Adaptive iterative learning control for upper limb rehabilitation robots considering unknown disturbance

As robots and other automated systems are introduced to unknown and dynamic environments, robust and adaptive control strategies are required to cope with disturbances, unmodeled dynamics and parametric uncertainties. In this paper, we propose and provide theoretical proofs of a combined L 1 adaptive feedback and iterative learning control (ILC) framework to improve trajectory tracking of a system subject to unknown and changing disturbances. The L 1 adaptive controller forces the system to behave in a repeatable, predefined way, even in the presence of unknown and changing disturbances; however, this does not imply that perfect trajectory tracking is achieved. ILC improves the tracking performance based on experience from previous executions. The performance of ILC is limited by the robustness and repeatability of the underlying system, which, in this approach, is handled by the L 1 adaptive controller. In particular, we are able to generalize learned trajectories across different system configurations because the L 1 adaptive controller handles the underlying changes in the system. We demonstrate the improved trajectory tracking performance and generalization capabilities of the combined method compared to pure ILC in experiments with a quadrotor subject to unknown, dynamic disturbances. This is the first work to show L 1 adaptive control combined with ILC in experiment.

SummaryRobust and adaptive control strategies are needed when robots or automated systems are introduced to unknown and dynamic environments where they are required to cope with disturbances, unmodeled dynamics, and parametric uncertainties. In this paper, we demonstrate the capabilities of a combined adaptive control and iterative learning control (ILC) framework to achieve high‐precision trajectory tracking in the presence of unknown and changing disturbances. The adaptive controller makes the system behave close to a reference model; however, it does not guarantee that perfect trajectory tracking is achieved, while ILC improves trajectory tracking performance based on previous iterations. The combined framework in this paper uses adaptive control as an underlying controller that achieves a robust and repeatable behavior, while the ILC acts as a high‐level adaptation scheme that mainly compensates for systematic tracking errors. We illustrate that this framework enables transfer learning between dynamically different systems, where learned experience of one system can be shown to be beneficial for another different system. Experimental results with two different quadrotors show the superior performance of the combined ‐ILC framework compared with approaches using ILC with an underlying proportional‐derivative controller or proportional‐integral‐derivative controller. Results highlight that our ‐ILC framework can achieve high‐precision trajectory tracking when unknown and changing disturbances are present and can achieve transfer of learned experience between dynamically different systems. Moreover, our approach is able to achieve precise trajectory tracking in the first attempt when the initial input is generated based on the reference model of the adaptive controller.

Iterative-learning-based tracking control of a two-wheeled mobile robot with model uncertainties and unknown periodic disturbances

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.

An adaptive iterative learning control approach based on disturbance estimation has been developed for trajectory tracking of manipulators with uncertain parameters and external disturbances. The external disturbances are estimated by the feedback iterative learning method, whereas the uncertain parameters are compensated by adaptive control. This approach which is based on the disturbance estimation technique provides a rapid convergence of trajectory tracking errors. According to the Lyapunov theory, the sufficient condition of the asymptotic stability has been developed for the 2-degrees of freedom (DOFs) manipulator system. The numerical results show that the adaptive iterative learning control approach based on disturbance estimation is feasible and effective for the 2-DOFs manipulator. A comparison of the adaptive iterative learning control method and the iterative learning control method is completed, which shows that the adaptive iterative learning control method performs a faster convergence of the disturbance to the steady state.

PurposeSoft 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/approachIn 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.FindingsThe 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/valueTracking 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.

