Angular Position Measurements Research Articles

Dynamics Parametrization and Calibration of Flexible-Joint Collaborative Industrial Robot Manipulators

Many collaborative robots use strain-wave-type transmissions due to their desirable characteristics of high torque capacity and low weight. However, their inherent complex and nonlinear behavior introduces significant errors and uncertainties in the robot dynamics calibration, resulting in decreased performance for motion and force control tasks and lead-through programming applications. This paper presents a new method for calibrating the dynamic model of collaborative robots. The method combines the known inverse dynamics identification model with the weighted least squares (IDIM-WLS) method for rigid robot dynamics with complex nonlinear expressions for the rotor-side dynamics to obtain increased calibration accuracy by reducing the modeling errors. The method relies on two angular position measurements per robot joint, one at each side of the strain-wave transmission, to effectively compensate the rotor inertial torques and nonlinear dynamic friction that were identified in our previous works. The calibrated dynamic model is cross-validated and its accuracy is compared to a model with parameters obtained from a CAD model. Relative improvements are in the range of 16.5% to 28.5% depending on the trajectory.

Simultaneous Measurement and Simulation of Angular Position and Angular Speed for Time Grating

A method is presented in order to realize the measurement of angular position and angular speed simultaneously based on the theory of time grating and the measurement of angular position and angular speed is transformed into the measurement of phase difference. Four orthogonal excitation signals are generated by the internal phase-locked loop module of FPGA. The excitation signals are superposed and input to the stator sensor. At this time, the rotation of the motor causes the rotation of the rotor sensor to generate the induction signal. The phase difference of the two signals will be obtained by the input comparison circuit of the induction signal and the excitation signal. The phase difference will be processed in FPGA, and finally the angular position and angular speed values will be obtained. The simulation results show that the method is feasible. The experimental results show that the accuracy error of angular position measurement can reach ±3", and the measurement speed stability can reach 3rpm(3%o) when the angular speed is 1000rpm.

Applied Sensor Fusion: Tuning Parameters of CF and KF by means of Evolution Strategies

From the point of view of metrology, inertial sensors acting separately present undesirable performance in the measurement of angular position. In order to provide measurements with greater precision and accuracy, the measures of each of these sensors are typically fused by means of filters. The performance parameters of these filters are hard to tune and several works have been using exhaustive search algorithm or manual experimental tests to tuning these parameters. However, the exhaustive search algorithm usually requires a large computational effort and adjusting parameters manually does not guarantee that the estimated parameters are optimized. In this work, it has been proposed the tuning of the Complementary Filter (CF) and the Kalman Filter (KF) through the heuristic method Evolutionary Strategies. Experimental results have shown that our method is a useful tool that considerably reduces the time to find the tuning of the FC and the FK. In addition, the use of the tuned FC and FK improved significantly metrological characteristics of the system. The use of Bland and Altman's statistical method show that the measurements of the angular position have a good agreement with the actual angular position of a servo motor.

Understanding process force transients with application towards defect detection during friction stir welding of aluminum alloys

The formation of sub-surface defects during friction stir welding has limited the adoption of the process in high volume production. A potential exists to eliminate/reduce the need for costly post weld inspection of such defects through the development of an in-process defect detection method based on a measured process output. The current state of in-process defect detection consists primarily of applying “black box” methods of correlating process outputs to defect occurrence without a fundamental physical understanding of what is producing the change in the output. This approach constrains the application of such methods when altering any aspect of the friction stir welding process. The current study seeks to provide a fundamental physical explanation as to what is driving the oscillation of friction stir welding process forces at the tool rotational frequency, as well as what is occurring when the tool interacts with defects and the oscillatory process forces are altered. A novel understanding was enabled through the synchronization of force measurements with angular position measurements of tool features. The results suggest that the eccentric motion of the tool and/or the rotation of a slanted shoulder surface are the primary drivers of process force oscillations. A fundamental explanation of the interaction between features on the tool probe and defective volumes has been proposed. The physical understanding helps to explain how altering the process will alter the force transients on which the detection method is based, which will enable a more robust and transferable method.

