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Muscles generate varying levels of force by recruiting different numbers of motor units (MUs), and as the force increases, the number of recruited MUs gradually rises. However, current decoding methods encounter difficulties in maintaining a stable and consistent growth trend in MU numbers with increasing force. In some instances, an unexpected reduction in the number of MUs can even be observed as force intensifies. To address this issue, in this study, we propose an enhanced decoding method that adaptively reutilizes MU filters. Specifically, in addition to the normal decoding process, we introduced an additional procedure where MU filters are reused to initialize the algorithm. The MU filters are iterated and adapted to the new signals, aiming to decode motor units that were actually activated but cannot be identified due to heavy superimposition. We tested our method on both simulated and experimental surface electromyogram (sEMG) signals. We simulated isometric signals (10%-70%) with known MU firing patterns using experimentally recorded MU action potentials from forearm muscles and compared the decomposition results to two baseline approaches: convolution kernel compensation (CKC) and fast independent component analysis (fastICA). Our method increased the decoded MU number by a rate of 135.4% ± 62.5 % and 63.6% ± 20.2 % for CKC and fastICA, respectively, across different signal-to-noise ratios. The sensitivity and precision for MUs decomposed using the enhanced method remained at the same accuracy level (p <0.001) as those of normally decoded MUs. For the experimental signals, eight healthy subjects performed hand movements at five different force levels (10%-90%), during which sEMG signals were recorded and decomposed. The results indicate that the enhanced process increased the number of decoded MUs by 21.8% ± 10.9 % across all subjects. We discussed the possibility of fully capturing all activated motor units by appropriately reusing previously decoded MU filters and improving the balance of activated motor unit numbers across varying excitation levels.

Accurate and reliable state estimation and mapping are the foundation of most autonomous driving systems. In recent years, researchers have focused on pose estimation through geometric feature matching. However, most of the works in the literature assume a static scenario. Moreover, a registration based on a geometric feature is vulnerable to the interference of a dynamic object, resulting in a decline of accuracy. With the development of a deep semantic segmentation network, we can conveniently obtain the semantic information from the point cloud in addition to geometric information. Semantic features can be used as an accessory to geometric features that can improve the performance of odometry and loop closure detection. In a more realistic environment, semantic information can filter out dynamic objects in the data, such as pedestrians and vehicles, which lead to information redundancy in generated map and map-based localization failure. In this paper, we propose a method called LiDAR inertial odometry (LIO) with loop closure combined with semantic information (LIO-CSI), which integrates semantic information to facilitate the front-end process as well as loop closure detection. First, we made a local optimization on the semantic labels provided by the Sparse Point-Voxel Neural Architecture Search (SPVNAS) network. The optimized semantic information is combined into the front-end process of tightly-coupled light detection and ranging (LiDAR) inertial odometry via smoothing and mapping (LIO-SAM), which allows us to filter dynamic objects and improve the accuracy of the point cloud registration. Then, we proposed a semantic assisted scan-context method to improve the accuracy and robustness of loop closure detection. The experiments were conducted on an extensively used dataset KITTI and a self-collected dataset on the Jilin University (JLU) campus. The experimental results demonstrate that our method is better than the purely geometric method, especially in dynamic scenarios, and it has a good generalization ability., Competing Interests: The authors have declared that no competing interests exist.

Objective: This study aims to develop an artificial intelligence‐based method to screen patients with left ventricular ejection fraction (LVEF) of 50% or lesser using electrocardiogram (ECG) data alone. Methods: Convolutional neural network (CNN) is a class of deep neural networks, which has been widely used in medical image recognition. We collected standard 12‐lead ECG and transthoracic echocardiogram (TTE) data including the LVEF value. Then, we paired the ECG and TTE data from the same individual. For multiple ECG‐TTE pairs from a single individual, only the earliest data pair was included. All the ECG‐TTE pairs were randomly divided into the training, validation, or testing data set in a ratio of 9:1:1 to create or evaluate the CNN model. Finally, we assessed the screening performance by overall accuracy, sensitivity, specificity, positive predictive value, and negative predictive value. Results: We retrospectively enrolled a total of 26 786 ECG‐TTE pairs and randomly divided them into training (n = 21 732), validation (n = 2 530), and testing data set (n = 2 530). In the testing set, the CNN algorithm showed an overall accuracy of 73.9%, sensitivity of 69.2%, specificity of 70.5%, positive predictive value of 70.1%, and negative predictive value of 69.9%. Conclusion: Our results demonstrate that a well‐trained CNN algorithm may be used as a low‐cost and noninvasive method to identify patients with left ventricular dysfunction. [ABSTRACT FROM AUTHOR]

