Spatial Iterative Learning Control Research Articles

Spatial Iterative Learning Control With Human Guidance and Visual Detection for Path Learning and Tracking

Spatial Iterative Learning Control With Human Guidance and Visual Detection for Path Learning and Tracking

Robust Higher-Order Spatial Iterative Learning Control for Additive Manufacturing Systems

In this article, a higher-order spatial iterative learning control (HO-SILC) scheme is proposed, targeting heightmap tracking for a class of 3-D structures fabricated by repetitive addition of material in a layer-by-layer fashion using additive manufacturing (AM) technology. AM processes are innately iteration-varying, resulting in large model uncertainties due to iteration-varying system parameters and surface variations. HO-SILC has been shown to be useful in repetitive systems with model uncertainties by improving system performance with respect to convergence speed and robustness. In this article, HO-SILC is used to iteratively construct a feedforward control signal to improve part quality in multilayered AM constructs. The system dynamics are approximated by discrete 2-D spatial convolution kernels that incorporate in-layer and layer-to-layer variations. The proposed HO-SILC framework incorporates data available from previously printed devices, as well as multiple previously printed layers, to enhance the overall performance. The condition for robust monotonic convergence (RMC) of the iteration-varying HO-SILC algorithm is based on the Lyapunov stability criteria. Simulation results of an AM process termed electrohydrodynamic jet (e-jet) printing demonstrate that a well-designed HO-SILC framework is effective and can improve the performance by 60 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\%$</tex-math> </inline-formula> . In addition, HO-SILC is robust to iteration-varying model uncertainties, especially at higher layers where iteration-varying surface variations are more pronounced.

Iterative learning control for piecewise arc path tracking with validation on a gantry robot manufacturing platform

The piecewise arc path tracking problem is a common feature of manufacturing systems operating in a repetitive mode, e.g. assembly production lines. Here, the system end-effector must follow a spatial path without any specific temporal tracking constraints, which makes the temporal profile not fixed a priori. The technique of iterative learning control (ILC) is well-suited to handle this problem, since compared to classical feedback control methods, ILC is capable of learning from previous trial information to minimize the tracking error over repeated trials. This paper extends the ILC task description to address piecewise arc path tracking tasks, and further formulates a more general design framework than existing spatial ILC approaches. A comprehensive ILC algorithm is designed to handle this class of piecewise arc path tracking problems, and practical implementation instructions are provided. Validation is conducted on a gantry robot manufacturing testbed to confirm its feasibility and efficiency in practice with a comparison to existing methods showing its higher path tracking accuracy.

Five-Axis Contour Error Control Based on Numerical Control Data

Improving contour accuracy is one of the significant goals of industrial machining. This paper proposes a contour error estimation and compensation algorithm for five-axis computer numerical control (CNC) machine tools based on modified numerical control (NC) codes. The expected path analyzed by NC data and the actual trajectory collected by sensors are spatially mapped by the hidden Markov model (HMM). Next, an evaluation function that hybrids the tool tip position and tool orientation change trend is proposed as the index of contour error estimation. Finally, spatial iterative learning control (ILC) is used to compensate the contour error, and high-precision machining instructions are obtained after multiple iterations. Experiments with different trajectories are performed on a five-axis platform to verify the proposed algorithm’s effectiveness. The results show that the proposed algorithm without using planned trajectories, has the same good control effect as traditional methods, which must know the planning trajectory for simple trajectories. At the same time, the method proposed in this paper has better performance than existing algorithms based on tool tip position nearest principle at sharp corners. In conclusion, on the basis of not depending on the planning trajectories, this method has a better compensation effect for the overall accuracy of trajectories and is easier to implement in industrial applications.

Five-Axis Contour Error Control Based on Spatial Iterative Learning

In this paper, a contour error control strategy based on spatial iterative learning control (sILC) is developed for repetitive processing of five-axis computer numerical control (CNC) machine tools. A curve approximation method with an adaptive moving window is developed to achieve accurate tool position and orientation contour error estimation, and a five-axis contour error control strategy based on sILC is proposed. The compensation method is derived using an sILC algorithm to modify the geometric reference path instead of modifying the controller. The experimental results show that the proposed control strategy reduces contour errors of five-axis CNC machine tools, and it outperforms the traditional tracking error control. Note to Practitioners—This paper aims to propose an effective five-axis contour error control scheme. At present, most of the five-axis contour error control methods rely on the modification of the controller, which is not allowed in commercial CNC systems. Therefore, we propose a five-axis contour error compensation algorithm based on sILC, which modifies the system’s reference path. Experimental results show that the proposed method can reduce the five-axis contour errors, while maintaining the machining efficiency.

