Tool Tip Position Research Articles

Enhancing five-axis CNC toolpath smoothing: Overlap elimination with asymmetrical B-splines

In the realm of five-axis Computer Numerical Control (CNC) machining, the challenge of minimizing velocity, acceleration, and jerk fluctuations has prompted the development of various local corner smoothing methods. However, existing techniques often rely on symmetrical spline curves or impose pre-set transition length constraints, limiting their effectiveness in reducing curvature and maintaining velocity at critical corners. To comprehensively address these limitations comprehensively, a novel approach for local smoothing of five-axis linear toolpaths is presented in this paper. The proposed method introduces two asymmetrical B-splines at corners, effectively smoothing both the tool-tip position in the workpiece coordinate system and the tool orientation in the machine coordinate system. To fine-tune transition curve scales and minimize velocity disparities between adjacent corners, an overlap elimination scheme is employed. Furthermore, the two-step strategy emphasizes the synchronization of tool-tip position and tool orientation while considering maximal approximation error. The outcome is a blended five-axis toolpath that significantly reduces curvature extremes in the smoothed path, achieving reductions ranging from 36.28 % to 45.51 %. Additionally, the proposed method streamlines the interpolation process, resulting in time savings ranging from 5.68 % to 8.78 %, all the while adhering to the same geometric and kinematic constraints.

Optical tool deflection measurement approach using shadow imaging

In incremental sheet forming, geometrical deviations occur due to deflections of the forming stylus. To compensate the deviations, a non-contact in-process tool deflection measurement is required that is capable of measuring the tool tip position with a measurement uncertainty of 15 μm in a volume of 2.0 m × 1.0 m × 0.2 m. For this purpose, an optical multi-sensor system is designed. Each sensor evaluates lateral shift and magnification of the shadow cast from the LED attached close to the tool tip, to enable measuring the lateral and axial tool tip position component, respectively. The experimental validation shows that the sensing principle is sufficiently robust regarding ambient light. As a result, despite a remaining systematic error after calibration that dominates the uncertainty, the measurement requirements are fulfilled by a single sensor regarding the lateral position component. For the axial position component, a triangulation with two sensors is necessary.

Toolpath smoothing with reduced curvature and synchronized motion for hybrid robots

G01 commands are the most commonly used toolpath format in Computer Numerical Control (CNC) machining. Due to the discontinuity between adjacent linear segments, toolpath smoothing is necessary to improve machining efficiency and machined surface quality. This paper proposes an analytical C3 continuous local toolpath smoothing and synchronization method for a five-axis hybrid robot. Position and orientation smoothing are decoupled, with quintic B-spline segments replacing the original linear segments. The curvatures of the toolpath are reduced under constrained smoothing errors by weaving transition splines along the linear segments instead of confining them within the corners. A synchronization method based on arc length parameterization tailored to the smoothing method is also proposed. Tool tip position and tool axis orientation are synchronized using another monotonic, C3 continuous spline, which achieves smoother joint motion along the toolpath. For the hybrid robot with highly nonlinear kinematics, improved results in feedrate scheduling considering joint constraints can be realized. Simulations and experiments validate the effectiveness of the proposed method.

A novel tool path smoothing algorithm of 6R manipulator considering pose-dependent dynamics by designing asymmetrical FIR filters

The joint dynamic constraints of robot manipulators are normally set to conservative constant values to meet the dynamic tolerances at different poses, which leads to incomplete utilization of the joint drive capability. To fully utilize the drive capability of joint drives, this paper proposes an asymmetrical finite impulse response (FIR) filter-based tool path smoothing algorithm, which considers the pose-dependent dynamics of the robot with 6 rotational (6R) joints. To analyze the pose-dependent motor drive capabilities, a simplified dynamics model is established by considering both the tangential and joint dynamic constraints. An asymmetrical FIR filter-based tool path smoothing algorithm is also proposed to realize different constraints of the acceleration and the deceleration limits at different positions of the linear segments. The tool tip position and the tool orientation commands are respectively smoothed in the Cartesian coordinate system and spherical coordinate system, with the constraints of the tool path deviations in the task frame. The synchronization of the position and the orientation is realized by adjusting the parameters of FIR filters. The simulation and experimental results show that the proposed algorithm guarantees the corner error tolerances of the tool tip position and the tool orientation. Moreover, the proposed method improves the robot motion efficiency by more than 10 % through the full utilization of the joint drive capability compared with the traditional tool path smoothing algorithm based on symmetrical FIR filters.

