Closed-loop Error Research Articles

Resilient cooperative platoon control for leader-following uncertain vehicular systems subject to cyber-physical attacks

This paper develops a resilient cooperative platoon control protocol for vehicle following systems under unreliable switching communication networks with cyber composite attacks, which includes actuator and sensors attacks, as well as denial of service (DoS) attacks. In this framework, to achieve leader-following platoon task, a novel resilient distributed adaptive control algorithm is designed by exploiting relative neighborhood information. First, a switching resilient turning mechanism with controller parameter updating laws is introduced into platoon controller architecture, which can compensate sensor and actuator attacks. Second, a topology-dependent analysis shows that cooperative leader-following platoon objective is achieved under some sufficient conditions, then the robust stability of the closed-loop coordination tracking error system is built. Finally, the simulation studies on a platoon of autonomous vehicles are provided to testify the design.

Bearing-driven approach for unknown target tracking by multi-unit uncertain underactuated marine autonomous surface vehicles

In this study, we successfully address the formation tracking challenge for underactuated autonomous surface vehicles (ASVs) in uncertain environments, despite the lack of direct target information. Leveraging only relative angle measurements, we develop a control scheme that ensures the closed-loop error trajectory remains globally uniformly ultimately bounded. The bound achieved is influenced by the precision of the dynamic controllers and the effectiveness of the adaptive mechanism, highlighting the robustness and adaptability of our approach. This work provides a practical solution for ASV formation tracking in real-world scenarios.

Barrier Lyapunov Function-based Backstepping Controller Design for Path Tracking of Autonomous Vehicles

This research proposes a novel BLF-based backstepping controller for path tracking of Autonomous Vehicles (AVs) with unknown dynamics and unmeasurable states. The proposed framework includes: (1) forming geometric-dynamic model of the vehicle by combining the dynamics of the vehicle with the kinematics of the visual measurement system, (2) designing a fixed-time Extended-State Observer (ESO) to estimate the unknown dynamics and unmeasurable states, and (3) introducing a BLF-based controller for faster response and more accurate path tracking compared to previous BLF-based controllers. Besides the novelty of the BLF-based controller, by transforming the closed-loop error dynamics into a unified proportional-derivative (PD)-type structure, an intuitive criterion is proposed to provide a systematic procedure for comparing BLF-based controllers. A combined BLF is further proposed based on this performance criterion to eliminate the sensitivity of BLF-based controllers to the magnitude of the constraint. The stability analysis is performed for the fixed-time ESO and the closed-loop control system. MATLAB/CarSim co-simulation is conducted to evaluate the performance of the proposed control system. The outcomes of the work show that the closed-loop control system is exponentially stable. In addition, it can provide a faster response and result in more accurate path tracking compared to previous BLF-based control systems.

Design and performance evaluation of a novel parallel kinematic micromanipulator

The targeted placement of selected carbon nanotubes is associated with low throughput rates. Hence, this paper presents a novel stage design for the fully automatic assembly of carbon nanotube field-effect transistors (CNTFETs) via mechanical dry transfer. It constitutes the core module of an assembly machine for the precise deployment of nanotubes onto a prefabricated wafer. The mechanical dry transfer approach allows high level of carbon nanotube selectivity with the aim of enabling a high-volume fabrication of ultra-clean devices. The previous production rate of such ultra-clean devices is less than one per hour, which offers a high potential for improvement. The stage consists of a parallel kinematic mechanism (PKM) with 3 degrees of freedom (X2Y2C1) carrying two additional stacked axes (Z1C2). The PKM is suspended on a vacuum preloaded aerostatic bearing, voice coil motors (VCM) and flexure hinges. Together with a combination of high precision and resolution touch probe measurement systems close to its tool center point (TCP), high accuracy and low settling time can be achieved. Based on realistic manufacturing tolerances, a sensitivity analysis of the mechanism’s pseudo rigid body model (PRBM) suggests a theoretical closed-loop error below 0.15μm over the entire XY workspace of 20mm×2.8mm. Measurements of positioning motions show that the settling time can be decreased by the compensation of friction resistances inside the internal bearings of the VCMs.

