Tracking Problem Research Articles

Adaptive neural network iterative learning control of long-stroke hybrid robots with initial errors and full state constraints

Research on initial errors and constraint restrictions is one of the main research directions in the field of control of uncertain robotic systems. An adaptive iterative learning control (AILC) method based on radial basis function (RBF) neural network is proposed to address the trajectory tracking problem of the long-stroke hybrid robot system with random initial errors and full state constraints. The RBF neural network is used to approximate the unknown nonlinear terms, and the network weights are updated using an iterative learning law that incorporates a projection mechanism. Additionally, a robust learning strategy is used to compensate for both the approximation error of the neural network and the external disturbances that vary with each iteration. To relax the requirement of traditional iterative learning control (ILC) for identical initial condition, an equivalent error function is constructed based on the time-varying boundary layer. The tangent-type barrier Lyapunov function (BLF) is designed to ensure that the joint position and speed of the robot system are bounded within a predetermined range. Through stability analysis based on barrier composite energy function (BCEF), it can be proved that the boundedness of all signals in the closed-loop system and the tracking error of the robot system will converge to an adjustable residual set asymptotically. Finally, through simulation experiments conducted on the MATLAB platform, the results demonstrate that the method overcomes the random initial errors of the system effectively, ensures that the system satisfies the full-state constraints, and realizes high-precision trajectory tracking.

Quadratic Tracking Control of Linear Stochastic Systems with Unknown Dynamics Using Average Off-Policy Q-Learning Method

This article investigates the optimal tracking control problem for data-based stochastic discrete-time linear systems. An average off-policy Q-learning algorithm is proposed to solve the optimal control problem with random disturbances. Compared with the existing off-policy reinforcement learning (RL) algorithm, the proposed average off-policy Q-learning algorithm avoids the assumption of an initial stability control. First, a pole placement strategy is used to design an initial stable control for systems with unknown dynamics. Second, the initial stable control is used to design a data-based average off-policy Q-learning algorithm. Then, this algorithm is used to solve the stochastic linear quadratic tracking (LQT) problem, and a convergence proof of the algorithm is provided. Finally, numerical examples show that this algorithm outperforms other algorithms in a simulation.

Searching for a Cheap Robust Steering Controller

The study of lateral steering control for Automated Driving Systems identifies new control solutions more often than new control problems. This is likely due to the maturity of the field. To prevent repeating efforts toward solving already-solved problems, what is needed is a cohesive way of evaluating all developed controllers under a wide variety of environmental conditions. This work serves as a step in this direction. Four controllers are tested on five maneuvers representing highways and collision avoidance trajectories. Each controller and maneuver combination is repeated on five sets of environmental conditions or Operational Design Domains (ODDs). The design of these ODDs ensures the translation of these experimental results to real-world applications. The commercial software, CarSim 2020, is extended with Simulink models of the environment, sensor dynamics, and state estimation performances to perform highly repeatable and realistic evaluations of each controller. The results of this work demonstrate that most of the combinations of maneuvers and ODDs have existing cheap controllers that achieve satisfactorily safe performance. Therefore, this field’s research efforts should be directed toward finding new control problems in lateral path tracking rather than proposing new controllers for ODDs that are already solved.

A group target track‐before‐detect approach using two‐stage strategy with maximum‐likelihood probabilistic data association

AbstractIn tracking scenarios involving groups with dense targets, achieving effective data association is challenging due to mutual occlusion and interference among targets. The complexity of the tracking problem is further exacerbated in low‐observable environments by the increase in false alarm rates. The track‐before‐detect (TBD) is an advanced technology for detecting and tracking low‐observable targets, effectively mitigating data association problems by integrating multi‐frame echo data. However, the existing multi‐target TBD algorithms typically assume that the targets are spatially separated and are not suitable for scenarios involving group targets. A group target maximum‐likelihood probabilistic data association (GT‐ML‐PDA) algorithm, based on the concept of TBD, is proposed to track group targets effectively in low‐observable environments. The proposed algorithm divides group target tracking into two stages: group centre trajectory estimation and individual target trajectory estimation. To enhance the performance of the proposed algorithm, two strategies are suggested: modifying the equivalent measurements and extracting independent measurement sets for individual targets. Simulation results demonstrate that the proposed algorithm is capable of effectively tracking numerous individual targets within a group, even in the presence of heavy clutter.

