Contour Error Estimation Research Articles

Accurate Contour Error Estimation-based robust contour control for dual-linear-motor-driven gantry stages

This article presents a novel adaptive contour control scheme for dual-linear-motors-driven gantry stages (DLMDGSs) with time-varying model parameters and disturbances, aiming to realize high-precision contour control. Specifically, a novel adaptive contour controller based on a coupled model is proposed, incorporating powerful projection adaption laws, to achieve the synchronization of multi-axis motors, regression of adaptive parameters, and high-precision contour performance. Additionally, a contour error estimation (CEE) method with four-order convergence rate is designed to ensure estimation accuracy, enhance estimation robustness, and reduce estimation time. Moreover, considering the periodicity of common control contour tasks, an iterative learning control (ILC) reference trajectory compensation structure is adopted to further improve the contour control effect. Finally, the stability and convergence of the closed-loop system are rigorously proven, and comparative experiments are conducted on a DLMDGS platform to demonstrate the superiority of the proposed control strategy.

A time-delay-based sliding mode controlling method for reducing contour errors of machine tools

This article presents a time delay-based sliding mode controller to reduce contour errors for machine tools subject to friction and model error. Through decoupling the actual dynamic model of machine tools into a nominal component and an error component, a proportional differential (PD) controller, which is mathematically deduced from the sliding mode controller (SMC), is designed for the nominal model. A time delay estimation (TDE) strategy that considers the friction effect is designed to compensate for the error component. Therefore, tracking accuracy is guaranteed. Based on TDE results, a Kalman state prediction method that considers model error is developed to make a high state prediction accuracy even if the model error is large. By adding the predicted contour errors of the next sampling time into the command trajectory, the pre-compensation of contour errors is realized. Moreover, a new contour error estimation (CEE) method that can improve computing efficiency is proposed. Experiments and comparisons are conducted to verify the effectiveness of proposed method.

A Feedrate Planning Method in CNC System Based on Servo Response Error Model

Reducing servo response error and further making reduction on contour error is crucial for high-precision computer numerical control (CNC) machine tools. For a permanent magnet synchronous motor (PMSM) servo system, there is always a response lag in feedrate tracking, which would introduce response error into the machining trajectory. Therefore, it is necessary to improve the performance of feedrate planning and interpolation for trajectory path. In this paper, a novel contour error compensation strategy is proposed. Compared with the mainstream methods, the proposed method offers a simplified alternative to existing contour error estimation techniques. Through a three-closed-loop control structure of a PMSM servo system, a response error model is founded. Afterwards, an improved S-model feedrate planning method is introduced according to the servo response error compensation. This predicted error is subsequently compensated in each interpolation cycle, resulting in a reduction of contour error. Finally, simulations and experiments are performed to demonstrate that the contour error can be reduced in both the ‘∞’-shaped Non-Uniform Rational B-Spline (NURBS) curve path and the butterfly-shaped NURBS curve path using the proposed method.

Real-time estimate and control contour errors for five-axis local smoothed toolpaths based on airthoid splines

Five-axis linear commands are blended as the local smoothed toolpaths by inserting clothoid and airthoid splines at corners in five-axis CNC machining. The contour error is the bottleneck to achieve the precise dimension of the machined parts, when following the local smoothed toolpaths. This paper presents a contour error estimation and control method for the five-axis smoothed toolpaths with airthoid splines, according to the geometric characteristics of the toolpaths. The tool-tip contour error is analytically calculated based on the expression of the smoothed toolpaths. Consequently, the tool-orientation contour error is obtained by synchronizing the tool-orientation contour point with the tool-tip item based on the motion time through the designed time scale coefficient, when the toolpaths are scheduled by the time-synchronization scheme. Furthermore, a contour error compensation strategy is constructed to adaptively determine the compensator gain. It can be qualified to maximally eliminate the contour errors and steadily hold the control stability of the feed drives, in spite of the modeling error between the nominal and actual control models. The simulation and experiment results show that the estimation algorithm has higher accuracy than traditional methods, and the compensation strategy effectively eliminates the five-axis contour error.