Shadow-Imaging-Based Triangulation Approach for Tool Deflection Measurement.

As incrementally formed sheets show large geometric deviations resulting from the deflection of the forming tool, an in-process measurement of the tool tip position is required. In order to cover a measuring volume of 2.0 m × 1.0 m × 0.2 m and to achieve measuring uncertainties of less than 50 µm, a multi-sensor system based on triangulation is realized. Each shadow imaging sensor in the multi-sensor system evaluates the direction vector to an LED attached to the tool, and the three-dimensional position of the LED is then determined from the combination of two sensors. Experimental results show that the angle of view from the sensor to the LED limits both the measurement range and the measurement uncertainty. The measurement uncertainty is dominated by systematic deviations, but these can be compensated, so that the measurement uncertainty required for measuring the tool tip position in the ISF is achieved.

Surgical tooltip motion metrics assessment using virtual marker: an objective approach to skill assessment for minimally invasive surgery.

Surgical skill assessment has primarily been performed using checklists or rating scales, which are prone to bias and subjectivity. To tackle this shortcoming, assessment of surgical tool motion can be implemented to objectively classify skill levels. Due to the challenges involved in motion tracking of surgical tooltips in minimally invasive surgeries, formerly used assessment approaches may not be feasible for real-world skill assessment. We proposed an assessment approach based on the virtual marker on surgical tooltips to derive the tooltip's 3D position and introduced a novel metric for surgical skill assessment. We obtained the 3D tooltip position based on markers placed on the tool handle. Then, we derived tooltip motion metrics to identify the metrics differentiating the skill levels for objective surgical skill assessment. We proposed a new tooltip motion metric, i.e., motion inconsistency, that can assess the skill level, and also can evaluate the stage of skill learning. In this study, peg transfer, dual transfer, and rubber band translocation tasks were included, and nine novices, five surgical residents and five attending general surgeons participated. Our analyses showed that tooltip path length (p [Formula: see text] 0.007) and path length along the instrument axis (p [Formula: see text] 0.014) differed across the three skill levels in all the tasks and decreased by skill level. Tooltip motion inconsistency showed significant differences among the three skill levels in the dual transfer (p [Formula: see text] 0.025) and the rubber band translocation tasks (p [Formula: see text] 0.021). Lastly, bimanual dexterity differed across the three skill levels in all the tasks (p [Formula: see text] 0.012) and increased by skill level. Depth perception ability (indicated by shorter tooltip path lengths along the instrument axis), bimanual dexterity, tooltip motion consistency, and economical tooltip movements (shorter tooltip path lengths) are related to surgical skill. Our findings can contribute to objective surgical skill assessment, reducing subjectivity, bias, and associated costs.

Global toolpath smoothing for CNC machining based on B-spline approximation with tool tip position adjustment

B-spline curve approximation is widely used for fitting linear toolpaths to improve machining quality and efficiency in CNC machining. For a high-quality smoothing method, the control of both approximation error and curve curvature needs to be taken into account. To reduce the maximum curve curvature while meeting the precision requirements, a B-spline approximation scheme with tool tip position adjustment is proposed in this paper. Toolpaths are first divided into several subdivisions according to the discrete curvature of each tool tip point. For subdivisions that need adjustment, tool tip positions are adjusted to minimize the maximum discrete curvature. An existing approximation method named energy-term-incorporated progressive and iterative approximation for least square fitting (ELSPIA) is selected and improved to fit the adjusted toolpaths and lower the chord errors. For improving the numerical stability of the ELSPIA method, the way of searching appropriate foot point parameters is discussed in this paper. Deviation expansion factors of tooltip points are also defined to make the ELSPIA method suitable for fitting the adjusted toolpaths. Both simulations and experimental studies are conducted to prove that the proposed method can significantly decrease the maximum curvature of fitted B-spline curves and improve the machining efficiency without exceeding the tolerance. For example, experimental results show that for the tested butterfly and rabbit toolpaths, the proposed method can improve the machining efficiency by 2.61% and 2.37%, compared with the ELSPIA method without tool tip position adjustment.

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.