Design and Realization of a Compact High-Precision Capacitive Absolute Angular Position Sensor Based on Time Grating

This article proposes a compact and high precision capacitive absolute angular position sensor based on time grating. The sensor consists of a stator and a rotor with three concentric capacitor structures forming primary and auxiliary angular displacement measurement components. The primary component combines a single middle-row capacitive structure with an outer-row capacitive structure to obtain high-precision displacement measurements composed of N measurement periods. The auxiliary component employs a single inner-row capacitive structure with a single spatial period over the 360° measurement range of the sensor in conjunction with a remodulation scheme to obtain displacement measurements composed of N - 1 measurement periods. Combining the measurements of the primary and auxiliary components in a manner similar to vernier calipers yields high-precision absolute angular position measurements. The sensor design and remodulation scheme facilitate good sensor compactness. The measurement performance of the proposed design is evaluated via tests of a prototype sensor with an outer diameter of 60 mm fabricated by printed circuit board technology. The prototype sensor is demonstrated to obtain a measurement resolution of 3" and a measurement accuracy of ±10" over the 360° measurement range of the sensor, indicating that the proposed sensor design has considerable potential for high precision applications.

Calibration, Compensation and Accuracy Analysis of Circular Grating Used in Single Gimbal Control Moment Gyroscope.

The accuracy of the circular grating is the key point for control precision of the single gimbal control moment gyroscope servo system used in civilian micro-agile satellites. Instead of using the multi reading heads to eliminate eccentricity errors, an algorithm compensation method based on a calibration experiment using a single reading head was proposed to realize a low-cost and high accuracy angular position measurement. Moreover, the traditional hardware compensation method using double reading heads was also developed for comparison. Firstly, the single gimbal control moment gyroscope system of satellites was introduced. Then, the errors caused by the installation of the reading head were studied and the mathematic models of these errors were developed. In order to construct the compensation function, a calibration experiment using the autocollimator and 24-sided prism was performed. Comparison of angle error compensation using the algorithm and hardware method was presented, and results showed that the algorithm compensation method proposed by this paper achieved the same accuracy level as the hardware method. Finally, the proposed method was further verified through a control system simulation.

Local geometric error corrections for a metrological scanning probe microscope

A local geometric error correction method is developed for a metrological scanning probe microscope. The method corrects geometric errors in stage displacements using the interferometric measurements of angular position and known geometric offsets. Local and global error correction methods are considered and general scaling dependences on the number of measured steps or points are derived and compared. For the local method, the total uncertainty scales the same or decreases with a sufficient number of measurement steps compared with the global method. Implementation of the local geometric error correction method is demonstrated on measurements of a three-dimensional height standard artefact. The applied error correction method reduces the contribution of geometric errors to the uncertainty budget by two orders of magnitude. The presented approach can be extended to any scanning technique where a measurement translation mechanism can be identified and accurately quantified by relating the measured values with a measurand.

Metod za samokalibraciju magnetno-rezistivnog senzora ugaone pozicije u servo sistemima

Magneto-resistive and Hall angular position sensors are frequently used in servo systems, due to their reliability, longevity, and tolerance to environmental conditions. In this paper, a measurement error compensation is integrated into the servo system control structure. The compensation consists of two steps: a linear compensation of the magnetic field vector measurement error, and harmonic compensation of the angular position measurement error. The selfcalibration method uses data collected during rotation with maximal speed to identify parameters of the measurement process model. Identification is executed periodically, each time when the shaft makes a full rotation. The least squares method is utilized for identification of the linear compensation parameters, while the average rotational speed is used as an internal reference for the harmonic compensation parameters identification. The method, together with a fast convergence, increases the measurement accuracy by an order of magnitude. Experimentally achieved measurement error is below 0.7°, with residual variance below 0.05°, comparable with sensor differentiability.

Radio interferometric location finding of VLF signal transmitters

The article presents some experimental results of using a very low frequency (VLF) interferometer designed in INRTU for radio direction finding of VLF transmitters. It is evaluated that amplitude angular-position measurements provides azimuth accuracy of several degrees. Distant VLF stations (3000 – 5500 km) can be located in a 2-6 km area if the signal azimuth is known with 0.001° accuracy. In order to minimize errors associated with antenna’s angular offset the authors developed a correcting algorithm. Using both radio direction finding methods and additional geophysical data (year and daily variations of solar terminator moving, signal disturbances during solar flares) the authors ascertained that 24.1 kHz and 25.0 kHz signals are emitted from the transmitter in Mokpo (South Korea). The phase measurements give about two times lower error of 1.5–2° for the NWC station (19.8 kHz, Australia) which is located more than 8200 km away from the VLF interferometer.