Time Parameter Mapping and Contour Error Precompensation for Multiaxis Input Shaping

When the trajectory with high speed and high acceleration contains frequency contents matching with the structure mode, the inertial vibration of the structure is easily excited, reducing machining accuracy and surface finish. Input shaping can avoid vibration, but it introduces time-delay that causes multiaxis trajectory distortion and affects the accuracy of contour error estimation. This article presents time parameter mapping and contour error precompensation for multiaxis input shaping to suppress vibration. The mapping of time parameter domain of trajectories is established by deducing the relation between the local curvature extremums of the trajectories before and after shaping, which provides reference points for contour error estimation. The actual trajectory is predicted by the closed-loop servo dynamics model and reference trajectory, and then the Newton iterative algorithm based on time parameter mapping is used to seek the contour error point. Finally, the calculated contour error is low-pass filtered and projected to each axis, and then the shaped trajectory is precompensated to simultaneously reduce the contour error and avoid structural vibration. Comparative experiments are conducted to validate the effectiveness of the proposed method. Experimental results illustrate that the proposed method not only suppresses structural vibration, but also significantly improves the estimation accuracy and contouring performance by time parameter mapping.

Modified Shadow Robot Control method for optimal path synthesis of mechanisms: Application to five-link mechanism

For optimal path synthesis of a mechanism with a single degree of freedom (DOF), a powerful method called Shadow Robot Control (SRC) has been recently proposed in the literature. However, this method is restricted to synthesis problems with prescribed timing (i.e. problems in which a particular input crank angle is associated with each point of the desired trajectory). In this paper, the SRC method was elaborated and modified to be capable of synthesizing both prescribed and nonprescribed timing problems. For this purpose, a new structure of contour error and objective function estimation was presented. As a result, there is no need to consider the input angles (crank angles) corresponding to desired path points as optimization parameters, even for non-prescribed timing problems. This prevents unnecessarily enlarging the search space, providing a more effective and robust optimization method (with respect to initial guess). The synthesis of a geared five-link mechanism was used to detail the proposed algorithm as a case study. Despite the five-link mechanism capability and simplicity of generating a complicated trajectory, this single DOF path generator seems less investigated in the literature. Few existing numerical problems of the five-link mechanism in the literature were solved. The comparison of the results shows the effective performance of the proposed algorithm in synthesizing the mechanism.

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 contouring control: Theory and application to biaxial systems

This paper is concerned with the iterative learning control (ILC) for the contouring control of multi-axis motion system. A novel ILC algorithm, which is called iterative learning contouring control (ILCC), is proposed and verified with biaxial motion systems. In motion control, conventional ILC requires that the number of control objectives is the same as the number of command inputs, which is called square property. This allows for the formulation of transfer function or matrix inversion. The unique feature of contouring control is its non-square property. For contouring control, conventional ILC circumvents the non-square property by adopting the configuration of cross-coupled control (CCC). In other words, the estimated contour error is decomposed into components of individual axis for compensation by ILC and thus the contour error is reduced indirectly. The proposed ILCC can deal with the non-square property and can directly reduce the contour error by adopting the equivalent contour error as the control objective of the ILC. The equivalent contour error represents an accurate contour error model and hence better contouring accuracy can be achieved. The ILCC algorithm is implemented on two platforms, an XY table and a commercial CNC machine tool. Experiments on the contouring control of a circular path with different speeds and a B-spline path are conducted. It is found that the contour error can be reduced about 88% after several learning iterations. The experimental results confirm the effectiveness of the proposed method and show the excellent contouring performance.

