Angular Position Error Research Articles

Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement. We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control (CNC) machine tools. This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method. We consider a three-axis gantry-type CNC machine tool, and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain. The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle. A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg–Marquardt nonlinear least squares method, and the geometric error is solved using Taylor’s first-order linearization iteration. The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer. For a volume of 800 mm × 1000 mm × 350 mm, the maximum differences of the linear, angular, and spatial position errors were 2.0 μm, 2.7 μrad, and 12.0 μm, respectively, which verifies the accuracy of the proposed algorithm. This research proposes a modeling method for the precise measurement of errors in machine tools, and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

Error mechanism analysis and accuracy enhancement method for circular gratings angle-measuring system

In order to raise the accuracy of the circular gratings angle-measuring system, a comprehensive error model is established, and a novel compensation method is proposed. Firstly, many error sources, including the rotary errors of axis system, the installation eccentricity and the inclination of the circular grating disc, the graduation line error of the circular grating disc, and the installation error of the multiple readingheads of the high precision circular gratings angle-measuring system are comprehensively taken into consideration. Secondly, the position and attitude errors are propagated to the angular position outputs, thus the mathematical relationships between error sources and the angular position error are established. Aiming at multiple readingheads system, the mechanism of influence of the error sources on the angular position error is unveiled, and the mechanical error identification and reduction method is proposed. After that, a checking system with a 23-mirrored polygon and an autocollimator is set up, and the complete combinatorial method of separating the angular position errors from the readouts of the autocollimator precisely is used. Finally, the angular position error compositions are separated by the harmonic analysis method, and the concerned error coefficients are compensated. The experimental results show that the nominal indication interval value of the angular position errors is reduced to 0.23" by the mechanical error reduction method, and then the nominal indication interval value of the angular position errors is reduced to 0.12" by software measurement method. And the two sets’ repeatability of the separated biases of the 23-mirrored polygon before and after compensating is 95%.

Geometric error compensation method using the Laser R-test

Traditional methods for measuring geometric errors in machine tools, including interferometry and Double Ball Bar (DBB), are known to be expensive and time-intensive. Consequently, a non-contact calibration system called the “Laser R-test” has been developed. This innovative system is designed to measure both position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) efficiently. Since its development in 2000, this tool has been instrumental in analyzing eccentricity errors, angular position errors, and simultaneous trajectory errors. Through extensive research, it has been determined that the total error in a five-axis machine tool can be controlled to below 40 µm after compensating for eccentricity parameters and angular position errors. However, reducing this error to below ± 10 µm is challenging, primarily due to wobble errors in the orientation of the rotary axis without compensating. In this study, a new methodology based on Laser R-test and Rodrigues’ rotation formula has been developed to establish a PIGE model of rotary axis. Based on the methodology, the 8 PIGEs can be analyzed by measuring 5 coordinate positions. The compensation of 8 PIGEs in the rotary axis is completed within 30 min using the inspection path. Compatibility with ISO-10791–6 standards for BK1, BK2, and BK4 path tests is confirmed, validating the compensation effects. A precision of below ± 10 µm is achieved, with inspection time reduced by over 50%. This system can complete multiple errors by simply using the different paths. This greatly reduces the setup time for future users, enhancing its commercial applicability.

Simulation analysis and collaborative optimization of key components of the precision detection platform for high precision encoder

To realize the error detection of the high-precision photoelectric encoder, the optical small-angle precision measurement principle of the photoelectric autocollimator and single-sided mirror, and the 360° full circle measurement principle of angle inversion of the compound biaxis turntable are used to establish the precision detection platform of the encoder. The error model of the biaxial structure in the photoelectric coding error detection platform is established by introducing the error sources of the biaxial structure, such as the coaxiality error, angular position error, and installation error. At the same time, the biaxis structure and error models are used to optimize the compound biaxis structure system. By analyzing the natural frequency and vibration characteristics of the structure, the rationality and reliability of the compound biaxis system of the high-precision encoder precision detection platform are verified.