Research on an Ice Tolerance Control Method for Large Aircraft Based on Adaptive Dynamic Inversion

Considering the effect of icing on aircraft control performance, this paper proposes an adaptive dynamic inverse ice tolerance control method based on piecewise constant. A control allocation algorithm is introduced to compensate for the change of control surface performance caused by icing. This method can achieve satisfactory disturbance estimation accuracy under a given sampling time, and thus ensure a closed-loop system error within an acceptable range. The proposed design method is applied to the design of a flight control law for a transport aircraft, aiming to solve the problem of ice-tolerant flight control, reduce the influence of icing conditions on controllability and safe flight of the transport aircraft, and thus improve the flight quality of the transport aircraft. The simulation results are verified under the influence of both standby ice type and failure ice type, and the interference effect on aircraft aerodynamic parameters is further added. The simulation results show that adaptive dynamic inverse control based on piecewise constant can overcome the influence caused by icing and aerodynamic parameter interference, achieve accurate tracking of command, and provide excellent fault tolerance and robustness, which ensures that the transport aircraft can achieve the desired control performance and safe flight capability.

Adaptive Formation Tracking Control of Multiple Vertical Takeoff and Landing UAVs With Bearing-Only Measurements.

This article studies the leader-following formation tracking control problem of multiple vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) subject to uncertain parameters, in which the target formation configuration is defined by using the interneighbors' bearing vectors. An adaptive formation control algorithm with bearing-only measurements is proposed under a hierarchical control framework. More specifically, a saturated adaptive distributed control force is developed in the position loop with bearing-only measurements. Since the bearing vectors with respect to the neighbors can be directly measured by low-cost onboard cameras, the proposed formation algorithm can be implemented without interagent communication. Subsequently, in the attitude loop, an adaptive hybrid control scheme via two modified Rodrigues parameters (MRPs) sets is proposed, which achieves the command attitude tracking globally and also avoids the unwinding problem of MRPs. Based on the Lyapunov stability analysis and hybrid theory, we prove that the overall closed-loop error system is globally asymptotically stable. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed control algorithm.

Coding–decoding-based synchronization of Markov jump neural networks with PDT switched topologies

This paper investigates the observer-based synchronization control issue for a class of discrete-time switched neural networks under the constraint that information exchange between the observer and controller is subject to coding–decoding communication protocol. The variation of network parameters is governed by a Markov chain while a set of pre-known persistent dwell-time switching sequence is introduced to describe the variation of communication topologies among neurons. To ensure the efficient and secure of information transmission, data received from the observer is encoded into a particular set of codewords before sending to the communication channel. Then, these codewords are transformed into corresponding decoded form via the designed decoder after transmission. The main attention is focused on devising a feasible coding–decoding procedure such that the coding–decoding-based controller can be established efficiently. By constructing suitable Lyapunov function that can reveal the variation characteristic of the network parameters and topologies properly, sufficient conditions which ensure the exponential mean-square boundedness of the closed-loop synchronization error systems are presented. Finally, the validity of the proposed control scheme is illustrated by a numerical example.

Neural Network-Based Distributed Consensus Tracking Control for Nonlinear Multi-Agent Systems with Mismatched and Matched Disturbances

In practice, disturbances, including model uncertainties and unknown external disturbances, are always widely present and have a significant impact on the cooperative control performance of a networked multi-agent system. In this work, the distributed consensus tracking control problem for a class of multi-agent systems subject to matched and mismatched uncertainties is addressed. In particular, the dynamics of the leader agent are modeled with uncertain terms, i.e., the leader’s higher-order information, such as velocity and acceleration, is unknown to all followers. To solve this problem, a robust consensus tracking control scheme that combines a neural network-based distributed observer, a barrier function-based disturbance observer, and a tracking controller based on the back-stepping method was developed in this study. Firstly, a neural network-based distributed observer is designed, which is able to achieve effective estimation of leader information by all followers. Secondly, a tracking controller was designed utilizing the back-stepping technique, and the boundedness of the closed-loop error system was proved using the Lyapunov-like theorem, which enables the followers to effectively track the leader’s trajectory. Meanwhile, a barrier function-based disturbance observer is proposed, which achieves the effective estimation of matched and mismatched uncertainties of followers. Finally, the effectiveness of the robust consensus tracking control method designed in this study was verified through numerical simulations.