Iterative Learning Control for Robotic Path Following With Trial-Varying Motion Profiles

Iterative learning control (ILC) aims to maximize the performance of systems performing repeated tracking tasks. However, in most existing applications, the motion profile is inherently specified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> , which has restricted both its application range and scope of performance improvement. For example, the typical repeated path-following task in robotics only requires a spatial path profile rather than a temporal trajectory profile, for which most existing ILC designs are unsuitable. To handle this requirement, this article extends the ILC task description by relaxing this postulate to enable a trial-varying motion profile and formulate an ILC path-following problem with system constraints. Under this extended problem setup, a spatial ILC algorithm is proposed with efficient implementation and robust convergence analysis, which updates the input signal and motion profile at the end of each trial to reduce the tracking error. This algorithm is implemented experimentally on a gantry robot test platform to verify performance, practical feasibility, and reliability. Comparisons with other control methods are also made to clarify its advantages, such as error reduction, control effort reduction, and constraint handling.

Spatial Iterative Learning Control for Robotic Path Learning.

A spatial iterative learning control (sILC) method is proposed for a robot to learn a desired path in an unknown environment. When interacting with the environment, the robot initially starts with a predefined trajectory so an interaction force is generated. By assuming that the environment is subjected to fixed spatial constraints, a learning law is proposed to update the robot's reference trajectory so that a desired interaction force is achieved. Different from existing iterative learning control methods in the literature, this method does not require repeating the interaction with the environment in time, which relaxes the assumption of the environment and thus addresses the limits of the existing methods. With the rigorous convergence analysis, simulation and experimental results in two applications of surface exploration and teaching by demonstration illustrate the significance and feasibility of the proposed method.

Iterative learning and feedback control for the curvature and contact force of a metal strip on a roll

This paper presents a novel model-based control strategy for the curvature and the contact force at the contact point of a metal strip and a roll. Due to the plastic deformation of the strip, the bending history of the strip has to be considered in the controller design. A multivariable two-degrees-of-freedom (2-DOF) control structure is used to track user-defined periodic references for the outputs. The proposed multi-input/multi-output (MIMO) feedback control structure consists of a spatial iterative learning control (ILC) combined with a multivariable PI controller. The control strategy is implemented in a real-time system and verified by measurements on an experimental test rig.

Synthesis of model predictive control and iterative learning control for topography regulation in additive manufacturing

This paper presents a spatially derived control solution for improving the performance of a high-resolution additive manufacturing (AM) process towards the fabrication of repeatable, thin-film functional devices. In particular, this work addresses challenges in fabrication of high-quality films using AM technology by incorporating knowledge about the interactions between printed layers of material within a control framework for improved repeatability and reliability in the fabrication of multi-layered micro devices using AM technology. We implement an SILC-MPC method that leverages the information from previous layers using spatial iterative learning control (SILC) and projects forward the data from future layers using model predictive control (MPC) to improve the tracking performance of iteration varying AM processes. Simulation results of an AM process termed electrohydrodynamic jet (e-jet) printing demonstrate that an SILC-MPC framework is effective and robust to repetitive and nonrepetitive model uncertainties and outperforms traditional SILC by converging faster to the nominal behavior with a lower tracking error.

Iterative Learning Operation Control of High-Speed Trains With Adhesion Dynamics

This article proposes a new spatial iterative learning control (ILC) algorithm that can track the desired trajectory for operation control of high-speed train (HST) in the presence of time-varying adhesion dynamics between wheel and track. Although the adhesion dynamics will affect the overall performance and might lead to an unsafe scenario, not much work has been done to handle them in the field of operation control of HST. As the operation process of HST is repetitive in spatial domain, the conventional ILC algorithms, in which finite time domain is always considered, cannot be directly applied to such kind of system. In order to address spatial learning, the train’s operation dynamics, including the adhesion dynamics, are first developed. By revealing the link between the temporal gradient and the spatial gradient, the operation dynamics can be converted from the time domain into the spatial domain, making the ILC design feasible. A novel ILC algorithm is then proposed to ensure the convergence with the help of a new composite energy function (CEF). It is highlighted that in this CEF analysis, dynamic systems are not required to be globally Lipschitz, which is one of the standing assumptions needed in the convergence analysis of ILC. The effectiveness of the proposed spatial ILC algorithm is demonstrated from a simulation example.