Position control based on Gaussian function applied on magneto-rheological fluid disc brake of a hybrid mechanical device (MR brake - DC motor)

This article presents an angular position control, based on the Gaussian function, of a Magneto-Rheological fluid disc brake (MR brake) driven by a DC motor. Our proposed control strategy is to apply a continuous magnetic flux density to the MR brake, which will be maximum when the proportional controller of the DC motor reaches the desired position to brake the hybrid device. The MR brake controller activates a braking torque that adopts the behavior of the Gaussian function instead of a pulsed braking torque as provided by other commonly used controllers (On-Off controllers). The response of the MR brake controller, which is presented in a closed-loop feedback system, depends on the angular position error of the shaft and a tuning parameter representing the critical angular position at which the magnetic flux density, which is applied to the MR brake, reaches 60.65% of its maximum value. The advantage is to avoid knowing the dynamic parameters, such as the inertia of the mechanical device or its speed, and to reject these perturbations by a simple tuning parameter of the MR brake. To show the effectiveness of the proposed controller, the dynamic model of a slider-crank mechanism is considered. The results showed similar behavior as conventional controllers, where overshoot and oscillations were minimized. This behavior has been obtained in other research articles using controllers that require a greater amount of data processing.

Model-based shared control approach for a power wheelchair driving assistance system using a force feedback joystick

This paper presents a haptic-based assistance system (AS) for power wheelchair users designed using the model-based shared control approach. The idea is to combine robust control with a high-level driving supervisor in order to successfully share control authority between the wheelchair user and the assistance system. This shared control strategy is composed of two parts, namely an operational part and a tactical part. Through the haptic joystick interface, this assistance system aims to reduce user’s effort when manipulating the joystick, guide the user to avoid any potential collisions, and maintain the active participation of the user in driving the wheelchair. In the operational part, an optimal Takagi-Sugeno fuzzy control approach is proposed to deal with the time-varying user’s intention represented by his desired longitudinal and angular position errors and velocities and hand torques. The control design is formulated as an LMI optimization problem which can be easily solved with numerical solvers. Two unknown input observers for Takagi-Sugeno fuzzy model have been designed to estimate the user’s intention in order to generate an assistance torque via a haptic force feedback joystick. The control supervisor in the tactical part, aims to provide a decision-making signal which allows for the conflict management based on the user hand torque estimation. A specific algorithm has been developed to solve the conflict between the user’s desired actions and the suggestions from the assistance system to ensure the user remains the final decision-maker. Experimental results show the effectiveness and the validity of the proposed assistance system.

Design and Analysis of Limited-Angle Wound Rotor Resolvers

In this study, the comprehensive design and analysis of a limited-angle wound rotor resolver (LAWRR) with high precision are presented. The effect of two major design parameters, including stator and rotor number of turns combinations, as well as the transformation ratio, on angular position accuracy is investigated. To determine the optimal number of turn combinations of LAWRRs with concentric windings (CWs), a simple analytical method consisting of calculating the total harmonic distortion (THD) percentage of the winding distribution waveform is employed. The fundamental operating principle and parametric analyses are carried out using finite element analysis (FEA), which is then followed by verification of the analytical calculations and determination of the optimal number of turn combinations. Moreover, the cross-correlation effect of the signal (stator) and excitation (rotor) winding configurations has been considered. Time-averaged, peak to peak, and maximum position errors were calculated for accuracy analyses. Finally, a prototype is built and tested to validate the analytical and numerical analyses, as well as the main parameters and angular position error.

Experimental comparison of the effect of the number of redundant rotors on the fault tolerance performance for the proposed multilayer UAV

In this paper, experimental investigation of the flight performance of the proposed universal Unmanned Aerial Vehicle (UAV) in case of rotor failures is presented. In the experimental flight tests, proposed universal UAV that can be converted to many different configurations due to its non-standard multi-layer structure was used in two different configurations as a standard octorotor and a multi-layer dodecarotor. Multiple outdoor experiments are conducted to show flight safety and reliability of the proposed UAV in terms of rotor failure tolerance. In order to evaluate flight safety and reliability of the proposed UAV, take-off, hovering and landing flight performance analyzes were performed in cases where one or two motors/propellers were completely lost. As performance criteria, errors in the UAV’s roll, pitch and yaw angles, altitude error and vibration in three axes were determined. The flight test results are presented both numerically and graphically. According to the results, multi-layer dodecarotor type has shown a more stable flight performance in terms of angular position errors. In addition, in both types of UAVs, in the case of failure of two rotors rotating in the opposite direction, it has been observed that the error in yaw angle is less than a rotor failure, as expected. Likewise, in the case of failure of two rotors rotating in the same direction, performance loss was observed in the control of yaw angle.