Multiple Discrete Adaptive Filter Based Position Error Reduction for Sensorless IPMSM Drives

The inverter nonlinearity and the flux spatial harmonics will lead to noticeable (6κ±1) harmonics in the observed back electromotive force (EMF), causing (6κ) pulsations in the rotor position estimation error and deteriorating the performance of sensorless interior permanent magnet synchronous motor (IPMSM) drives. To improve the sensorless IPMSM control accuracy, a multiple discrete adaptive filter (MDAF) embedded between sliding mode observer (SMO) and normalized quadrature phase-locked loop (PLL) is adopted to solve the above problem in this paper. The MDAF consists of a fundamental extraction block and a harmonic cancellation block. Harmonic cancellation works similarly to fundamental extraction, simply by removing the dominant 5th and 7th harmonics from the distorted back-EMF in a frequency multiplicative manner. The proposed algorithm is designed directly in the discrete domain, avoiding the complex discretization process. The open-loop amplitude-frequency characteristic curves show that the method is able to achieve infinite gain exactly at the expected frequency, thus allowing closed-loop zero steady-state error tracking of the back-EMF and providing higher precision for harmonic estimation. The excellent performance of the suggested method is validated based on a 1.5kW sensorless IPMSM control system.

Observer-based finite-time H∞ control for discrete-time singular Markovian jump systems with asynchronous modes

The asynchronous observer-based finite-time [Formula: see text] control problem for discrete-time singular Markovian jump systems with time-varying delays is studied, where the asynchronism of the controller and observer with respect to the original system is fully taken into consideration. By the use of finite-time analysis theory and the construction of suitable Lyapunov-Krasovskii functionals, sufficient conditions to determine the closed-loop error system is singular stochastic finite-time boundedness are given with [Formula: see text] performance level. Then, by applying linear matrix inequalities, the desired observer parameters and controller parameters can be computed. Finally, the effectiveness of our proposed method is confirmed by simulation.

Asynchronous sampled-data control for connected vehicles with heterogeneous delays

This study investigates an asynchronous sampled-data control problem of vehicular platoons, with heterogeneous sampling, subjected to actuator delays. Without a synchronized clock, a completely asynchronous sampled-data controller is designed for each follower, where the state of the ith follower itself and its neighboring vehicles are sampled at their own sampling time instants. The caused closed-loop tracking error dynamics for the entire platoon considering the effect of the nonuniform sampling time intervals, heterogeneous vehicle dynamics, inter-vehicle topology and heterogeneous time delays. To simplify the stability analysis and controller design, the tracking-error dynamics of the entire platoon are decomposed into individual subsystems with reduced-order dynamics. Based on Lyapunov stability theory, the optimal conditions are explored to design an asynchronous sampled-data controller to guarantee the desired stability performance. Moreover, the exact values for the maximum allowable sampling interval and time delay are calculated for each follower using the designed feedback controller gain. The proposed asynchronous sampled-data control method is extended to a vehicular platoon using an event-based sampling scheme. Numerical examples are used to verify the effectiveness of the proposed sampled-data control method.

Sampled-Data-Based Distributed Output Feedback Leader–Following Consensus for Time-Delay Multiagent Systems

This paper addresses the distributed output feedback leader-following consensus problem for high-order nonlinear multiagent systems (MASs) with time delays and disturbances under the directed network. Using sampled relative outputs to neighbors and the discrete control input, the continuous-discrete time compensator is constructed in each agent to compensate for the consensus errors, where the sampling time instants can be asynchronous and aperiodic without exceeding an explicit upper bound of sampling intervals. Based on the compensator, we propose a co-design algorithm for constructing the dynamic event-triggered protocol with a corresponding event-triggering mechanism which is a combination of discrete-time control input, continuous dynamic variables of each agent's own compensator, and a given threshold. The proposed methods can not only achieve consensus tracking under the effects of time delays in states and communications but also implement the discrete-time execution of measurement, communication, and control. Based on the novel lemmas, it is proved that the resulting closed-loop consensus error system is globally stable. Finally, a simulation is given to illustrate the effectiveness of proposed methods.