Here we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to planning cylindrical cutter location for flank (or side) milling of ruled surfaces. It contains two steps: tool positioning and re-positioning. In the former step, first an adaptive mesh is constructed on the designed ruled surface with the existing algorithm, and then a sequence of initial cutter locations (CLs) is determined using the offset points of the grid sampled points via semidefinite programming (SDP). In the latter step, a smooth tool axis surface is generated by interpolating the initial CLs using the dual mapping theory; afterwards, the tool is re-positioned by adjusting the offset value of each sampled point on the designed surface according to the predicted cutting errors. The cutter positioning methods for rough and finish milling are both developed in this framework. Example and numerical simulation illustrate the efficiency of the novel strategy. [ABSTRACT FROM AUTHOR]

With the increasing demands of low noise and high strength from industry applications for spiral bevel and hypoid gears, it is significant to consider the tooth contact performances, which dependents on tooth contact analysis (TCA) technology. The initial contact point, especially its initial value problem, is always of a great influence on TCA results. Furthermore, misalignments condition in the actual manufacturing is an important factor affecting tooth contact performance. A new multi-step integrated analytical identification approach is proposed to identify the initial contact point considering misalignments. First, the initial contact points on gear and pinion are identified to solve for the accurate initial values of TCA by considering the misalignments. In the consideration of misalignments, the assembly distance and the instantaneous transmission ratio are set the two constraints on solution of TCA. Then, the geometric kinematic transformation relation in tooth contact process is investigated to identify the initial contact point. Finally, a conic self-adaptive trust region algorithm is employed to get the contact points. The numerical test is given to validate the proposed methodology. [ABSTRACT FROM AUTHOR]

Process damping generated between the clearance face of the tool and wavy finish workpiece surface has a strong effect on cutting dynamics and stability, especially at low cutting speeds, resulting into higher chatter stability limit. It is particularly important for hard-to-machine materials, such as titanium, nickel super alloys, and hardened steels, which need to be machined at low cutting speed. However, process damping has been mostly ignored in chatter analysis as there is no practical model for estimation of it. In the meantime, the existing studies on the process damping encounter the challenges of computational efficiency. In this study, process damping effect is equivalent to a linear viscous damping which is described by the process damping coefficients. An energy dissipation principle is established to relate the flank-wave indentation area to the process damping coefficients. Two methods are proposed to calculate the indentation area, which is involved in the cutting stability computation and occupies the most time. In analytical integration method, the sinusoidal expression of workpiece surface undulation is fitted by piecewise polynomial to calculate the indentation area. In numerical integration method, the area is realized by summation of the divided small area unit. The time for establishing stability lobes by the above two methods is greatly reduced compared with the detailed method proposed by Ahmadi and Ismail (Int J Mach Tools Manuf 51:296-308, 2011) which took 10 min to compute one single lobe. It demonstrates that the stability lobes established in frequency domain by the proposed methods are extremely efficient. Moreover, the stability lobes maintain enough accuracy compared with stability lobes established for different amplitudes of vibration as reported by Ahmadi and Ismail (Int J Mach Tools Manuf 51:296-308, 2011), especially the finite amplitude stability, with that, the vibration stabilizes at an amplitude between fully stably and fully unstable due to process damping. [ABSTRACT FROM AUTHOR]