Assessment of the Accuracy of Determining the Angular Position of the Unmanned Bathymetric Surveying Vehicle Based on the Sea Horizon Image.

The paper presents the results of research on assessing the accuracy of angular position measurement relative to the sea horizon using a camera mounted on an unmanned bathymetric surveying vehicle of the Unmanned Surface Vehicle (USV) or Unmanned Aerial Vehicle (UAV) type. The first part of the article presents the essence of the problem. The rules of taking the angular position of the vehicle into account in bathymetric surveys and the general concept of the two-camera tilt compensator were described. The second part presents a mathematical description of the meters characterizing a resolution and a mean error of measurements, made on the base of the horizon line image, recorded with an optical system with a Complementary Metal-Oxide Semiconductor (CMOS) matrix. The phenomenon of the horizon line curvature in the image projected onto the matrix that appears with the increase of the camera height has been characterized. The third part contains an example of a detailed analysis of selected cameras mounted on UAVs manufactured by DJI, carried out using the proposed meters. The obtained results including measurement resolutions of a single-pixel and mean errors of the horizon line slope measurement were presented in the form of many tables and charts with extensive comments. The final part presents the general conclusions from the performed research and a proposal of directions for their further development.

A High-Precision Absolute Angular Position Sensor With Vernier Capacitive Arrays Based on Time Grating

This paper presents a high-precision absolute capacitive angular position sensor based on time grating. The sensor includes two single ring incremental type sensors arranged as outer and inner rings of capacitive arrays forming $N$ and $N-1$ measurement periods, respectively. The outer ring incremental sensor is employed as a fine measurement component to provide high-precision angular displacement values. The phase difference between the two incremental sensors is employed as a coarse measurement component to achieve absolute angular positioning according to a measurement principle similar to that of a vernier caliper. The proposed design is validated and optimized via tests conducted for a prototype sensor with $N\,\,=180$ and a diameter of 154 mm fabricated using standard printed circuit board manufacturing technology. Based on these results, a differential induction electrode structure is proposed to greatly reduce the magnitude of crosstalk interference signals captured by the induction electrodes of one array produced by the lead wires of the excitation electrodes of the other array. The optimized sensor achieves absolute angular position measurements with an original measurement accuracy of ±2” over a full 360° measurement range. The proposed sensor has advantages of low cost, high measurement precision, simple positioning method, and ease of manufacture.

A High-Precision Absolute Angular-Displacement Capacitive Sensor Using Three-Stage Time-Grating in Conjunction With a Remodulation Scheme

This paper presents a novel absolute angular-displacement capacitive sensor developed by combining three incremental angular-displacement time-grating capacitive sensors according to a developed three-stage remodulation scheme. In the multistage remodulation scheme, the output signals of the first-stage induction electrodes with N measurement periods provide the input signals of the second- and third-stage excitation electrodes. This novel scheme provides a fine measurement component in the second stage with 2 N measurement periods, and a coarse measurement component in the third stage with a measurement period corresponding to a single 360° revolution of the sensor. This effective doubling in the periodicity of the second-stage sensor achieves higher resolution and measurement accuracy than that achieved by standard devices of an equivalent size fabricated under an equivalent precision, while the single period of the third-stage sensor achieves an absolute positioning capability. As a result, their combination facilitates the measurement of absolute angular positions with high accuracy and resolution. A prototype sensor with a diameter of 57 mm was fabricated using standard printed circuit board technology, and the signal-processing components of the sensor were integrated on the back of the stator. Experimental results demonstrate an achievable measurement accuracy of ±25 over a full 360° range.