Learning systems represent a particularly important class of practical data-driven systems that adapt to their environment based on the environment's response to the system's action. In some settings traditional robust and adaptive control techniques have been verified to be effective when plants are large scale and/or have very complex dynamics (e.g., industrial processes, power grid networks, and transportation systems). However, often in these plants the problems of parameter mismatch and unmodeled dynamics are encountered, and thus the techniques of robust or adaptive control methods in the framework of modern control may no longer be sufficient. As an alternative to robust or adaptive methods, various learning paradigms have been established, for example, reinforcement learning, deep learning, artificial neural networks, and iterative learning, among others. These learning paradigms construct controllers or control signals directly with the data collected and stored when the system operates, typically without the need of identifying system models. However, even such “model-independent” control systems must make assumptions about the system dynamics. One such common assumption is that the system dynamics are linear. Another is that they are time-invariant (autonomous). When the dynamics do not meet these assumptions, traditional learning paradigms may also fail. Despite the success of learning-based methods, finding suitable control frameworks for learning systems when there is uncertainty in the assumptions related to the system dynamics is still an open problem. The aim of this special issue is to collect recent research results that address issues involved in data-driven control methods and related algorithms for learning-based systems that operate under uncertainty. The special issue consists of fourteen papers covering several key areas of activity in which progress has been achieved. Many of the papers also include results of simulation or experimental tests of the presented control methods. Next we give a brief description of each of the fourteen papers. We have organized the papers thematically into four categories: (1) iterative learning control (ILC), (2) neural networks and machine learning, (3) identification and control, and (4) applications. The first five papers describe research on the control method of ILC, which is a process developed especially for applications where the same operation needs to be repeated over a limited period of time. In the first of these papers, Ding and Li give results on an adaptive ILC algorithm for nonlinear continuous nonparameterized systems. This adaptive ILC algorithm, which can adjust the adaptive parameters in both the iteration domain and the time domain, is proposed to track different reference trajectories repetitively over a finite time interval, and also to provide a unified adaptive control strategy for nonlinear continuous nonparameterized systems that have asymmetric control gain matrices for trajectory tracking in different domains. In the next paper, Chen and Chu address the fact that in multiagent collaborative tracking tasks, the system often encounters constraints in practice that cause challenging difficulties in the case of handling large-scale systems. They propose a novel constrained ILC design and further develop a decentralized implementation of the resulting ILC algorithm using the alternating direction method of multipliers, allowing the design to scale up to handle large-scale and varying system dynamics. The next three papers consider the special problem of ILC when there are quantization and intersample behavior effects. In the third paper, Ohnishi et al. develop a framework for a state-tracking ILC that mitigates the oscillatory intersample behavior that is often encountered in output-tracking ILC. The paper addresses stability in the iteration domain, introducing the idea of a robustness filter, designed in the frequency domain. The last two ILC papers both consider quantization effects. Zhang et al. simultaneously tackle the problems of predictive compensation, unknown nonlinearity, and nonaffine structure found in a quantized ILC analysis and design under a data-driven framework. Using the concept of a virtual iterative linear data model, the authors develop control laws that are completely data driven and model free. The established results are also generalized to a class of multi-input multi-output, nonlinear, nonaffine, discrete-time systems. Finally, Huo et al. investigate a quantized ILC method with an encoding–decoding mechanism for networked control systems subject to constrained transmission bandwidths and random data dropouts on both the measurement and the actuator side. Their approach is to utilize an intermittent update principle to develop a control algorithm that can demonstrate enhanced tracking performance. The next three papers use neural network and machine learning (ML) approaches to deal with uncertain systems. First, with the aid of neural networks, Xin et al. develop a neural network-based learning design for a class of high-order nonlinear systems involving full-state constraints in the form of output feedback control. Then, Chen et al. consider non-repetitive time-varying systems. They propose an ML-based nominal model updating mechanism that uses linear regression techniques to update the nominal model in each ILC trial, with only the current trial information, which improves the performance of the ILC. This paper provides information on how ML/ILC parameters can be tuned to achieve desired performance. The ideas are illustrated through experiments on a real gantry robot test platform. Another ML-based problem considers robust approximate optimal control of an air-breathing hypersonic vehicle in the paper by Han et al. The learning-based control framework can guarantee practical finite-time convergence of the tracking error, without chattering. Further, the proposed controller adopts a critic-only network design instead of an actor-critic structure, which simplifies the implementation procedure. The next three papers consider the issue of data-driven identification and control. With the aid of subspace methods and an average consensus algorithm, Cheng et al. develop a data-driven design for distributed fault detection of dynamic systems using measurements in a complex sensor network. Due to advantages such as high reliability and low communication loads, each sensor node has the ability to execute a fault detection scheme using the average consensus algorithm. The correctness and effectiveness of the proposed scheme are demonstrated in a three-phase flow facility. Next, Sun et al. describe a technique whereby a dynamic parameterization is employed to produce linear, time-varying, parameterized models that equivalently describe a general class of nonlinear systems. The parameters in these models can be identified using an iterative learning least squares technique. The third and final paper in this group, by Lan et al., presents a data-driven policy learning strategy. The authors show how to design controllers for automated vehicles based on vehicle-to-vehicle communications. The learned control policy can be implemented using a prescribed vehicle-to-vehicle communication topology, which can establish a safe, robust, and stable mixed platoon. The final three papers in the special issue consider applications of learning systems. Yang et al. propose neural learning-based adaptive impedance control for a lower limb rehabilitation exoskeleton with flexible joints. In order to improve the control performance and enhance the system robustness, periodic dynamics are considered according to the repetitive motion of the rehabilitation process and are handled by a repetitive learning algorithm. The method studied is used for a full model consisting of both the rigid link and the flexible joints. Next, the authors He and Shen investigate the distributed transient control problem for heating ventilation and air condition systems such that each unit of the large-scale building can consistently maintain the desired temperature. For this problem, a distributed ILC algorithm with a decreasing gain is proposed and analyzed. To accelerate the convergence speed, an adaptation mechanism is introduced to generate an adaptive learning gain sequence. The final paper in the special issue, by Li et al., investigates the robust lateral tracking control problem for autonomous vehicles subject to unmodeled system uncertainties, external disturbances, and input constraints that commonly exist in vehicle dynamics. A robust adaptive learning control approach is proposed based on a parametric vehicle model, where an input-dependent auxiliary system is leveraged to compensate for the influence of the input constraints. This approach is proven to be able to achieve impressive path tracking performances under perturbed and constrained scenarios. Furthermore, the proposed robust adaptive learning technique for tackling the under-actuated dynamics is novel and can also be applied to deal with other generic nonsquare systems.