An experimental study of the sensorized strain wave gear RT1-T and its capabilities for torque control in robotic joints.

The idea of sensorizing a strain wave gear to measure the transmitted torque has been reported since the 1980s. The strain in the elastic flex spline is typically measured by strain gages attached to it. The resulting voltages relate to the transmitted torque in the gear. However, periodic inaccuracies in the measured torque signal (sensing ripple), resulting from positioning inaccuracies of strain gages on the flex spline, prevented this technology from being used outside a lab environment. Regardless of these difficulties, measuring the torque directly in the strain wave gear would bring many advantages, especially in robotic applications, where design space is highly limited. Traditionally, robotic joints are equipped with link-sided torque sensors, which reduce the available design volume, lower the joint stiffness, and require complex cable routing. This paper presents an experimental study of a novel sensorized strain wave gear named RT1-T, which was developed by Schaeffler Technologies. The study was implemented on a joint testbed, including a high-resolution reference torque sensor at the link side. In addition to the measurement accuracy and linearity, a torque ripple analysis is performed. The joint torque control capabilities are determined along dynamic trajectories and compared to the performance achieved with a link-sided reference sensor. The sensor employed in the testbed has a static torque error of 0.42 Nm and an average closed-loop torque control error of 0.65 Nm above the reference sensor.

Multi-stage trajectory tracking of robot manipulators under stochastic environments

For robot manipulators composed of Lagrange subsystems driven by direct current (DC) motors under stochastic environments, multi-stage trajectory tracking is investigated in this paper. The main challenge is how to achieve the end-effector drive of manipulators from a given initial state to a final state. First, the inverse kinematics method and the partition of the task space are adopted to tackle multi-stage trajectory planning. Second, the adaptive backstepping technique is used to design tracking controller for stochastic Lagrangian subsystems. Then, based on the state-dependent switching signal, a multi-stage switched controller is designed for trajectory tracking of robot manipulators. All signals in the close-loop error switched system are bounded in probability, and the tracking error in mean square can be made arbitrarily small enough by parameters-tuning The effectiveness of the proposed control method is illustrated by simulation results.

A High-Precision Planar NURBS Interpolation System Based on Segmentation Method for Industrial Robot

NURBS curve parameter interpolation is extensively employed in precision trajectory tasks for industrial robots due to its smoother performance compared to traditional linear or circular interpolation methods. The trajectory planning systems for industrial robots necessitate four essential functional modules: first, the spline curve discretization technique ensuring chord error compliance; second, the contour scanning technique for determining the maximum feasible feed rate for multi-constraint and multi-segment paths; third, the technique for achieving a smooth feed rate profile; and fourth, the continuous curve parameter interpolation technique. Therefore, this paper proposes a high-precision planar NURBS interpolation system for industrial robots. Firstly, a segmentation method for NURBS curves based on a closed-loop chord error constraint is proposed, which segments the original global NURBS curve into a collection of Bezier curves that strictly meet the chord error constraint. Secondly, a bidirectional scanning technique is presented to meet the joint space constraint, establishing an analytical mapping between the tool tip kinematic constraint and the joint kinematic constraint. Then, based on the traditional S-shaped feed rate profile, an adaptive algorithm with a displacement constraint is introduced, considering the real-time speed adjustment requirements of robots. Finally, a compensation interpolation strategy based on arc length parameterization is adopted to solve the accumulated error problem in parameter interpolation. The effectiveness of and potential for enhancing the quality of planar machining of the proposed planar NURBS interpolation system for industrial robots are validated through simulations and experiments. The results demonstrate the system’s applicability and accuracy, and its ability to improve planar machining quality.

