other sources (seaweed and organic microfilaments). SEM-EDX analysis identified 81.58% of PRMPs as MPs. The average error made by one observer was 36.32%. These findings highlight the need for a method to assess identification error in MPs quantification and recommend SEM-EDX analysis of microfilaments to gauge observer error.

A Sensor Fusion Approach to Observe Quadrotor Velocity.

The growing use of Unmanned Aerial Vehicles (UAVs) raises the need to improve their autonomous navigation capabilities. Visual odometry allows for dispensing positioning systems, such as GPS, especially on indoor flights. This paper reports an effort toward UAV autonomous navigation by proposing a translational velocity observer based on inertial and visual measurements for a quadrotor. The proposed observer complementarily fuses available measurements from different domains and is synthesized following the Immersion and Invariance observer design technique. A formal Lyapunov-based observer error convergence to zero is provided. The proposed observer algorithm is evaluated using numerical simulations in the Parrot Mambo Minidrone App from Simulink-Matlab.

Pitot tube measure-aided air velocity and attitude estimation in GNSS denied environment

This paper addresses the problem of estimating air velocity and gravity direction for small autonomous fixed-wing drones in GNSS11Global Navigation Satellite Systems.-denied environments. The proposed solution uses a minimal sensor suite, relying on Pitot tube measurements and Inertial Measurement Unit (IMU) signals, including only gyrometers and accelerometers. The approach combines the Riccati observer and Equivariant Filter designs, using an over-parametrization technique to design an observer on SO(3)×R3 and subsequently re-project to S2×R3 to estimate the gravity direction. The system’s observability is analyzed, and local exponential stability of the origin of the observer error is demonstrated as long as the aircraft attitude is persistently exciting. The observer was evaluated using simulated and real flight data to showcase the estimator’s performance.

Development and validation of a fully automated tool to quantify 3D foot and ankle alignment using weight-bearing CT

IntroductionFoot and ankle alignment plays a pivotal role in human gait and posture. Traditional assessment methods, relying on 2D standing radiographs, present limitations in capturing the dynamic 3D nature of foot alignment during weight-bearing and are prone to observer error. This study aims to integrate weight-bearing CT (WBCT) imaging and advanced deep learning (DL) techniques to automate and enhance quantification of the 3D foot and ankle alignment. MethodsThirty-two patients who underwent a WBCT of the foot and ankle were retrospectively included. After training and validation of a 3D nnU-Net model on 45 cases to automate the segmentation into bony models, 35 clinically relevant 3D measurements were automatically computed using a custom-made tool. Automated measurements were assessed for accuracy against manual measurements, while the latter were analyzed for inter-observer reliability. ResultsDL-segmentation results showed a mean dice coefficient of 0.95 and mean Hausdorff distance of 1.41 mm. A good to excellent reliability and mean prediction error of under 2 degrees was found for all angles except the talonavicular coverage angle and distal metatarsal articular angle. ConclusionIn summary, this study introduces a fully automated framework for quantifying foot and ankle alignment, showcasing reliability comparable to current clinical practice measurements. This operator-friendly and time-efficient tool holds promise for implementation in clinical settings, benefiting both radiologists and surgeons. Future studies are encouraged to assess the tool's impact on streamlining image assessment workflows in a clinical environment.

Risk assessment of unmanned aerial vehicle accidents based on data-driven Bayesian networks

With the popularity of unmanned aerial vehicles (UAVs) in different application scenarios, a series of potential risks and challenges have emerged. Few quantitative studies in the existing literature analyze the risk factors that affect and cause UAV accidents. Therefore, this study aims to reveal the dependency relationships among the risk factors associated with UAV accidents by using a data-driven tree-augmented naïve Bayesian network (TAN-BN) method. Firstly, UAV accident reports from transportation departments of various countries are collected and analyzed to establish a dataset on the risk factors inducing different UAV accidents. Then, a data-driven UAV risk analysis model is constructed through data learning and training approaches to reveal the interdependency of risk factors and their comprehensive impacts on the severity of UAV accidents. Sensitivity analysis is comprehensively conducted to show the rationality of the proposed TAN-BN. The results reveal that the risk factors “other aircraft”, “observer errors”, “non-powerplant”, “preconditions for unsafe acts”, “powerplant”, and “adverse weather” are the key factors resulting in UAV accidents. In addition, “observer errors”, “other aircraft”, “non-powerplant” and “adverse weather” are more likely to incur severe “accidents”. Some potential proactive plans and measures are proposed to help prevent the occurrence of UAV accidents.

Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.

Sliding mode disturbance observer based control with arbitrary convergence time

In this study, an arbitrary finite-time backstepping control method for a class of uncertain nonlinear systems in the presence of external disturbance is proposed based on disturbance observer. Motivated by the desire to attain external disturbance compensation, a sliding mode disturbance observer with arbitrary convergence time is presented to estimate the disturbance. This arbitrary prespecified time is independent of initial conditions and system parameters. The designed observer is very simple with only one tuning parameter used to tune the convergence rate. Only the upper bound of the first derivative of the disturbance is necessary. Then, based on the proposed disturbance observer, a backstepping control technique is developed in which the convergence time can be chosen arbitrarily. Utilizing the Lyapunov stability criterion, it is proven that the system states, as well as the disturbance observer error converge to the origin in arbitrarily chosen time. Finally, some numerical examples are presented to demonstrate the validity and applicability of the proposed disturbance observer-based controller.

Digital image processing: A new tool for morphological measurements of freshwater turtles under rehabilitation.

Freshwater fauna is facing an uphill task for survival in the Ganga Basin, India, due to a range of factors causing habitat degradation and fragmentation, necessitating conservation interventions. As part of the ongoing efforts to conserve the freshwater fauna of the Basin, we are working on rehabilitating rescued freshwater chelonians. We carry out various interventions to restore rescued individuals to an apparent state of fitness for their release in suitable natural habitats. Morphometric measurements are crucial to managing captive wild animals for assessing their growth and well-being. Measurements are made using manual methods like vernier caliper that are prone to observer error experience and require handling the specimens for extended periods. Digital imaging technology is rapidly progressing at a fast pace and with the advancement of technology. We acquired images of turtles using smartphones along with manual morphometric measurements using vernier calipers of the straight carapace length and straight carapace width. The images were subsequently processed using ImageJ, a freeware and compared with manual morphometric measurements. A significant decrease in the time spent in carrying out morphometric measurements was observed in our study. The difference in error in measurements was, however, not significant. A probable cause for this may have been the extensive experience of the personnel carrying out the measurements using vernier caliper. Digital image processing technology can cause a significant reduction in the stress of the animals exposed to handling during measurements, thereby improving their welfare. Additionally, this can be used in the field to carry out morphometric measurements of free-ranging individuals, where it is often difficult to capture individuals, and challenges are faced in obtaining permission to capture specimens.

FTDO-based adaptive fuzzy fixed-time tracking control for uncertain unmanned helicopter with output constraints

During the actual flight of unmanned helicopters, there are widespread output constraints, system uncertainties and external disturbances, which bring significant threats to their safe flight. To keep the output constraints from violating predefined boundaries, the barrier Lyapunov function (BLF) is utilized in this paper. The system uncertainties are estimated by the fuzzy logic system (FLS). The compound disturbances composed of the external disturbances and the approximation errors caused by FLS are approximated by the fixed-time disturbance observers (FTDOs). According to the analysis of FTDOs and fixed-time stability theory, the observer errors and state errors converge to a region of the origin in fixed-time, and the appropriate parameters of FTDOs and controller are designed to ensure that the disturbance convergence time is faster than the one of the proposed controller, which further improves the stability of the system. Moreover, the convergence time of the FTDOs FTDOs and the proposed approach only depends on the design parameters under any initial conditions with constrained outputs. The performance of the proposed control approach is verified through the simulation results.

Trajectory Tracking Control of Human Support Robots via Adaptive Sliding-Mode Approach.

In this article, the tracking problem of the adaptive sliding-mode control (SMC) design for human support robots based on a disturbance observer is investigated. First, a finite-time controller using nonsingular fast terminal SMC is proposed. Then, a robust disturbance observer is developed to estimate system uncertainties and disturbances. Simultaneously, to deal with the unknown bounded disturbance observer error, an adaptive control technology is developed. Furthermore, the proposed controller is synthesized to ensure that the tracking errors can be stabilized in finite time. Finally, simulations are performed to demonstrate that human support robots employing the proposed controller can converge to the desired trajectory.

Output Feedback for Nonlinear Systems With Nonlinear and Discontinuous Inputs

The paper aims to design a high-gain observer for nonlinear systems with nonlinear and discontinuous sensor signal. The ultimate boundedness and exponential stability of the estimation error of high-gain observer are presented. The performance recovery property of output feedback control using high-gain observer is demonstrated. Simulation examples are illustrated to validate the proposed results of this paper.