High-accuracy contouring error estimation is the premise of effective contouring error control. However, two key factors make it complex to estimate contouring error for multi-axis machines with rotary axes: the nonlinear kinematics and the synchronization requirement of the tool tip position and tool orientation. This paper proposes a generalized online estimation algorithm of multi-axis contouring errors for CNC machine tools with rotary axes. The nearest reference tool pose to the actual one is searched at first, and then the corresponding contouring error components on each axis are estimated by using linear ratio estimation, where the tool tip position and tool orientation are naturally synchronized to one same pose on the desired trajectory. The advantage of the proposed contouring error estimation algorithm is that only the interpolated reference poses and drive commands are needed in the calculation, which increases the generality of the algorithm to different trajectory types and machine topologies. On the other hand, the calculation load is reduced when compared with existing iterative multi-axis contouring error estimation approaches. Simulation results on both five- and four-axis machines show that the proposed contouring error estimation algorithm can estimate axis components of contouring errors with high accuracy. Experiment results on an in-house developed five-axis experiment platform verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: Machining parameters optimization in a chatter-free milling process is a common issue for practical engineers at shop floor. The detailed and easily applicable optimization algorithm taking the milling mechanism into account is absent to date. This communication deals with the procedures of optimization of machining parameters in the chatter-free milling process. First, the model of machining parameters optimization is given based on the milling dynamics. The optimization objects are to minimize the tool vibration response and maximize the material removal rate, and the constraint conditions are to keep the milling process chatter-free or stable and let the spindle speed below a predefined one. Emphasis is put on how to select the spindle speed for reducing the tool vibration response and maximization of the material removal rate simultaneously. Augmented Lagrangian function method is employed to solve the nonlinear optimization problem. A numerical example is provided to show the effectiveness of the developed results. Besides, improvements on the calculation scheme of the tool vibration response have been made. [Copyright &y& Elsevier]

Multiple sets of magnetic couplings are widely used in many industrial applications. Accurate analysis and efficient optimal design are essential to avoid costly trials. We present an example of simultaneously optimizing two sets of radial magnetic couplings with 3-D finite-element analysis (FEA) modeling. First, we list the preliminary design specifications and set up a simplified mathematical model with novel criteria. We then establish an FEA model. Finally, we implement an optimizing strategy consisting of the 3-D FEA, the design of experiments (DOE), and an exhaust algorithm in a small range to obtain the near-optimal parameter set. This strategy increased efficiency by about 99.4% with sufficient accuracy, compared with the method of exhaustion without DOE. The optimizing strategy can also be employed in various similar industrial applications. [ABSTRACT FROM AUTHOR]

Computation of grasps with form/force closure is one of the fundamental problems in the study of multifingered grasping and dextrous manipulation. Based on the geometric condition of the closure property, this paper presents a numerical test to quantify how far a grasp is from losing form/force closure. With the polyhedral approximation of the friction cone, the proposed numerical test can be formulated as a single linear program. An iterative algorithm for computing optimal force-closure grasps, which is implemented by minimizing the proposed numerical test in the grasp configuration space, is also developed. The algorithm is computationally efficient and generally applicable. tt can be used for computing form/force-closure grasps on 3-D objects with curved surfaces, and with any number of contact points. Simulation examples are given to show the effectiveness and computational efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a hierarchical approach to generating precedence graphs for assembly planning. The basic idea of the approach is to identify constraint direction sets for all components of an assembly, hierarchically abstract out precedence relations for them, then obtain and evaluate all precedence graphs for each layer. The input to the approach consists of the mating relation graph (MRG), and hierarchical relation graph (HRG), which is deduced from MRG through geometric reasoning and knowledge. According to the MRG of an assembly, a revised algorithm to generate the non-directional blocking graph (NDBG) is proposed. Using the stored constraint direction sets and HRG of an assembly, all feasible precedence graphs for each layer are generated by another algorithm. In terms of operation replacement and graph transformation, the number of possible sequences allowed by a precedence graph is computed, from which an optimal precedence graph in a certain layer is selected. To verify the validity and efficiency of the approach, a variety of assemblies including some complicated products from industry are tested, and the corresponding results are also presented. [Copyright &y& Elsevier]

Explores possible applications of distance and pseudo distance functions. Significance of a fast and accurate collision detection and distance calculation in the field of robotics; Surveys the level of sophistication in the theory and algorithms of distance and pseudo distance functions between convex sets; Demonstration of their applications to robotics.