Reference Trajectory Modification Based on Spatial Iterative Learning for Contour Control of Two-Axis NC Systems

Contour error is a main factor that affects the quality of products in numerical control (NC) machining. This article presents a contour control strategy based on digital curves for high-precision control of computer numerical control (CNC) machines. A contour error estimation algorithm is presented for digital curves based on a geometrical method. The dynamic model of the motion control system is transformed from time domain to space domain because the contour error is dependent on space instead of time. Spatial iterative learning control (sILC) is developed to reduce the contour error, by modifying the reference trajectory in the form of G code. This allows system improvement without interference of low-level controllers so it is applicable to many commercial controllers where interpolators and feed-drive controllers cannot be altered. The effectiveness of this method is verified by experiments on a NC machine, which have shown good performance not only for smooth trajectories but also for large curvature trajectories.

Spatial Iterative Learning Control for Multi-material Three-Dimensional Structures

Abstract Iterative learning control (ILC) is a powerful technique to regulate repetitive systems. Additive manufacturing falls into this category by nature of its repetitive action in building three-dimensional structures in a layer-by-layer manner. In literature, spatial ILC (SILC) has been used in conjunction with additive processes to regulate single-layer structures with only one class of material. However, SILC has the unexplored potential to regulate additive manufacturing structures with multiple build materials in a three-dimensional fashion. Estimating the appropriate feedforward signal in these structures can be challenging due to iteration varying initial conditions, system parameters, and surface interaction dynamics in different layers of multi-material structures. In this paper, SILC is used as a recursive control strategy to iteratively construct the feedforward signal to improve part quality of 3D structures that consist of at least two materials in a layer-by-layer manner. The system dynamics are approximated by discrete 2D spatial convolution using kernels that incorporate in-layer and layer-to-layer variations. We leverage the existing SILC models in literature and extend them to account for the iteration varying uncertainties in the plant model to capture a more reliable representation of the multi-material additive process. The feasibility of the proposed diagonal framework was demonstrated using simulation results of an electrohydrodynamic jet printing (e-jet) printing process.

Robust Monotonically Convergent Spatial Iterative Learning Control: Interval Systems Analysis via Discrete Fourier Transform

Additive manufacturing (AM) systems use a layer-by-layer paradigm to build three-dimensional structures. There are myriad of advantages to AM; however, challenges with real-time actuation and sensing relegate AM processes to be largely open-loop processes. In this paper, we build upon the spatial iterative learning control (SILC) strategy to close the loop in the iteration domain in AM systems, enabling autonomous process control in the absence of real-time sensing. We approximate the steady-state partial differential equations of AM systems by discrete two-dimensional convolution operators and assume uncertain spatially varying kernels to have a more realistic representation of these complex processes. From this system description, we formalize the robust monotonic convergence (RMC) criterion for SILC. Importantly, we use discrete Fourier transform-based tools to study spatial dynamics, a practical framework for data-rich spatial sensors used in AM. The theoretical results are complemented with experiments on the AM process electrohydrodynamic jet printing, demonstrating that the RMC criterion can predict the design boundary for convergent behavior for norm-optimal SILC.

Multi-Layer Spatial Iterative Learning Control for Micro-Additive Manufacturing

Spatial iterative learning control (SILC) has been used in the control of additive manufacturing systems that can be described by their spatial dynamics. Since the current framework is limited to single-layer parts, the aim of this paper is to provide an approach to multi-layer SILC using learning in the layer-to-layer dimension. Mathematical formulation of a multi-layer SILC controller is provided, and active feedback control is demonstrated to reduce the error accumulation over the iterations. Simulation results using a model of high-resolution e-jet printing verify performance improvements for the proposed framework.