Error compensation of a 2TPR&2TPS parallel mechanism based on particle swarm optimization

This paper solves the problem of the precise compensation of the pose error of a 2TPR&2TPS parallel mechanism. First, the inverse solution of the mechanism is solved, the error source of the mechanism is analyzed, and a closed-loop vector method error model based on the inverse solution is established. Then, the ball screw commutation gap is measured with a high-precision grating ruler, and a laser tracker is used to measure the comprehensive position error of the mechanism under the set trajectory (circle). Finally, an error compensation algorithm based on the particle swarm algorithm is constructed, the measured trajectory data are substituted into the compensation algorithm, the position accuracy of the mechanism is significantly improved, and the compensation effect is remarkable. The compensation algorithm has good versatility, is simple and feasible, and can be applied to the error compensation of various mechanisms.

Closed-Loop Output Error Approaches for Drone's Physics Informed Trajectory Inference

The design of adequate countermeasures against drone's threats needs accurate trajectory estimation to avoid economic damage to the aerospace industry and national infrastructure. As trajectory estimation algorithms need highly accurate physics informed models or off-line learning algorithms, radical innovation in on-line trajectory inference is required. In this paper, a novel drone's physics informed trajectory inference algorithm is proposed. The algorithm constructs a physic informed model and infers the drone's trajectories simultaneously using a closed-loop output error architecture. Two different approaches are proposed based on a physics structure and an admittance filtering model which considers: i) full states measurements and ii) partial states measurements. Stability and convergence of the proposed schemes are assessed using Lyapunov stability theory. Simulations studies are carried out to demonstrate the scope and high inference capabilities of the proposed approach.

Trajectory Tracking Control of a Mobile Robot using Neural Networks

This paper presents a novel soft computing-based machine learning technique designed to enhance the trajectory tracking capabilities of mobile robots through the application of neural networks. The goal of this approach is to enhance the accuracy and overall performance of trajectory tracking without the need for manual gain recalibration, which is a tedious and time-consuming task for the designer when setting up the robot. This improvement is achieved by creating a kinematic controller based on neural networks, which are constructed using the kinematic model of the robot. In the initial phase, the controller requires gains defined by the designer. Subsequently, during the application phase, the backpropagation algorithm is used to dynamically adjust the gains of the neural network, aiming to minimize the closed-loop error. One of the key innovations introduced by this controller is the potential for automatic online gain tuning, thereby eliminating the need for a pre-learning phase, typically required by traditional neural controllers. To validate the effectiveness of this approach, the results are systematically analyzed and compared against those obtained using a conventional kinematic controller. Performance metrics reveal the improved precision in trajectory tracking achieved by the controller, with reduced effort, highlighting the performance enhancements in different trajectories. Doi: 10.28991/ESJ-2023-07-06-01 Full Text: PDF

Robust nonlinear 3D control of an inverted pendulum balanced on a quadrotor

This paper addresses the nonlinear control problem of balancing an inverted pendulum on an underactuated unmanned aerial vehicle. In view of the system’s slow and quick transients, a convenient error transformation is employed to render the attitude subsystem less sensitive to translational errors. Linearizations are not involved, making this controller suitable beyond the limited scope of trim maneuvers. Furthermore, the controller features an adaptive bounded law that is used to compensate for unknown exogenous perturbations. The Lyapunov-based control design is rooted in an integral backstepping process, wherein the origin of the closed-loop total system error is shown to be almost globally asymptotically stable. Simulation results are presented to validate our strategy, and experimental results are also provided to demonstrate its accuracy and robustness.

A delay-dependent dissipativity and passivity-based synchronization analysis for Markovian jumping complex dynamical network models with distributed coupling delays

This paper studies the issue of delay-dependent dissipativity and passivity-based synchronization analysis for Markovian jumping complex dynamical network (MJCDN) models with distributed coupling delays. The state feedback control scheme is designed for the synchronization of the MJCDN closed-loop error model. By constraining the appropriate Lyapunov functional along with the properties of the Kronecker product and using integral inequality techniques,several new delay dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs), which ensure that the dissipativity and passivity performance of the considered MJCDN model. The results of this analysis are verified using the MATLAB LMI control toolbox. Illustrative examples are provided to demonstrate the feasibility of the results