An adaptive fuzzy iterative learning control (ILC) algorithm is designed for the iterative variable reference trajectory problem of nonlinear discrete-time systems with input saturations and unknown control directions. Firstly, an adaptive fuzzy iterative learning controller is constructed by combining with the fuzzy logic system (FLS), which can compensate the loss caused by input saturation. Then, the discrete Nussbaum gain technique is adopted along the iteration axis, which can be embedded to the learning control method to identify the control direction of the system. Finally, based on the nonincreasing Lyapunov-like function, it is proven that the adaptive iterative learning controller can converge asymptotically when the number of iterations tends to infinity, and the system signals always remain bounded in the learning process. A simulation example verifies the feasibility and effectiveness of the learning control method.

To solve the trajectory tracking problem of robotic manipulators with uncertain model information and unknown external disturbances, an adaptive iterative learning control method with second-order terminal sliding mode method is proposed in this paper. This method adopts nonsingular fast terminal sliding mode surface and second-order sliding mode control to improve the convergence speed of system states and robustness. Adaptive iterative learning control is used to approximate system model and bounded external disturbance for getting rid of the dependence on specific mathematical model and improving control precision. The convergence of this controller along iterative times is proved by composite energy function. With Denso VP6242G manipulator as the controlled object, this proposed controller has better performance comparing to traditional iterative learning controller designs.

SummaryIn this article, an observer‐based adaptive boundary iterative learning control law is developed for a class of two‐link rigid‐flexible manipulator with input backlash, the unknown external disturbance, and the endpoint constraint. To tackle the backlash nonlinearities and ensure the vibration suppression, the disturbance observers based upon the iterative learning conception are considered in the adaptive boundary control design. A barrier Lyapunov function is incorporated with boundary control law to restrict the endpoint state. Based on the defined barrier composite energy function, the tracking angle error convergence of the rigid part is guaranteed, and the vibrations of the flexible part are suppressed through the rigorous analysis. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control.

An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator

This work studies the adaptive iterative learning control algorithm for nonlinear systems with nonparametric uncer-tainty and time-iteration-varying parametric uncertainty generated from a high-order internal model(HOIM) under nonzero initial errors condition. We apply time-varying boundary layer technique to deal with the initial position problem of ILC, adopt robust learning control approach to compensate nonparametric uncertainty, and take advantage of adaptive learning strategy to handle the time-iteration-varying parametric uncertainty generated from HOIM. Lyapunov synthesis is adopted for design the iterative learning controller and analyzing control performance. As the iteration number increases, the filtering error can converge to a tunable residual set. In the end, numerical simulation is given to show the effectiveness of propose adaptive learning control algorithm.

Adaptive Iterative Learning Control of an Industrial Robot during Neuromuscular Training

This article proposes an adaptive vibration iterative learning (ILC) control for a flexible beam subject to periodic boundary disturbance for vibration suppression. Based on backstepping technique, boundary adaptive control is adopted to handle the parametric uncertainties. In order to eliminate the effect of periodic boundary disturbance, the iterative learning control is designed in the control design part. With the designed control strategy, the stability of the close-loop system is certified based on Lyapunov's method. Finally, the numerical simulation are carried out to demonstrate the effectiveness of the proposed control law.

Based on combination of an optimal PI type iterative learning controller and projection like adjusting algorithm, an adaptive iterative learning control scheme is presented for repetitive control of uncertain systems. This adaptive iterative learning controller is designed without any priori knowledge of system parameters. The convergence of the presented scheme is analyzed and its convergence condition is obtained in terms of adjusting algorithm step size. An illustrative example is given to demonstrate the effectiveness of the proposed technique.