Probabilistic ensemble neural network model for long-term dynamic behavior prediction of free-floating space manipulators

For complicated dynamic systems, such as free-floating space manipulators (FFSMs), building a sufficiently precise model to predict their long-term behavior is still quite challenging, as nonlinearities that are too complicated to describe always exist. In this paper, a probabilistic ensemble neural network (PENN) is proposed to predict the long-term dynamic behavior. The PENN combines the probabilistic deep network dynamics model with the ensemble method and uses sampling-based uncertainty propagation for long-term prediction to address the aleatoric and epistemic uncertainties in dynamic system estimation. A simulation demonstrates the effectiveness of the PENN. The joint angular position error is approximately 0.05 deg for one-step prediction and 10 deg for 100-step propagation. A comparison with cases in which only either probabilistic NNs or the ensemble method is used shows the urgent need to combine them to deal with the compounding error of long-term prediction. The effects of different hyperparameters are evaluated in terms of the predictive error after 100 steps of bootstrap propagation. The results show that the PENN is robust to the hyperparameters.

Improvement of Position Estimation of PMSMs Using an Iterative Vector Decoupling Algorithm

This paper presents an improvement of sensorless techniques based on anisotropy for the estimation of the electrical angular position of synchronous machines by means of an iterative algorithm. The presented method reduces the effect of the fourth saliency harmonics on the measured signals avoiding the use of an observer or filter, thus, no additional dynamics are introduced on the system. Instead, a static algorithm based on iterative steps is proposed, minimizing the angular position error. The algorithm is presented and applied using the DFC (Direct Flux Control) technique but it is not limited to this choice. The advantages and limitations of this method are presented within this paper. The proof of the algorithm convergence is given. Simulations and experimental tests are performed in order to prove the effectiveness of the proposed algorithm.

Trajectory-tracking control of a planar parallel robot using generalized predictive control with constraints

This paper presents the generalized predictive control with constraints, implemented to a planar parallel robot in order to calculate and track the desired trajectory of the end-effector of this robot. The manipulator is driven by three brushless direct current motors, and each one has an encoder to measure the velocity and rotation angles of the motors. Three constraints were considered to interact with the control law: control signal, terminal response and the over impulse constraints. The performance of the control law is evaluated in the simulation environment using Matlab/Simulink with the physic model developed through simscape multibody. The angular position and velocity errors for each of the three motors were calculated. Likewise, the output torques for each one were estimated. The results proved that the control law proposed with the constraints imposed for each motors has a good efficiency with a stable response time of the robot in performing the trajectory tracking, contributing to the scientific community a strategy of predictive optimization of control actions with multiple constraints applied on parallel robots.

High Precision Fiber-Optic Gyroscope Resolution Test Method Based on Low Precision Turntable

Aiming at the inability of low precision ordinary turntable to effectively measure the resolution of the high-precision fiber-optic gyroscope (FOG), this paper proposes a method for a high-precision FOG resolution test based on a low-performance turntable with the earth's angular velocity as the input value. Taking a two-axis turntable with 1 arc-minute angular precision as an example, the Two-Degrees-Of-Freedom (2-DOF) theoretical angle range is obtained, through stationary gyro biaxial angular position error incremental output analysis. The method can be used for high-precision FOG including, 0.001 deg/h, 0.0001 deg/h, 0.00001 deg/h (three typical accuracies) resolution measurements. The detailed test steps are presented. Simulation results show that traditional test methods fail under the same working conditions, while the proposed method can effectively measure the high-resolution gyro resolution effective coverage within the theoretical angle range of the corresponding two-axis turntable. Experimental results demonstrate that the two-axis turntable based on with 1 arc-minute angular precision can effectively perform a high-precision FOG resolution of 0.005 deg/h.