Formation tracking control with disturbance rejection in leader-follower multi-agent systems under dynamic event-triggered mechanism

This paper investigates the problem of time-varying formation tracking (TVFT) in a linear multi-agent systems (MASs) with external disturbance in a type of directed network topology, and proposes a formation control strategy in a leader-follower control framework with disturbance rejection under a dynamic event-triggering mechanism (DETM). Firstly, in order to improve the overall performance of the system, an extended state observer is used to estimate the status of the follower and the presence of external disturbance in real time. Secondly, a DETM is designed to avoid continuous communication between adjacent intelligent agents. And the formation tracking error between adjacent multi-agents is used to formulate a distributed TVFT control strategy. Furthermore, a compensation function is designed to actively offset the impact of time-varying disturbances on system. A Lyapunov function is then established for stability analysis, verifying the absence of Zeno behavior with this DETM. Finally, a comparative numerical simulation was conducted using an unmanned aerial vehicle (UAV) cluster case to verify that the proposed method can save communication resources to a greater extent and has good control performance.

Adaptive neural network‐based practical fixed‐time consensus tracking for second‐order nonlinear multi‐agent systems with switching topologies

AbstractThe current study concerns the practical fixed‐time consensus tracking problem of second‐order nonlinear multi‐agent systems (MASs) with switching topologies. The neural network (NN) and adaptive technique are adopted to compensate the unknown nonlinearities of the followers. Then, an adaptive NN‐based fixed‐time controller is designed under switching interaction topologies. In order to give the rigorous proof of the practical fixed‐time consensus tracking, a novel lemma for analyzing the practical fixed‐time stability of the switched error system is firstly established, then by constructing appropriate topology‐dependent multiple Lyapunov functions, we theoretically show that the practical fixed‐time consensus tracking of the closed‐loop MASs can be ensured provided that the dwell time of the switching topologies is larger than a predefined threshold and further the involved control parameters are suitably selected. Moreover, the settling time estimation is explicitly given, which is regardless of the system's initial values. The theoretical results are finally verified via a numerical simulation.

Quantised adaptive consensus control of heterogeneous nonlinear multi-agent systems under external disturbance

This paper is primarily devoted to the distributed consensus tracking control for heterogeneous nonlinear multi-agent systems (MASs) with a directed communication topology. Taking the considered heterogeneous nonlinear MASs own unknown nonlinear term and quantised input signals, the adaptive radial basis function neural networks (RBFNNs)-based approximator is utilised to tackle these interesting challenges. Next, considering the boundness of disturbances, the upper bound of time-varying disturbance is utilised in the controller design. Then, a distributed dynamic compensator is developed to complete coordination task, which only requires to exchange output information via the communication network. In addition, the compensator transforms the adaptive output consensus problem into asymptotic tracking problem, without needing extra stability conditions. Finally, by means of the Lyapunov stability theory, the satisfying result of the consensus error converging to zero asymptotically can be obtained. Through simulations, the effectiveness of the developed protocol is illustrated.

Examining the performance of Laguerre-based and nonlinear predictive control models for wheeled mobile robots when facing obstacles

This focuses on the problem of controlling the formation of a team of rotating robots that are not homonomic and are not able to interact in a barrier environment. The virtual structure formation control strategy is obtained here to calculate each path of the robot separately while the reference path of the virtual center of the formation is generated by artificial potential fields. In this presentation, we will introduce a new control algorithm that utilizes Model predictive control and nonlinear system dynamics. Three traditional model prediction control controllers (MPC): logger-based MPC, nonlinear MPC, and traditional MPC are used to apply the control algorithm for the nonlinear system. Model predictive control is used to calculate the torques required to track the path by using the dynamic model of the Rotary moving robot. A proposed control rule is the most effective approach to solving the formation and tracking problems. Model Predictive Control will be introduced through the introduction of basic ideas and terms. Traditional MPC, logger-based MPC, and non-linear MPC are among the three MPC methods to be offered. The discrete time display of the power plant under control is taken into account by developing MPC methods for linear or nonlinear systems for practical implementation. The model predictor controller optimizes a cost function to calculate an optimal control sequence at any sampling point. While ignoring the rest, the system only achieves the first control action of this sequence. During subsequent sampling, the optimization problem is resolvable with the use of updated process measurements and a different horizon. The cost function formula is determined by the controller’s purpose. An error function often plays a role in determining the objective by revealing the difference between the desired and actual response. The shape of the formation can be preserved by the law of control by utilizing information from other robots, which can be assured through a new cost function. In the current conditions of disruption, the proposed controllers can also achieve the goal of tracking the path and maintaining formation, according to the results.