This paper presents a novel algorithm for evaluating the circularity of a mechanical part by using measurement points obtained with a coordinate measuring machine (CMM). Following the minimum zone criterion set forth in the current ANSI and ISO standards, evaluation of circularity is formulated as a non-differentiable unconstrained optimization problem, and based on the geometric representation of the necessary and sufficient condition for the optimal solution, an efficient steepest descent optimization procedure is proposed to find the circularity value. The steepest descent direction is determined by the method of calculating the minimum translational distance between two convex polygons, which is initially introduced in the field of robot path planning, and the length of the moving step is exactly determined by a presented geometrical method. A computational geometry-based method for pre-processing the measured data is also proposed. In comparison with existing methods, this algorithm has the advantages of computational efficiency and high precision. Simulations and practical example confirm the validity of the presented algorithm. [Copyright &y& Elsevier]

This paper applies kinematic geometry to investigate the problem of determining the cylindricity error of a mechanical part by using measurement points obtained with a coordinate measuring machine. For a point expressed in the machine reference frame and a nominal surface represented in its own model frame, a signed point-to-surface distance function is defined, and its increment with respect to the differential motion of the surface is derived. On this basis, four commonly used cylindricity evaluation methods, i.e., minimum zone cylinder method, maximum inscribed cylinder method, minimum circumscribed cylinder method and least-squares cylinder method, are formulated as nonlinear constrained optimization problems and nonlinear least-squares problem, and efficient sequential approximation algorithms are developed to solve them. For enhancing the performance of the algorithms, two relevant optimization problems and corresponding algorithms, i.e., localization of cylinder and minimum variance fitting of cylinder, are introduced to analytically provide proper initial solutions. By organizing all involved algorithms in a hierarchical structure, four complete cylindricity evaluation algorithms are presented. Comparing with existing methods, they have the advantages of implementational simplicity, computational efficiency and robustness. Examples confirm the validity of the proposed hierarchical algorithms. [Copyright &y& Elsevier]

High-accuracy on-line contouring error estimation plays a significant role in contouring accuracy control of multi-axis CNC machining. This paper focuses on developing a high-accuracy on-line estimation algorithm of five-axis contouring errors based on three-point arc approximation (TPAA). The nearest reference tool tip position related to the actual one is searched at first, then the tool tip position contouring error is estimated by the distance between the actual position and the arc formed by the nearest reference tool tip position and its two adjacent reference positions. Similar to the tool tip position, the TPAA algorithm is also conducted to estimate the tool orientation contouring error in the unit spherical coordinate system, where equal proportional factors of the tool tip position and the tool orientation arc-lengths are adopted to ensure the synchronization of the tool tip position contouring error and the tool orientation contouring error. The proposed contouring error estimation algorithm is adapted to different trajectory types and has higher estimation accuracy than linear segment approximation (LSA) algorithm for trajectory segments with high curvature. Various experiments with different testing tool paths are performed on an in-house developed five-axis experiment platform to verify the effectiveness of the proposed algorithm, and the results show that the proposed TPAA algorithm can estimate contouring errors with higher accuracy than existing algorithms based on the curvature arc iterative (CAI) algorithm and the LSA algorithm. [ABSTRACT FROM AUTHOR]

Abstract: To reduce contour error in contour-following tasks, a common approach is to design a controller based on the contour error information. Hence, real-time contouring error estimation plays an important role in contour-following control. However, the available second-order estimation formulas only apply to biaxial motion systems, and cannot be generalized to handle arbitrary contours tracked by multi-axis motion systems. In this paper, a point-to-curve distance function is defined, and its properties are investigated, especially, its second-order Taylor approximant is derived. On this basis, a novel second-order approach for calculating contour errors of arbitrary contours in real time is proposed. The inter-correlations between the present approach and four commonly used ones are classified. Simulation and experimental results demonstrate the effectiveness of the proposed contour error estimation algorithm. [Copyright &y& Elsevier]