Design and Development of a Self-Calibration- Based Inductive Absolute Angular Position Sensor

This paper presents an inductive-based sensor for absolute angular position measurement. Its structure is basically similar to a resolver, but it has two groups of pickup coils that use the same magnetic field to produce two different signals for absolute measurement and online self-calibration. The proposed sensor mainly consists of a ferromagnetic stator, two ferromagnetic rotors, and four groups of coils. Two groups of coils in the stator working as excitation coils are supplied with quadrature alternating current (AC) signals to generate quadrature magnetic fields both in temporal and spatial domains. The other two groups of coils in the rotors working as pickup coils receive magnetic fields to produce two sine signals whose phases are proportional to the displacement of the rotors. However, the phases of the sine signals have different periods of variation in the full measurement range. The sensor uses this different phase variation to determine the absolute angular position and perform the online self-calibration. A sensor model has been built and simulated first to verify the feasibility of the sensor. Then, a sensor prototype was developed based on the sensor model. The experimental results of the sensor prototype show that the sensor has big but regular measurement error using any group of pickup coils before conducting calibration, and finally, the measurement error reduced up to 85% by use of the online self-calibration method presented in this paper.

A Linear Direct-Digital Converter for Sinusoidal Encoders

This paper proposes a novel linear direct-digital converter for sinusoidal encoders (LDCS) to measure the angular position of a rotating shaft. The outputs of a sinusoidal encoder vary as sine and cosine functions of the shaft angle. The proposed LDCS, which has a low component count, processes these outputs and renders a linear accurate direct-digital output for full-circle range. The LDCS is suitable for both static and dynamic measurements of the shaft angular position. The working principle of the LDCS is mathematically derived and explained in this paper. An elaborate evaluation of non-ideal parameters affecting the LDCS operation is carried out and reported. Furthermore, the static and dynamic performances of the LDCS are verified using simulation and emulation studies. The output nonlinearity obtained during emulation studies, for static measurement, is 0.027 %. A close agreement between simulation and emulation results is observed during these studies. Later, a tunneling magnetoresistance (TMR) angle sensing unit which acts as a representative sinusoidal encoder is fabricated. The LDCS is interfaced with the sensing unit, and several experimental tests are carried out. The worst-case nonlinearity in the static measurement of shaft angle is 0.29 %. Additional tests which study the dynamic performance and effect of mechanical misalignments of the combined TMR-LDCS system is also revealed in this paper.

Design of Inclinometer Based On STM32

This paper introduces an angle sensor based on STM32 microprocessor. Firstly, it introduces the power circuit module. Then it analyzes the angle acquisition principle and signal output type of MPU9250, then analyzes the CAN transceiver module, and finally introduces the software architecture. The sensor has a CAN output interface that can be directly applied to the CAN network architecture. The experimental results show that the sensor measurement accuracy reaches ±0.1°, which can meet the needs of industrial angular position measurement.

Higher frequencies in stall flutter moment development

An experimental study of stall flutter kinematic, moment, and fluid dynamic development is presented. This study focuses upon understanding the higher frequency content observed in stall flutter limit cycle oscillations and how that content relates to specific fluid dynamic structures and states. This is accomplished using angular position, pitching moment, and particle image velocimetry measurements of a cyber–physically mounted, NACA 0018 rigid finite span wing undergoing stable limit cycle oscillations. The wing model is mounted with a single degree of freedom in pitch. A conceptual argument is introduced to predict the model’s stall flutter susceptibility from the static moment response using two static equilibrium conditions. These conditions lead to a bound on the range of stiffnesses and reduced frequencies where stall flutter is expected to occur. These bounds, which are related to the attached and separated flow states, account for the fundamental frequency of oscillation. It is then shown that stable limit cycle oscillations contain multiple harmonic frequencies and it is argued that these higher harmonics represent important physics. In particular, it is found that the fifth harmonic is correlated with the dynamic stall vortex shedding frequency. Finally it is noted that pitching moment overshoot linearly scales with normalized pitch rate with a correlation coefficient R=0.85.

Construction and Control of the Bipedal Walking Robot

This article describes the design and testing of a walking robot. In the first stage, the mechanical behaviour of human’s lower limbs during the walk was observed and described to acquire data for the development of a simplified algorithm to control the legs of a walking robot. The second phase was the designing stage of the bipedal walking. Each robotic leg was equipped with six servo-drives. A gyroscope module with an accelerometer was used to measure the current position of the robot’s structure in space. The controller of a walking robot was developed and programmed based on Arduino Mega. The control algorithm stabilises the robot in an upright position. Potentiometers placed in the axes enabled measurements of angular positions of individual servos during the movement and were used to control walking. The programming of the movement is done through a smartphone which communicates with the robot's main controller using Bluetooth. Finally, the article describes the testing of the developed bipedal walking robot, documenting satisfactory results in walking.