Combined Predictive and Feedback Contour Error Control With Dynamic Contour Error Estimation for Industrial Five-Axis Machine Tools

This article proposes a real-time method to control the contour error for industrial five-axis machine tools by combining the generalized predictive control (GPC) and the feedback correction (FBC) with dynamic contour error estimation (CEE). The CEE is developed by well considering the curve’s curvature and torsion based on Taylor series expansion and Frenet frame theory. By utilizing the spherical linear interpolation, the tool orientation and the tool tip position are synchronized with respect to the curve length. A novel dynamic foot point searching procedure is established to weaken the influences of the tracking errors’ magnitude on the CEE precision. To tackle the transmission effect, the GPC is adopted to predict the servo systems’ outputs, and then, the induced tool pose deviations, which are subsequently utilized to counteract the contour errors, are predicted by constructing Jacobian matrixes. Especially, the FBC loops are constructed to suppress the influences of disturbances and further to reduce the magnitudes of contour errors. Simulations and experiments are conducted to verify the effectiveness of the proposed methods.

Task Space Contouring Error Estimation and Precision Iterative Control of Robotic Manipulators

The task space contouring performance is significant for the machining accuracy of industrial robotic manipulators, but the contouring control of end-effector which is important in the industry has received scant attention. In this letter, a novel task space contouring error estimation and control scheme is developed to address the end-effector precision contouring problem of robotic manipulators. In order to quantify manipulator contouring performance, a 6-DOF synchronized contouring error is defined in the task space. Based on the definition, an optimization problem is constructed and solved to achieve high precision contouring error estimation. The proposed method shows excellent estimation accuracy even under extreme contouring conditions, which is the prerequisite for accurate contouring control. Then the solved contouring error is iteratively compensated into the end-effector reference in a feedforward way to achieve contouring error reduction. The effectiveness of the proposed method is derived theoretically under the assumption of small error and nonsingularity. Comparative experiments are conducted on an industrial manipulator. Quantitative results on different extreme trajectories demonstrate that the proposed control scheme not only has advantages in control stability and implementation simplicity, but also outperforms traditional joint space iterative learning control and cross-coupled iterative learning control on the end-effector contouring accuracy. The proposed method actually provides a practical solution to high-precision contouring applications for industrial manipulators.

Cross-coupled control for contour tracking error of free-form curve based on fuzzy PID optimized by improved PSO algorithm

Aiming at the free-form curve contour tracking error problem of CNC machining, a cross-coupled controller based on Fuzzy PID using an improved PSO algorithm is proposed. First, the exact formulas of the linear and circular arc contour errors under a plane trajectory are derived, and an estimation method for the free curve profile error under a plane trajectory based on the principle of approximate approximation of preferred points is designed. Second, a cross-coupled controller based on Fuzzy PID using an improved PSO algorithm is achieved. An improved PSO algorithm, whose learning factor is adjusted with the inertia weight, is used to optimize the controller parameters and achieve contour tracking of the free curve. Finally, a two-dimensional biaxial experimental platform is used to test the proposed method. The results demonstrate that the optimal gain parameters obtained by the proposed strategy can significantly improve contour control accuracy in biaxial contour tracking tasks. The proposed contour error control scheme can achieve not only a nearly perfect contouring error estimation, but also an obvious promotion of contouring accuracy.

An iterative contouring error compensation scheme for five-axis precision motion systems

Contouring error is one of the most important performance indexes for multi-axis motion systems, especially for five-axis ones. The contouring control performance of five-axis motion systems is difficult to improve mainly due to the following two factors. Firstly, the dynamic coupling between the translational and the rotary axes is strong. Secondly, the contouring error in five-axis systems includes tool tip error and tool orientation one, which are difficult to suppress simultaneously. In this paper, a novel contouring error iterative compensation scheme is proposed to realize the coordination control of spatial contouring error with multi-degree-of-freedom. Accurate contouring error estimation is firstly achieved through a numerical calculation method. And then the estimated contouring error is compensated to the reference trajectory by means of the proposed model-free compensation law. By iteratively implementing the above process, the convergence of which has been theoretically proved, the contouring performance can be further improved. A series of experiments have been conducted on a five-axis motion system. The experimental results consistently illustrate that, in comparison with existing contouring control methods, the proposed scheme can achieve excellent promotion of contouring accuracy, especially in extreme contours with large curvature and sharp corners.