Abstract: Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. To solve this problem, a real-time path-smoothing method is proposed, which adopts a curvature-continuous B-spline with five control points to blend the adjacent straight lines. The advantage of the transition scheme is that, G 2 continuity, analytical calculation of the curvature extrema, approximation error control and real-time performance are considered simultaneously. Then, a bidirectional scanning algorithm for jerk limited S-shape feedrate profile is proposed to evaluate the feedrate constraints. On this basis, a real-time look-ahead scheme, which comprises of path-smoothing, bidirectional scanning and feedrate scheduling, is developed to acquire a feedrate profile with smooth acceleration. Also, an arc-length based interpolation algorithm for mixed linear and parametric segments is proposed to overcome the difficulty of crossing different segments. With these schemes, the smoothness of both tool path and feedrate is guaranteed. Simulation and experiments on an X–Y–Z platform are conducted. The results demonstrate the feasibility and efficiency of the present algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, optimum positioning of the conical cutter for five-axis flank milling of slender surfaces is addressed from the perspective of approximating the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. Based on the observation that a conical surface can be treated as a canal surface, i.e. envelope surface of one-parameter family of spheres, the swept envelope of a conical cutter is represented as a sphere-swept surface. Then, an approach is presented to efficiently compute the signed distance between a point in space and the swept surface without constructing the swept surface itself. The first order differential increment of the signed point-to-surface distance with respect to the differential deformation of the tool axis trajectory surface is derived. By using the distance function, tool path optimizations for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework, and a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are given to confirm the validity and efficiency of the proposed approach. Comparing with the existing approaches, the present one improves the machining accuracy greatly. The rationale developed applies to general rotary cutters. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel model for fitting of spatial straight line based on Chebyshev norm. The problem is firstly formulated as a minimax problem, and then reformulated as a semidefinite programming (SDP) problem, which could be solved by many interior-point algorithms. The application of the proposed approach to two problems arising from manufacturing engineering, i.e. planning of the initial location of cylindrical cutter for flank milling and evaluation of the spatial straightness error, is discussed. Examples and numerical simulations illustrate the efficiency of the novel model. [Copyright &y& Elsevier]

Abstract: This paper demonstrates that a modern optimization method known as semi-definite programming (SDP) can serve as a unified tool for circularity and spatial straightness evaluation. Based on the minimum zone criterion (MZC), the problems of circularity and spatial straightness evaluation are formulated as differentiable constrained optimization problems firstly, and then reformulated as SDP problems. Within the SDP framework, both of the two aforementioned problems can be solved efficiently using recently developed interior-point algorithms, which are available in many efficient software packages. The effectiveness and efficiency of the novel approach are illustrated by examples and numerical simulations. [Copyright &y& Elsevier]

Abstract: For the purpose of controlling an X–Y table driven by linear motors with a high precision, an adaptive robust motion tracking control method is first introduced. The controller is developed based upon a class of SISO nonlinear systems whose nonlinear part can be linearly parameterized. The advantage of such a controller is that parametric uncertainties and unknown disturbances can be dealt with, which is essential for a high precision of the control of linear-motor-driven X–Y table. With the prior knowledge of the bounds of the system parameters, a discontinuous projection is utilized in the adaptive law to ensure the boundedness of the parameters estimates. The algorithm is then implemented on a real X–Y table driven by the linear motors. In the modeling of such a system, fiction effects are also considered, which is useful for the derivation of the adaptive law. Experiments on the X–Y table are carried out and the results show excellent tracking performance of the system. [Copyright &y& Elsevier]

Abstract: This paper presents a frequency domain method for estimating the parameters of a multi-frequency signal from the discrete-time observations corrupted by additive noise. With two weak restrictions on the window function used, a concise non-linear least squares-based parameter estimation model, which exploits the joint information carried by the spectral samples nearby each spectrum peak, is established, and utilising its particular structure an efficient two-step iterative algorithm is developed to solve it. The derived analytical expressions of the estimator variances indicate that this approach has superior accuracy over other computationally efficient frequency domain estimation methods. Simulation results confirm the validity of the presented method. [Copyright &y& Elsevier]