Motion Estimation for a Compact Electrostatic Microscanner via Shared Driving and Sensing Electrodes in Endomicroscopy.

We present a method to estimate high frequency rotary motion of a highly compact electrostatic micro-scanner using the same electrodes for both actuation and sensing. The accuracy of estimated rotary motion is critical for reducing blur and distortion in image reconstruction applications with the micro-scanner given its changing dynamics due to perturbations such as temperature. To overcome the limitation that no dedicated sensing electrodes are available in the proposed applications due to size constraints, the method adopts electromechanical amplitude modulation (EAM) to separate motion signal from parasitic capacitance feedthrough, and a novel non-linear measurement model is derived to characterize the relationship between large out-of-plane angular motion and circuit output. To estimate motion, an extended Kalman filter (EKF) and an unscented Kalman filter (UKF) are implemented, incorporating a process model based on the micro-scanner's parametric resonant dynamics and the measurement model. Experimental results show that compared to estimation without using the measurement model, our method is able to improve the rotary motion estimation accuracy of the micro-scanner significantly, with a reduction of root-mean-square error (RMSE) in phase shift of 86.1%, and a reduction of RMSE in angular position error of 78.5 %.

On-machine calibration of angular position and runout of a precision rotation stage using two absolute position sensors

A calibration method for a precision rotation stage is proposed to evaluate angular position error and runout of the stage with robustness to alignment error and a simple setup. It consists of two absolute position sensors and a two-dimensional (2D) scale. Therefore, it is proper for on-machine calibration where enough install place and fine adjustment might be unavailable. Angular positions are obtained using two coordinate values on the 2D scale fixed on the rotating plate, and the complete runout is calculated by processing these values through Fourier analysis. The calibrated angular positions of a rotation stage agreed with the reference values within ±1″. The proposed system measured runout with the repeatability of 80 nm and error of 120 nm. An effective compensation method for measurement error caused by out-of-plane motion of the rotation stage was discussed and its feasibility was proved though experiments.

Design of Terminal Sliding Position Control for Electronic Throttle Valve System: a Performance Comparative Study

This research article presents the design of two sliding mode control schemes represented by sliding mode backstepping controller (SMBC) and terminal sliding mode controller (TSMC) to control robustly the angular position of electronic throttle (ET) plate. The stability analysis of throttle valve system controlled by SMBC and TSMC has been studied and the asymptotic convergence of angular position errors based on each controller has been proved. In addition, the finite-time convergence concerning the sliding variable of the terminal sliding mode control strategy has been investigated and addressed. Moreover, the paper has taken into account the constrained control effort dictated by the limited supply battery. The effectiveness of the proposed sliding mode control schemes for throttle valve system has been verified using computer simulations on MATLAB format. Accordingly, the comparison in performance is established between the proposed control schemes and the results based on computer simulations have showed that the terminal sliding mode controller outperforms the sliding mode backstepping controller in terms of robustness and transient characteristics.

Optimal measurement angles of the three-probe spindle error motion separation technique

The three-probe error separation technique uses three displacement sensors to separate the spindle radial error motion from the artefact roundness error. The choice of appropriate sensor angles is crucial for an accurate and complete separation. This work discusses the optimal arrangement of the sensors’ angular positions in detail, including the influence of angular position errors of the sensors on the separation results. The optimization goal is to find a suitable sensor arrangement to simultaneously maximize the minimum value and the average value of the transfer function, in order to improve the anti-interference ability and ensure measurement precision of the three-probe method without harmonic suppression. The result shows that there is a global optimum for the sensor angles for a specific range of harmonics. The obtained optimal measurement angles under different harmonic ranges should be useful for applications of the three-probe method.