Agreement analysis between Vive and Vicon tracking systems to monitor lumbar postural changes

Virtual reality (VR) has been shown to be an effective treatment for specific phobias, post-traumatic stress disorder, and chronic pain. Combined with a 3D motion capture system, VR becomes a valuable rehabilitation tool giving the clinician real-time measurements of joint movements. While 3D motion capture is prohibitively expensive, a tracking system released by Vive in March 2017, provides an inexpensive method to provide 6-Degrees of freedom (DOF) motion data. The aim of this study was to assess the accuracy of position and orientation measures reported by Vive Tracker pucks in comparison to Vicon with movements in healthy adults performing trunk motions in a VR game. Light-reflective markers were mounted on custom designed 3D printed plates along with Vive Tracker pucks. The plates were attached to the thorax and pelvis with elastic straps. Movement of the marker clusters were recorded by twelve Vicon Bonita 10 cameras (spatial resolution of 0.1 mm) using Vicon Tracker and The Motion Monitor software packages. Position and orientation of the Vive Tracker pucks were tracked by two infrared laser emitter units and recorded using the Unity game engine. Both Vicon and Vive data were recorded at 100 Hz. The two data streams were aligned based on game event markers with custom designed Matlab programs. The root meat square error was then calculated across a series of trials. The root mean square (RMS) difference between Vicon cluster markers and the Vive Tracker pucks was, on average, 0.26 degrees for the angular displacement and 0.336 mm for the positional data. The Vive Tracker pucks provide an accurate measurement of angular displacement and position that is consistent with the gold standard of the Vicon opto-electric system. This finding will help in translating laboratory based VR treatments to the clinic at very little cost.

Evoking and tracking zebrafish eye movement in multiple larvae with ZebEyeTrack

Reliable measurement of spontaneous and evoked eye movement is critical for behavioral vision research. Zebrafish are increasingly used as a model organism for visual neural circuits, but ready-to-use eye-tracking solutions are scarce. Here, we present a protocol for automated real-time measurement of angular horizontal eye position in up to six immobilized larval fish using a custom-built LabVIEW-based software, ZebEyeTrack. We provide its customizable source code, as well as a streamlined and compiled version, ZebEyeTrack Light. The full version of ZebEyeTrack controls all required hardware and synchronizes six essential aspects of the experiment: (i) stimulus design; (ii) visual stimulation with moving bars; (ii) eye detection and tracking, as well as general motion detection; (iv) real-time analysis; (v) eye-position-dependent closed-loop event control; and (vi) recording of external event times. This includes optional integration with external hardware such as lasers and scanning microscopes. Once installation is complete, experiments, including stimulus design, can be completed in <10 min, and recordings can last anywhere between seconds and many hours. Results include digitized angular eye positions and hardware status, which can be used to compute tuning curves, optokinetic gain, and other custom data analysis. After the experiment, or based on existing videos, optokinetic response (OKR) performance can be analyzed semi-automatically via the graphical user interface, and results can be exported. ZebEyeTrack has been used successfully for psychophysics experiments, for optogenetic stimulation, and in combination with calcium imaging.

Laser autocollimation based on an optical frequency comb for absolute angular position measurement

Laser autocollimation is innovated for absolute angular position measurement based on an optical frequency comb. The conventional laser autocollimation can only make relative angle measurement due to the unknown angular distance between the incident laser beam and the axis of the autocollimation unit. In the proposed absolute laser autocollimation employed with the femtosecond laser autocollimator, in which a femtosecond laser and a diffraction grating are employed as the measurement light source and the reflector, respectively, a new method is proposed for accurate identification of the angular distance through taking use of first-order diffracted beams from the reflector associated with the optical frequency comb of the femtosecond laser source. With the identified angular distance, the absolute angular position of the grating reflector, which is defined by the angle between the normal axis of the reflector surface and the incident laser beam, can be determined from the information of optical frequencies of the first-order diffracted beams based on the fact that each of the first-order diffracted beams from the grating reflector has a deterministic angular position corresponding to the optical frequency of each comb mode of the femtosecond laser. Principle of the proposed absolute laser autocollimation and an experimental setup as well as experimental results demonstrating the effectiveness and potentiality of the proposed method are presented.