Advanced Contouring Compensation Approach via Newton-ILC and Adaptive Jerk Control for Biaxial Motion System

To achieve the precision contouring performance, this article presents a contouring compensation approach for the biaxial motion system even under extreme contour tasks. Two permanent magnet linear synchronous motors are installed in the biaxial motion platform. First, the dynamics of the biaxial motion servo system with the uncertainties such as model parameter variations, additive disturbance, and nonlinear friction are introduced. Since Newton algorithm is provided to realize dynamic contouring error estimation, accurate estimation of the contouring error can be achieved, even for the high velocity and complex contour with sharp corners and large curves. Then, iterative learning control (ILC) is used to control the contouring error for contouring performance improvement. An adaptive PD-type learning law based on an asymmetric Gaussian-like function is applied to improve the performance of the system. Moreover, adaptive jerk control (AJC) integrated with adaptive feedback gain is designed to address the negative effect of the uncertainties and enhance the robustness. The adaptive feedback gain is dominated and tuned by a novel adaptation law without the need for prior bound knowledge of the uncertainties. Meanwhile, parameter estimation is employed to handle the model parameter variations. Finally, the experimental results are presented to validate the efficiency and the achievable contouring performance of the proposed Newton-ILC and AJC approach.

A contour error definition, estimation approach and control structure for six-dimensional robotic machining tasks

Robots are increasingly employed in machining applications, such as milling, grinding and polishing, etc, and contour error can be used to assess the robotic machining accuracy quantitatively. For the robotic machining tasks, such as the grinding of complex surface parts, the reduction of contour error needs to consider the six dimensions of the robotic task space. However, at present, there is no suitable research work directly related to the contour error definition and estimation for the six-dimensional (6D) robotic machining tasks, and the corresponding control structure is rarely involved. For resolving the above problems, this article presents a contour error definition, estimation approach and control structure for the 6D robotic machining tasks. To be specific, the definition of robotic contour error in the 6D machining is first introduced. Then, based on the bidirectional search, Fibonacci search and spherical linear interpolation algorithms, a locally iterative robotic contour error estimation approach with high accuracy and high efficiency is provided. Finally, by compensating the weighted contour error components to the velocity commands in the robotic task space, a simple as well as effective components-based contouring control structure is designed. The real experiments are performed on a six-degrees-of-freedom robot. The results reveal that the definition of robotic contour error given is intuitive, and the discrepancies between the position and orientation contour error estimates and the corresponding true values are very small within 0.01062 µm and 0.8959 µrad, respectively. The designed contouring control structure can reduce effectively the contour errors, and compared with the tracking control only, the mean position and orientation contour errors are reduced by about 30% and 28%, respectively.

Accelerated Iteration Algorithm Based Contouring Error Estimation for Multiaxis Motion Control

As the basis of contouring motion control, the estimation of contouring error is one of the most important research topic in the field of multiaxis coordination control. In extreme contour cases with high speed, large curvature and sharp corner, inaccurate contouring error estimation and poor real-time performance are two key problems for existing estimation methods. In order to guarantee the real-time performance of the iterative based contouring error estimation methods, a novel iterative calculation method based on Atiken acceleration is proposed in this article. By means of local linearization of the iteration points, the proposed method can not only accelerate the solution of contouring error points, but also effectively prevent the divergence problem caused by improper selection of initial value points, thus guaranteeing the accuracy of contouring error estimation. The proposed accelerated iterative algorithm is verified on a three-axis motion system and compared with the existing numerical iteration method and noniterative method for contouring error estimation. The experimental results show that the proposed method is significantly improved in both calculation speed and solution accuracy, especially in the case of extreme contour.