A unified controller of global trajectory tracking and posture regulation for a car‐like mobile robot

SummaryThis work proposes a smooth time‐varying controller for trajectory tracking and posture regulation problems of car‐like mobile robots (CLMR). Currently, few studies focus on the control problems of CLMR's kinematic model. Global trajectory tracking or global posture stabilization controller for CLMR has not yet been proposed. In this study, we propose a global trajectory tracking controller for CLMR for the first time. By setting a specific reference trajectory, the controller is generalized to the posture stabilization task. Obstacle avoidance is also taken into consideration in posture stabilization task. Unlike the prototypical method of transforming the model into a nonholonomic chained‐form system, the proposed method is designed based on the original tracking error equation. Therefore our approach does not have singularities and has a global attraction region. Furthermore, the global convergence of the proposed controllers is strictly proved using the proof by contradiction and Barbalat's lemma. Finally, simulated and actual experiments on a car‐like robot demonstrate the effectiveness of the proposed control scheme.

Target Tracking Systems on a Sphere With Topographic Information.

We consider the target tracking problem on a sphere with topographic structure. For a given moving target on the unit sphere, we suggest a double-integrator autonomous system of multiple agents that track the given target under the topographic influence. Through this dynamic system, we can obtain a control design for target tracking on the sphere and the adapted topographic data provides an efficient agent trajectory. The topographic information, described as a form of friction in the double-integrator system, affects the velocity and acceleration of the target and agents. The target information required by the tracking agents consists of position, velocity, and acceleration. We can obtain practical rendezvous results when agents utilize only target position and velocity information. If the acceleration data of the target is accessible, we can get the complete rendezvous result using an additional control term in the form of the Coriolis force. We provide mathematically rigorous proofs for these results and present numerical experiments that can be visually confirmed.

Evolution-guided value iteration for optimal tracking control

In this article, an evolution-guided value iteration (EGVI) algorithm is established to address optimal tracking problems for nonlinear nonaffine systems. Conventional adaptive dynamic programming algorithms rely on gradient information to improve the policy, which adheres to the first order necessity condition. Nonetheless, these methods encounter limitations when gradient information is intricate or system dynamics lack differentiability. In response to this challenge, evolutionary computation is leveraged by EGVI to search for the optimal policy without requiring an action network. The competition within the policy population serves as the driving force for policy improvement. Therefore, EGVI can effectively handle complex and non-differentiable systems. Additionally, this innovative method has the potential to enhance exploration efficiency and bolster the robustness of algorithms due to its population-based characteristics. Furthermore, the convergence of the algorithm and the stability of the policy are investigated based on the EGVI framework. Finally, the effectiveness of the established method is comprehensively demonstrated through two simulation experiments.

Closed-Loop Subspace Predictive Control of Gyroscope

Control moment gyroscope (CMG) is used in many applications, especially related to spacecraft navigation. Hence, the trajectory tracking problem of the CMG control is important and worth researching. To address this problem, a closed-loop subspace predictive control (CSPC) of the gyroscope is presented in this paper. The proposed control technique constructs an auxiliary variable based on the known controller information. The constructed auxiliary variable assists to handle the inherent correlation between control inputs and noises in the closed-loop system. Additionally, an unbiased prediction of the system output is obtained to calculate the optimal control input. The theoretical analysis of the recursive feasibility and stability of the proposed control technique is also provided. Ultimately, the effectiveness of the proposed control technique is verified on a real-time experimental platform of the CMG. The experimental results demonstrate the improved trajectory tracking and predictive performance of the proposed control technique. Overall, this paper provides a solution for the trajectory tracking problem of the CMG control.