Overlap classification-based and kinematically coordinated corner rounding using double asymmetrical transitions for five-axis short-segmented tool path

For traditional corner rounding methods that adopt a pair of symmetrical and asymmetrical transition curves to round the corners in tool tip position and tool orientation, there are still two critical issues remain unsolved. One is the overlaps between adjacent transition curves have to be eliminated specifically to avoid the excessive approximation of the transition curves to the corners, the other is the asynchronous motions between tool tip position and tool orientation on the transition curves need to be addressed in addition to achieving smoothness at the junctions between transition curves and linear segments. For solving these two issues, this paper proposes the overlap classification-based and kinematically coordinated double asymmetrical transitions to round the corners. In this method, the overlaps between adjacent transition curves in tool tip position and tool orientation are first classified. Then, parameter synchronization is derived analytically and a targeted overlap elimination strategy is also proposed, so that the transition lengths without forcing the transition curves over-approach the corners are determined. Furthermore, to alleviate the asynchronous motions, the kinematics coordination between tool tip position and tool orientation is introduced, which is utilized to further evaluate the transition lengths to improve the kinematics performance of rotary axes. Finally, the computer simulations and machining experiment both demonstrate that our method can improve the feedrate and achieve the low acceleration and jerk of rotary axes indeed.

Digital Twin Modelling Method of Five-Axis Machine Tool for Predicting Continuous Trajectory Contour Error

The CNC machine tool is the passive executor of machining code. It cannot predict the machining accuracy during machining. If the error is found to be out of tolerance after processing, it will not only scrap the parts, but also greatly affect the processing efficiency. This phenomenon is very prominent when machining sculptured surface parts with five-axis machine tools. Therefore, this paper proposes a Digital Twin (DT) modeling method of five-axis machine tools for predicting Continuous Trajectory Contour Error (CTCE) caused by tracking errors and geometric errors. The DT consists of three parts: the Setpoints Trajectory (ST) model, the Actual Trajectory (AT) model considering tracking errors and geometric errors and the CTCE model. For a specific machine tool, according to the basic geometric information of the machine tool (tool length, kinematic chain information, etc.) and 41 geometric errors, the DT can be established. Inputting the Setpoints Positions (SPs) and the Linear Encoder Detection Positions (LEDPs), the DT can be used to predict the Tool-Tip Position Trajectory (TTPT) contour error and the Tool Orientation Trajectory (TOT) contour error. In order to verify the proposed method experimentally, the KMC400S U five-axis machine tool is selected to establish its DT by which the contour error of the S-shaped trajectory are predicted offline. Then, the DMU50 five-axis machine tool is selected to establish its DT to predict the contour error of the circular trajectory in real time. Combined with the deep motion mechanism, this paper proposes a DT modeling method for the vertical application scene of parts machining accuracy prediction, which is of great significance to developing the DT application theory and ensuring the machining accuracy of parts.

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.

A novel contour error evaluation index of the five-axis machine tools

The accuracy of high speed five-axis machine tool is mainly determined by the contour accuracy of machine tools. The contour accuracy evaluation and improvement of 5-axis machine tools have always been concerned. In order to simplify the calculation of five-axis contour error considering the synchronization between tool tip position and tool orientation, a novel five-axis contour evaluation index TCCE(Two-point Cutter location Contour Error) is proposed in this paper, which is based on the tool axis trajectory surface. The calculating method of the proposed index by NC servo encoder input from 5-axis machine tools is introduced. Finally, the experiment is performed to evaluate the trajectory accuracy and servo matching performance of the machine tool with the proposed contour error evaluation index and the calculating method.

An Analytical Corner Rounding Algorithm With G01 Shape Preserving for Five-Axis Computer Numerical Controlled Machining

Abstract G01 blocks are the widespread format of toolpath in computer numerical controlled (CNC) machining. For achieving smooth motion and eliminating the geometrical discontinuity at the block transitions, various local corner smoothing methods have been developed. However, in these methods, the loss of featured information of parts is inevitable. Focused on this topic, this article proposes a new analytical G2 continuous corner smoothing method with G01 shape preserving for five-axis linear toolpath by locally inserting specially designed B-splines into the corners of consecutive segments. First, by analyzing the condition of G01 shape preserving, the configuration expression of control points for B-splines is yielded for passing through G01 point. On this basis, the tool tip position is smoothed by symmetrical B-splines with minimum curvature in the workpiece coordinate system (WCS). Then, another asymmetrical B-splines is used to smooth tool orientation in the machine coordinate system (MCS). After that, the satisfaction conditions of parametric synchronization between tool tip position and tool orientation are mathematically derived at junctions, while the corresponding maximum smoothing errors are also constrained in WCS. Compared with the existing methods, not only the tool tip points and orientation vectors specified in original G01 blocks are preserved but also the optimal control points considering the curvature of smooth splines can be obtained analytically. Finally, simulations and experiments are performed to validate the effectiveness of the developed method.