Optimal-arrangement-based four-scanning-heads error separation technique for self-calibration of angle encoders

Conventional methods for the calibration of angle encoders typically only consider the graduation error of the encoder’s circular scale. However, the radial motion of the circular scale during its rotation, due to its eccentricity and the axis of rotation radial error motion, can also introduce noticeable errors to the angle measurement in most practical applications. Based on the analysis of the influence of radial motion, an optimal-arrangement-based four-scanning-heads error separation technique for in situ self-calibration of angle encoders is presented. This Fourier-based technique uses the basic self-calibration model to measure the first-order Fourier component of the encoder error which includes the contribution of eccentricity. Meanwhile, the separation technique is utilized to separate the residual Fourier components of the graduation error from the measurement deviation due to radial error motion. The effect of the scanning heads’ angular position errors on the calibration results is discussed. Optimal arrangements of the four heads are achieved to avoid the suppression of the Fourier components, and reduce the propagation of errors. Numerical results and experimental comparisons demonstrate the effectiveness of the proposed method. Moreover, this technique can also be used for measuring the spindle radial error motion for some users.

Exact laser beam positioning for measurement of vegetation vitality

PurposeThe purpose of this paper is to present a novel application for a newly developed Technical Vision System (TVS), which uses a laser scanner and dynamic triangulation, to determine the vitality of agriculture vegetation. This vision system, installed on an unmanned aerial vehicle, shall measure the reflected laser energy and thereby determine the normalized differenced vegetation index.Design/methodology/approachThe newly developed TVS shall be installed on the front part of the unmanned aerial vehicle, to perform line-by-line scan in the vision system field-of-view. The TVS uses high-quality DC motors, instead of previously researched low-quality DC motors, to eliminate the existence of two mutually exclusive conditions, for exact positioning of a DC motor shaft. The use of high-quality DC motors reduces the positioning error after control.FindingsPresent paper emphasizes the exact laser beam positioning in the field-of-view of a TVS. By use of high-quality instead of low-quality DC motors, a significant reduced positioning time was achieved, maintaining the relative angular position error less than 1 per cent. Best results were achieved, by realizing a quasi-continuous control, using a high pulse-width modulated duty cycle resolution and a high execution frequency of the positioning algorithm.Originality/valueThe originality of present paper is represented by the novel application of the newly developed TVS in the field of agriculture. The vitality of vegetation shall be determined by measuring the reflected laser energy of a scanned agriculture zone. The paper’s main focus is on the exact laser beam positioning within the TVS field-of-view, using high-quality DC motors in closed-loop position control configuration.

Dynamic Learning from Adaptive Neural Control of Uncertain Robots with Guaranteed Full-State Tracking Precision

A dynamic learning method is developed for an uncertain n-link robot with unknown system dynamics, achieving predefined performance attributes on the link angular position and velocity tracking errors. For a known nonsingular initial robotic condition, performance functions and unconstrained transformation errors are employed to prevent the violation of the full-state tracking error constraints. By combining two independent Lyapunov functions and radial basis function (RBF) neural network (NN) approximator, a novel and simple adaptive neural control scheme is proposed for the dynamics of the unconstrained transformation errors, which guarantees uniformly ultimate boundedness of all the signals in the closed-loop system. In the steady-state control process, RBF NNs are verified to satisfy the partial persistent excitation (PE) condition. Subsequently, an appropriate state transformation is adopted to achieve the accurate convergence of neural weight estimates. The corresponding experienced knowledge on unknown robotic dynamics is stored in NNs with constant neural weight values. Using the stored knowledge, a static neural learning controller is developed to improve the full-state tracking performance. A comparative simulation study on a 2-link robot illustrates the effectiveness of the proposed scheme.

Relative Position Error Analysis for Mars Probes

Abstract: The relative angular position error covariance model of two deep space probes is propagated based on the error covariance analysis method, and is used for the relative angular position error analysis for multiple deep space probes. The differential time delay model of Same Beam Interferometry (SBI) about the relative right ascension and relative declination of two deep space probes is established, and the information matrixes of two ground-based baseline differential time delay measurements are obtained. The relative angular position error covariance is established, and the influence of measurement error and measurement geometry on relative angular position error is analyzed. The results show that in appropriate measurement geometry the relative right ascension and relative declination error of Mars probe are in order of 0.1nrad when the measurement error is in order of pico-second.