Adaptive iterative learning control of soft robot for beating heart tracking

Purpose Soft robots are known for their excellent safe interaction ability and promising in surgical applications for their lower risks of damaging the surrounding organs when operating than their rigid counterparts. To explore the potential of soft robots in cardiac surgery, this paper aims to propose an adaptive iterative learning controller for tracking the irregular motion of the beating heart. Design/methodology/approach In continuous beating heart surgery, providing a relatively stable operating environment for the operator is crucial. It is highly necessary to use position-tracking technology to keep the target and the surgical manipulator as static as possible. To address the position tracking and control challenges associated with dynamic targets, with a focus on tracking the motion of the heart, control design work has been carried out. Considering the lag error introduced by the material properties of the soft surgical robotic arm and system delays, a controller design incorporating iterative learning control with parameter estimation was used for position control. The stability of the controller was analyzed and proven through the construction of a Lyapunov function, taking into account the unique characteristics of the soft robotic system. Findings The tracking performance of both the proportional-derivative (PD) position controller and the adaptive iterative learning controller are conducted on the simulated heart platform. The results of these two methods are compared and analyzed. The designed adaptive iterative learning control algorithm for position control at the end effector of the soft robotic system has demonstrated improved control precision and stability compared with traditional PD controllers. It exhibits effective compensation for periodic lag caused by system delays and material characteristics. Originality/value Tracking the beating heart, which undergoes quasi-periodic and complex motion with varying accelerations, poses a significant challenge even for rigid mechanical arms that can be precisely controlled and makes tracking targets located at the surface of the heart with the soft robot fraught with considerable difficulties. This paper originally proposes an adaptive interactive learning control algorithm to cope with the dynamic object tracking problem. The algorithm has theoretically proved its convergence and experimentally validated its performance at the cable-driven soft robot test bed.

Fault-tolerant control for satellite autonomous rendezvous with quality characteristics and actuator uncertainties

An autonomous fault detection and fault-tolerant control solution combining Model Predictive Control (MPC) and Label Distributed Learning (LDL) is developed for the position tracking and attitude synchronization problems in autonomous satellite rendezvous and docking. The proposed algorithm can deal with center of mass (CM) variations and time-varying mass characteristics due to satellite fuel consumption, actuator saturation and fault, and external disturbances. Firstly, a six-degree-of-freedom (6-DOF) satellite translation-rotation coupling model was established to express the relative motion between the satellite and the target, taking the above factors into account. Subsequently, an on-board autonomous closed-loop fault-tolerant control algorithm using MPC is proposed, in which an LDL-based fault detection mechanism is embedded. The scheme specifies that propulsion faults are estimated by calculating the difference between the MPC's prediction of the satellite's future state and the measured change in the actual state. And the mapping matrix between the commanded force/torque and the actual force of the propulsion system is updated in real time to achieve autonomous fault detection and compensation on board the satellite. Among them, the LDL-based fault detection scheme is trained offline. It requires only simple matrix operations for on-orbit use, which is low-cost and suitable for resource-limited space environments. The additional creation of a time-varying disturbance observer allows the estimation and compensation of unmodelled errors and external disturbances. The stability of the proposed fault-tolerant control algorithm is rigorously demonstrated using Lyapunov analysis. Finally, numerical simulations show that the proposed method can successfully achieve autonomous satellite docking under different combinations of thruster faults.

An Adaptive Tracking Method for Moving Target in Fluctuating Reverberation Environment

In environments with a low signal-to-reverberation ratio (SRR) characterized by fluctuations in clutter number and distribution, particle filter-based tracking methods may experience significant fluctuations in the posterior probability of existence. This can lead to interruptions or even loss of the target trajectory. To address this issue, an adaptive PF-based tracking method (APF) with joint reverberation suppression is proposed. This method establishes the state space model under the Bayesian framework and implements it through particle filtering. To keep the weak target echoes, all the non-zero entries contained in the sparse matrix processed by the low-rank and sparsity decomposition (LRSD) are treated as the measurements. The prominent feature of this approach is introducing an adaptive measurement likelihood ratio (AMLR) into the posterior update step, which solves the problem of unstable tracking due to the strong fluctuation in the number of point measurements per frame. The proposed method is verified by four shallow water experimental datasets obtained by an active sonar with a uniform horizontal linear array. The results demonstrate that the tracking frame success ratio of the proposed method improved by over 14% compared with the conventional PF tracking method.