基于位置域迭代学习的激光导引头测试系统时变周期干扰抑制

基于位置域迭代学习的激光导引头测试系统时变周期干扰抑制

Application of robust monotonically convergent spatial iterative learning control to microscale additive manufacturing

Microscale additive manufacturing μ-AM processes are a class of manufacturing processes used to fabricate micron-sized structures in a sequence of direct additions of materials as instructed by a digital file, as opposed to the lithographic patterning and subtractive etching used in traditional microscale manufacturing. Despite being sophisticated, numerically controlled tools, material addition is an open-loop process which requires continual user intervention to heuristically tune process parameters. This paper details the first experimental demonstration of a run-to-run feedback algorithm termed Spatial Iterative Learning Control (SILC), a framework previously introduced by the authors to enable robust, auto-regulation of sensitive μ-AM processes [1, 2]. We demonstrate that SILC enables us to autonomously fabricate complex topography structures with as small as 5 µm x- and y-axis resolution and ∼ 113 nm feature height accuracy, without any heuristic tuning by a user. Lastly, it was observed that an SILC design was robust to system faults, as demonstrated by the ability to recover from both an actuator and sensor fault in two iterations.

Composite Energy Function-Based Spatial Iterative Learning Control in Motion Systems

In this brief, a novel spatial iterative learning control (ILC) method is proposed for a class of high-order nonlinear motion systems in the presence of both parametric and nonparametric uncertainties. Since the system performs the tracking task iteratively in the spatial domain and the uncertainties are functions of spatial coordinates, the traditional ILC that updates the control signals in the time domain is not applicable. The proposed spatial ILC aims at improving the system tracking performance by making full use of the spatial periodicity. First, the dynamics of the motion systems are converted from the temporal domain to the spatial domain via feedback linearization. Then, the learning law is designed to tackle the system uncertainties. By utilizing a newly defined space-based barrier composite energy function, the boundedness and the convergence of state tracking error are ensured rigorously. In the end, an illustrative example is shown to demonstrate the efficacy of the proposed ILC scheme.

Spatial Iterative Learning Control: Output Tracking

This paper focuses on tracking spatially repeatable tasks. In addition, these tasks are not necessarily temporally repeatable in the sense that the finite length of the corresponding time interval may change with each repetition. Because of that, the standard Iterative Learning Control (ILC) framework is not directly applicable. Namely, the standing assumption that the finite length of the time interval is fixed with each repetition, is violated. Motivated by human motor learning, this paper proposes a Spatial ILC (SILC) framework which leverages the spatial repeatability. In particular, the concept of spatial projection, closely related to temporal rescaling, is proposed. This allows to spatially relate the relevant information from the past repetition to the present repetition. To demonstrate the proposed framework, a class of nonlinear time-varying systems with relative degree zero is selected. In particular, using contraction mapping technique, it is shown that under appropriate assumptions, the corresponding tracking error converges under the proposed SILC control law. Finally, simulation results support the obtained result.

A multi-objective iterative learning control approach for additive manufacturing applications

Iterative learning control (ILC) is a method for improving the performance of stable, repetitive systems. Standard ILC is constructed in the temporal domain, with performance improvements achieved through iterative updates to the control signal. Recent ILC research focuses on reformulating temporal ILC into the spatial domain, where 2D convolution accounts for spatial closeness. This work expands spatial ILC to include optimization of multiple performance metrics. Performance objectives are classified into primary, complementary, competing, and domain specific objectives. New robustness and convergence criteria are provided. Simulation results validate flexibility of the spatial framework on a high-fidelity additive manufacturing system model.

On Spatial Iterative Learning Control via 2-D Convolution: Stability Analysis and Computational Efficiency

Iterative learning control (ILC) is an effective control strategy for improving control performance in stable or stabilizable systems that track a repetitive trajectory in time. The ILC paradigm has previously been extended to the spatial domain; however, spatial ILC (SILC) methods have most commonly been applied to problems in which there is a natural bijective map between the temporal and spatial domains to simply redefine processes in space instead of time. Yet, there are applications in which there does not exist a unique mapping between time and space, such as additive manufacturing (AM) systems utilizing a raster trajectory. In this exploratory work, we present a novel reformulation of ILC that is derived from 2-D convolution in spatial coordinates, compared with 1-D convolution employed in temporal ILC, which innately informs the algorithm of the spatial proximity of measured data points. We present our SILC framework in a tutorial fashion, providing the essential lifted- and frequency-domain system formulations and stability and performance criteria. A simulation-based demonstration using an empirically derived model of a microscale AM system examines SILC update law designs. Importantly, as a spatial sensor for an AM system will record as many as $10^{8}$ measurements, we demonstrate that a frequency-domain framework reduces the computation time by three orders of magnitude and increases the tractable number of measurements by three orders of magnitude, in comparison with the lifted-domain framework.