The linear filtering model is widely adopted because it can effectively control the areal autocorrelation function (AACF). However, these methods either constrain only half of the AACF or add the assumption of symmetry along one coordinate axis, which leads to a limited scope of applicability of the model. In this paper, a new AACF constraint for all spatial information is present. The new constraint function can provide objectives for all AACFs, and thus both isotropic rough surfaces, anisotropic surfaces of arbitrary orientation, and cross-textured surfaces can be reconstructed. The numerical experimental results show that the AACF fits well for isotropic as well as arbitrarily oriented anisotropic surfaces. For cross-textures surfaces, the errors are significant, indicating that the linear filtering model still has potential for improvement. • The generalized form of the optimization objective of the linear filter reconstruction model is presented. • Rough surface reconstruction problems with arbitrary texture orientations merged into a unified model. • L-BFGS algorithm is adopted to solve the optimization problem in the reconstructed model. [ABSTRACT FROM AUTHOR]

A novel analytical five-axis path-smoothing algorithm is developed for the high speed machining of a linear five-axis tool path. Segment junctions of the linear tool path in the machine tool coordinate system, which are tangent-discontinuous points, are all blended by two transition cubic Bézier curves. One cubic Bézier curve is used to smooth the segment junction of the translational path, and the other Bézier curve is used to smooth the segment junction of the rotational path. The tangency and curvature continuities are both guaranteed in the new path. The dual-Bézier transition algorithm has three advantages: (1) Compared with the path-smoothing method in the workpiece coordinate system, the new dual-Bézier transition method directly and simultaneously smooths the machine tool axis trajectories of both translational path and rotational path. The feed speed and stability will both be improved because the tool path discontinuities are the most important source of feed fluctuation. (2) The constraints of approximation error and the synchronization of parametrization of two smoothed curves, which are the most challenging problems in the smoothing of 5-axis tool path, are both considered. (3) The transition cubic Bézier curve pair has an analytical solution and can be easily integrated in the real-time interpolator. Computational examples and the cutting experiment of an impeller blade show that the novel path-smoothing method has obvious advantages in both feed smoothness and cutting efficiency over the original linear interpolator. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a full-discretization method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-discretization method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix. [Copyright &y& Elsevier]

• An algorithm is developed to estimate form errors of the non-circular turning in real time within the preset tolerance of calculation errors. • A novel control structure is designed to reduce form errors of the non-circular turning through compensating the motion commands of the fast radial servo drive. • Comparisons with the traditional cross-coupled contour error controller show that the proposed error compensation strategy has better dynamic performance. • Experimental results show that the proposed control strategy reduces about 30% of form errors compared with traditional controllers which only focused on tracking errors of individual drives. Parts with non-circular profiles are widely used in the automobile, navigation and aerospace areas, such as camshafts and convex ellipse pistons etc. The form accuracy of non-circular profiles directly affects the transmission accuracy and efficiency. However, existing non-circular turning studies mainly focused on improving the positioning accuracy of fast radial servo drives but neglected the form accuracy caused by the mismatch motions among all feed drives. In order to improve the form accuracy of non-circular turning, this paper proposes a novel control structure which treats the form error as a direct objective. The form error is estimated in real time at first within preset tolerance of calculation error. Then an on-line control strategy is designed to reduce form error through compensating the motion commands of the fast radial servo drive. The control loops of individual drives are decoupled and only position commands of the fast radial servo drive are compensated without touching the inside velocity and current loops. Comparisons with traditional contouring error control structure based on cross-coupled compensations of all axes show that the proposed error compensation strategy has better dynamic performance. Experimental results on the in-house developed non-circular turning prototype show that the proposed form error estimation and compensation methodology significantly improves the contouring accuracy than traditional controllers which only focused on tracking error control of individual drives. [ABSTRACT FROM AUTHOR]