Robust tracking and model following of uncertain nonlinear systems with some uncertainties and dead-zone inputs

The problem of robust tracking and model following is reconsidered for a class of uncertain nonlinear systems with some uncertainties and dead-zone input constraints. In this paper, the system uncertainties are regarded as some nonlinear functions which are not required to must satisfy the matching conditions. That is, being different from traditional robust control theory, the matched structures of uncertainties are sufficient, but not necessary, for being able always to design some types of robust tracking control schemes. In addition, the external disturbances of dynamical systems are assumed to be any bounded functions which is not also required to satisfy the matching condition. By making use of the integral inequality, instead of Lyapunov function, a class of robust tracking control schemes is constructed to guarantee the uniform exponential boundedness of the model tracking errors. Moreover, the upper bounds of nonlinear uncertainties are not required to be known, and it is also unnecessary to know or estimate the characteristic parameters of dead-zone functions. Therefore, the resulting robust tracking control schemes have a simple structure. Actually, the resulting robust tracking control scheme is a linear feedback control one with a self-tuning control gain. Finally, an illustrative numerical example is provided to demonstrate the validity of the presented theoretical results.

Global adaptive practical tracking control for high‐order uncertain nonstrict feedback nonlinear systems with unknown control coefficients

SummaryIn this article, the problem of global adaptive practical tracking for high‐order uncertain nonstrict feedback nonlinear systems with unknown control coefficients is studied. To avoid the algebraic loop problem associated with the nonstrict feedback condition and guarantee the controllability of the tracking error, a novel dual dynamic gain scaling method is introduced to compensate nonlinearities and the tracking error simultaneously. Besides, by incorporating the sign functions into the design of adding a power integrator, a general approach for the handing of unknown control coefficients and the direction design of the controller is developed. The presented control scheme can ensure that all system states are globally bounded without constraints on state variables while the reference signal is tracked with expected precision. Three simulation examples, including a practical application, are provided to illustrate the validity of the control scheme.

Adaptive neural network control of robotic manipulators with input constraints and without velocity measurements

AbstractThis paper addresses the trajectory tracking problem for a class of uncertain manipulator systems under the effect of external disturbances. The main challenges lie in the input constraints and the lack of measurements of joint velocities. An extend‐state‐observer is utilized to estimate the velocity signals; then, a neural‐network‐based adaptive controller is proposed to solve the problem, where a term based on the nominal model is included to enhance the tracking ability, and the effect of uncertainties and disturbances are compensated by a neural‐network term. Compared with the existing methods, the main distinctive features of the presented approach are: (i) The control law is guaranteed to be bounded by design, instead of directly bounded by a saturation function. (ii) The trade‐off between the performance and robustness of the presented controller can be easily tuned by a parameter that depends on the size of model uncertainties and external disturbances. By virtue of the Lyapunov theorem, the convergence properties of the proposed controller are rigorously proved. The performance of the controller is validated via both simulations and experiments conducted on a two‐degree‐of‐freedom robot manipulator.

Nonlinear disturbance observer-based geometric attitude fault-tolerant control of quadrotors

This paper is concerned with nonlinear disturbance observer (DO)-based geometric attitude fault-tolerant control (FTC) problem of quadrotor unmanned aerial vehicles (UAVs) subject to system uncertainties, exogenous disturbances, and actuator faults. A disturbance observer-based control (DOBC) framework is devised to tackle the difficulties caused by system uncertainties and external disturbances. The FTC is proposed to cope with the occurrence of actuator faults which can be modelled as a constant loss of effectiveness. The proposed design scheme can provide an effective way to analyse the stability of the closed-loop system, which can ensure the asymptotical convergence of the error. The other method considers actuator failures as part of the lumped disturbance, and the attitude tracking problem of quadrotors concerning the lumped disturbance is solved by the DO-based control method, which can ensure the exponential convergence of the error. The numerical simulations are performed to illustrate the effectiveness of the design techniques.

Quadrotor UAV Trajectory Tracking Control Based on Adaptive Non-singular Terminal Sliding Mode

To address the issue of the quadrotor unmanned aerial vehicle (UAV) being susceptible to external disturbances and model uncertainties during flight, an adaptive non-singular terminal sliding mode controller with disturbance compensation is proposed. Firstly, the quadrotor UAV dynamic model considering system disturbances is constructed using the Newton-Euler method. Next, the trajectory tracking problem is transformed into a command tracking control problem for each channel. To enhance the adaptability and robustness of trajectory tracking for the quadrotor UAV, an adaptive law is designed to dynamically adjust the sliding mode surface gain. In addition, a disturbance observer is introduced to estimate and compensate for external disturbances and model uncertainties. Finally, the stability of the designed controller is proven through the Lyapunov function. Simulation results demonstrate that the proposed controller effectively enhances the disturbance resistance and trajectory tracking response speed of the quadrotor UAV.