Prediction and Compensation of Contour Error of CNC Systems Based on LSTM Neural-Network

This article proposes a contour error estimation (CEE) and compensation method for computer numerical control (CNC) systems based on the long short-term memory neural network. This is achieved by performing modeling of each axis to predict the tracking error, calculating the actual trajectory, estimating the contour error, and modifying the reference trajectory. First, linear feature selection based on a simplified single-axis model and nonlinear feature selection based on a circular test are performed to achieve tracking error prediction. Then, a spline-approximation-based CEE method is proposed to estimate the contour error between the reference trajectory and the predicted trajectory. Finally, contour error compensation is performed on the reference trajectory before it is run on CNC systems. The proposed method is validated through experiments on a three-axis CNC system.

Trajectory modification method based on frequency domain analysis for precision contouring motion control systems

For multi-axis motion system widely used in CNC machine tools, contouring following control is an important research topic. For most existing contouring motion control methods, it is usually necessary to estimate the contouring error of multi-axis system and then design contouring controller to suppress it. However, additional contouring error estimator and controller requiring complicated hardware adjustment is not suitable for existing commercial CNC systems with built-in control systems. In this paper, a frequency domain analysis based trajectory modification method is proposed to improve contouring control performance through a way that is easier to implement. In the proposed method, the modified trajectory can be calculated off-line just according to the instantaneous frequencies of the reference trajectories and the closed loop frequency characteristics of each axis. After the modification, the amplitude attenuation of the actual position output can be effectively suppressed, and the output of each axis has the same phase lag, thus improving the contouring control performance. Compared with other existing contouring control methods, the main contribution of this paper is to analyze and control contouring error from the angle of frequency. Various of simulations and comparative experiments are conducted to verify the effectiveness of the proposed contouring control method. The experimental results demonstrate the advantages of the proposed scheme over other methods, i.e. excellent contouring control performance can be achieved without additional contouring error estimation and control.

Cross-coupled control based on real-time Double Circle contour error estimation for biaxial motion system

In contour machining, contour error is a major factor affecting machining quality. In order to improve the performance of contour following, many control techniques based on real-time contour error estimation have been developed. In this paper, a Double Circle contour error estimation method is proposed. First, based on the kinematic information of the reference point on the command trajectory, five interpolation points closest to the actual point are obtained. Then the approximate contour error is obtained by employing the Double Circle approximation method. Compared with the common contour error approximation methods, the proposed method can achieve high precision approximation. In addition, according to the proposed contour error approximation method, the cross-coupled control strategy is improved. Experiments prove the effectiveness of the proposed estimation method and control strategy.

Prediction-Model-Based Contouring Error Iterative Precompensation Scheme for Precision Multiaxis Motion Systems

In order to achieve both accurate contouring error estimation and excellent contouring control performance for multiaxis motion systems, this article proposes an online iterative precompensation control method based on a third-order contouring error prediction model. Specifically, the closed-loop dynamical model of each axis is first used to predict tracking errors at future sampling instants. And then the related contouring error of the multiaxis system at future time can be expressed by the predicted tracking error and the theoretical third-order model of the reference contour. To reduce the influence of modeling error and uncertain disturbances on the prediction performance of contouring error, the numerical calculation method is utilized to obtain absolutely accurate contouring error, through which the deviation between the proposed contouring error model and the accurate one can be corrected accordingly. Based on the accurate contouring error prediction model, the optimal contouring error compensation can be generated through online iterative calculation. To achieve excellent contouring performance, the compensation is added to the original reference contour as a kind of trajectory precompensation. Comparative experiments are carried out on an industrial three-axis machine tool. A series of contour tracking experiments consistently demonstrate that the proposed method can predicate the contouring error accurately. Additionally, the contouring motion performance can also be significantly improved in the case of a variety of different trajectories.