A Novel Perception Framework for Automatic Laparoscope Zoom Factor Control Using Tool Geometry.

In conventional Minimally Invasive Surgery, the surgeon conducts the operation while a human or robot holds the laparoscope. Laparoscope control is returned to the surgeon in teleoperated camera holding robots, but simultaneously controlling the laparoscope and surgical tools might be cognitively demanding. On the other hand, fully automated camera holders are still limited in their performance. To help the surgeon to better focus on the main operation while maintaining their control authority, we propose an automatic laparoscope zoom factor control framework for Robot-Assisted Minimally Invasive Surgery. In this paper, we present the perception section of the framework. It extracts and uses the surgical tool's geometric characteristics to adjust the laparoscope's zoom factor, without any artificial markers. The acceptable range and tooltip's position frequency during operations are analysed based on the gallbladder removal surgery dataset (Cholec80). The common range and tooltip's heatmap are identified and presented quantitatively.

Stochastic Force-based Insertion Depth and Tip Position Estimations of Flexible FBG-Equipped Instruments in Robotic Retinal Surgery.

Vitreoretinal surgery is among the most delicate surgical tasks during which surgeon hand tremor may severely attenuate surgeon performance. Robotic assistance has been demonstrated to be beneficial in diminishing hand tremor. Among the requirements for reliable assistance from the robot is to provide precise measurements of system states e.g. sclera forces, tool tip position and tool insertion depth. Providing this and other sensing information using existing technology would contribute towards development and implementation of autonomous robot-assisted tasks in retinal surgery such as laser ablation, guided suture placement/assisted needle vessel cannulation, among other applications. In the present work, we use a state-estimating Kalman filtering (KF) to improve the tool tip position and insertion depth estimates, which used to be purely obtained by robot forward kinematics (FWK) and direct sensor measurements, respectively. To improve tool tip localization, in addition to robot FWK, we also use sclera force measurements along with beam theory to account for tool deflection. For insertion depth, the robot FWK is combined with sensor measurements for the cases where sensor measurements are not reliable enough. The improved tool tip position and insertion depth measurements are validated using a stereo camera system through preliminary experiments and a case study. The results indicate that the tool tip position and insertion depth measurements are significantly improved by 77% and 94% after applying KF, respectively.

Constrained haptic-guided shared control for collaborative human–robot percutaneous nephrolithotomy training

Percutaneous nephrolithotomy is a procedure used to treat patients with large or irregularly shaped kidney stones. Surgical instruments are inserted through a small incision to access the kidney and remove the calculi. Surgeons who have less experience with the procedure manifest significantly higher rates of complications due to the procedure’s steep learning curve. This issue is further exacerbated by a lack of training opportunities in clinical settings. This paper introduces a teleoperative framework that can provide training to surgeons as well as assistance during procedures, based on two main components. Firstly, a type of constrained inverse kinematics that decouples the tooltip position from its orientation using a remote centre of motion, and incorporates the joint limits analytically. This reduces the workload of the procedure by having the surgeon control only the tooltip position rather than the position and the orientation while preventing the inverse kinematics from returning joint angles outside of the robot’s abilities. This kinematic framework also allows a three-degrees-of-freedom haptic device to control a six-degrees-of-freedom manipulator. Secondly, haptic feedback is provided to help guide and teach the surgeon during the procedure. Haptic feedback allows the surgeon to remain in full control during the procedure while still receiving haptic cues and assistance.Experimental results indicate that the haptic cues improved user’s accuracy, and they had shorter and smoother paths. This leads to a shorter procedure time overall. The results also indicate that the haptic assistance helped teach users the ideal trajectory of the procedure and that users who were taught with haptic feedback performed better than those who never experienced any haptic feedback.

Feedrate blending method for five-axis linear tool path under geometric and kinematic constraints

To tackle the bottlenecks of the linear interpolation and two-step geometry-based corner smoothing methods in five-axis machining, an analytical one-step corner smoothing method based on feedrate blending is proposed in this paper. In the proposed algorithm, the maximum kinematics adjustments scheme together with the variable acceleration and jerk optimization algorithms are first adopted to determine the dynamic performances along the linear segments. Meanwhile, the smooth feedrate profiles of the tool tip position in the workpiece coordinate system (WCS) and tool orientation in the machine coordinate system (MCS) are generated by the tool tip mastered jerk-limited feedrate scheduling scheme, with which the tool tip feedrate and angular feedrate in the WCS, together with the translational and rotatory feedrate in the MCS are well bounded. Then, the blending time is calculated based on the specified tool tip error and tool orientation error in the WCS, and the feedrate profiles are blended to generate the smooth trajectories under axial kinematic constraints along the whole paths in both the WCS and MCS. Since the proposed method can generate the smooth corner trajectory by directly blending the feedrate profiles, it eliminates the construction and interpolation process of parametric splines in two-step corner smoothing algorithms and shows better tracking and real-time performances. Finally, simulation and experimental results validate the effectiveness and feasibility of the proposed method.

A G3 continuous tool path smoothing method for 5-axis CNC machining

The chain of short linear tool path segments is the most common form for the five-axis machining by Computer Numerical Control (CNC) machines. The connection points of the linear path segments lead to the discontinuities in position, velocity, acceleration, and jerk, resulting in fluctuation of machine motion which leaves undesired marks on the finished surface. This paper presents a geometric smoothing algorithm by enforcing the continuity of first, second, and third geometric derivatives of the splined path segments at their meeting points for the five-axis machining of curved surfaces. The linear tool path segments are first smoothed by Bezier splines while constraining the path errors within a set tolerance. The tool path segments, that cannot be smoothed within the path error limit, are smoothly connected at the connection points. The tooltip position and tool axis orientation displacements are synchronized to avoid discontinuous displacements along the tool axis. The proposed algorithms are demonstrated with simulations and experiments in following a five-axis, curved tool path on a CNC machine tool. It is shown that the proposed G3 continuous tool path algorithm gives smoother tool-tip and tool axis orientation, reduces the tracking errors, contour errors and amplitudes of jounce at the connections of segments along the tool path, leading to the smoother surface for the precision five-axis machining of sculptured surfaces.

Tool Path Optimization for Robotic Surface Machining by Using Sampling-Based Motion Planning Algorithms

Abstract This paper develops a tool path optimization method for robotic surface machining by sampling-based motion planning algorithms. In the surface machining process, the tool-tip position needs to strictly follow the tool path curve and the posture of the tool axis should be limited in a certain range. But the industrial robot has at least six degrees-of-freedom (Dof) and has redundant Dofs for surface machining. Therefore, the tool motion of surface machining can be optimized using the redundant Dofs considering the tool path constraints and limits of the tool axis orientation. Due to the complexity of the problem, the sampling-based motion planning method has been chosen to find the solution, which randomly explores the configuration space of the robot and generates a discrete path of valid robot state. During the solving process, the joint space of the robot is chosen as the configuration space of the problem and the constraints for the tool-tip following requirements are in the operation space. Combined with general collision checking, the limited region of the tool axis vector is used to verify the state’s validity of the configuration space. In the optimization process, the sum of the path length of each joint of the robot is set as the optimization objective. The algorithm is developed based on the open motion planning library (OMPL), which contains the state-of-the-art sampling-based motion planners. Finally, two examples are used to demonstrate the effiectiveness and optimality of the method.

An analytical G3 continuous corner smoothing method with adaptive constraints adjustments for five-axis machine tool

In this paper, an analytical local corner smoothing method is proposed with two specially designed quartic curves to generate smooth motion trajectories of five-axis linear segments. One symmetrical quartic B-spline curve is used to smooth the tool tip position in workpiece coordinate system (WCS); meanwhile, another asymmetrical quartic B-spline curve is used to smooth the tool orientation in machine coordinate system (MCS). With the proposed method, not only the transition error of tool tip position and the smoothing error of the tool orientation are mathematically constrained in WCS, but the G3 continuity of the tool tip position and tool orientation are guaranteed along the entire toolpath. Besides, the maximum possible machining error of tool tip position caused by transition error and chord error is also controlled analytically by transition error adjustment. What’s more, in feedrate scheduling, the feedrate of tool tip is moderately adjusted by smooth feedrate profile, which can limit the maximum feedrate of tool orientation and achieve continuous axial feedrate and acceleration. Finally, the effectiveness and feasibility of the proposed method have been validated via simulations.