Journal articles: 'Absolute angular position'

1

Lemarquand, V., and G. Lemarquand. "Inductive absolute angular position sensor." IEEE Transactions on Magnetics 28, no. 5 (September 1992): 2199–201. http://dx.doi.org/10.1109/20.179442.

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de Jong, Gerben W., Gerard C. M. Meijer, Koert van der Lingen, Jo W. Spronck, Arthur M. M. Aalsma, and Dorus (Th ). A. J. M. Bertels. "A smart capacitive absolute angular-position sensor." Sensors and Actuators A: Physical 41, no. 1-3 (April 1994): 212–16. http://dx.doi.org/10.1016/0924-4247(94)80113-4.

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Zhang, Zijian, Fenglei Ni, Yangyang Dong, Minghe Jin, and Hong Liu. "A novel absolute angular position sensor based on electromagnetism." Sensors and Actuators A: Physical 194 (May 2013): 196–203. http://dx.doi.org/10.1016/j.sna.2013.01.040.

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4

Kul’chin, Yu N., O. B. Vitrik, and A. V. Dyshlyuk. "Adaptive fiber-optic absolute angular position transducer optophysical measurements." Measurement Techniques 49, no. 4 (April 2006): 372–77. http://dx.doi.org/10.1007/s11018-006-0116-6.

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Zhang, Fan, Hengjun Zhu, Kan Bian, Pengcheng Liu, and Jianhui Zhang. "Absolute Position Coding Method for Angular Sensor—Single-Track Gray Codes." Sensors 18, no. 8 (August 19, 2018): 2728. http://dx.doi.org/10.3390/s18082728.

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Single-track Gray codes (STGCs) is a type of absolute position coding method for novel angular sensors, because it has single-track property over traditional Gray codes and mono-difference over linear feedback shift register codes. However, given that the coding theory of STGCs is incomplete, STGC construction is still a challenging task even though it has been defined for more than 20 years. Published coding theories and results on STGCs are about two types of STGC, namely, necklace and self-dual necklace ordering, which are collectively called as k-spaced head STGCs. To find a new code, three constraints on generating sequences are proposed to accelerate the searching algorithm, and the complete searching result of length-6 STGCs is initially obtained. Among the entire 132 length-6 STGCs, two novel types of STGCs with non-k-spaced heads are found, and the basic structures of these codes with the general length n are proposed and defined as twin-necklace and triplet-necklace ordering STGCs. Furthermore, d-plet-necklace ordering STGC, which unifies all the known STGCs by changing the value of d, is also defined. Finally, a single-track absolute encoder prototype is designed to prove that STGCs are as convenient as the traditional position coding methods.

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Gao, Zhenyi, Bin Zhou, Chao Li, Bo Hou, Haobo Sun, Qi Wei, and Rong Zhang. "Design and Implementation of a System-on-Chip for Self-Calibration of an Angular Position Sensor." Applied Sciences 9, no. 22 (November 8, 2019): 4772. http://dx.doi.org/10.3390/app9224772.

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In this study, a novel signal processing algorithm and hardware processing circuit for the self-calibration of angular position sensors is proposed. To calibrate error components commonly found in angular position sensors, a parameter identification algorithm based on the least mean square error demodulation is developed. A processor to run programs and a coprocessor based on the above algorithm are used and designed to form a System-on-Chip, which can calibrate signals as well as implement parameter configuration and control algorithm applications. In order to verify the theoretical validity of the design, analysis and simulation verification of the scheme are carried out, and the maximum absolute error value in the algorithm simulation is reduced to 0.003 %. The circuit’s Register-Transfer Level simulation shows that the maximum absolute value of the angular error is reduced to 0.03%. Simulation results verify the calibration performance with and without quantization and rounding error, respectively. The entire system is prototyped on a Field Programmable Gate Array and tested on a Capacitive Angular Position Sensor. The proposed scheme can reduce the absolute value of angular error to 4.36%, compared to 7.68% from the experimental results of a different calibration scheme.

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Zhang, Zijian, Yangyang Dong, Fenglei Ni, Minghe Jin, and Hong Liu. "A Method for Measurement of Absolute Angular Position and Application in a Novel Electromagnetic Encoder System." Journal of Sensors 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/503852.

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For the encoders, especially the sine-cosine magnetic ones, a new method to measure absolute angular position is proposed in the paper. In the method, the code disc of the encoder has only two circle tracks and each one was divided intoNand (N-1) equal code cells. The cell angles, changing from 0° to 360° between any two neighboring code cells, are defined to represent any position on the code disc. The position value of the same point can be represented by different cell angle values of different tracks and the absolute angular position of the point can be obtained by the difference value between the cell angle value of the outer track and the inner one. To validate the correctness of the method theoretically, the derivation process of the method was provided. An electromagnetic encoder system was designed and the experimental platform was established to test the method. The experimental results indicate that the electromagnetic encoder can measure the absolute angular position. Besides, it shows that the method is easy to be realized in algorithm and can reduce computational complexity and decrease dimension of the encoder.

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Nakajima, Hajime, Kazuhiko Sumi, and Hiroshi Inujima. "Absolute Rotary Angular Measurement by Using Multi Electrode Circular Position Sensitive Detector." IEEJ Transactions on Industry Applications 129, no. 10 (2009): 989–94. http://dx.doi.org/10.1541/ieejias.129.989.

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Akkaya, Ramazan, and Fatih Alpaslan Kazan. "A New Method for Angular Speed Measurement with Absolute Encoder." Elektronika ir Elektrotechnika 26, no. 1 (February 16, 2020): 18–22. http://dx.doi.org/10.5755/j01.eie.26.1.25307.

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The encoders are electromechanical devices that give information about the angular position and the number of turns of the shaft, which they are connected. These devices are divided into digital or analogue according to output types. On digital outputs, the output can be binary coded, gray coded or pulsed. The frequency (M) or period (T) method produces accurate results in pulse-output encoders. However, these methods alone cannot give accurate results in some encoder types, which are saw tooth type encoders that produce analogue outputs in different shapes. In this study, a new method was proposed, which reduces the relative error ratio too much below 1 % in an absolute encoder that produces an analogue output ranging from 0 V to 5 V according to the angular position of the shaft. Unlike in the studies in the literature, M method and Analog Digital Converter (ADC) were used together. Thanks to this proposed method (M + ADC), it is possible to increase the measurement accuracy of the encoders with analogue output in all speed regions.

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Sreenivasan, S. V., and K. J. Waldron. "A Drift-Free Navigation System for a Mobile Robot Operating on Unstructured Terrain." Journal of Mechanical Design 116, no. 3 (September 1, 1994): 894–900. http://dx.doi.org/10.1115/1.2919466.

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The orientation and the angular rates of the body of a robotic vehicle are required for the guidance and control of the vehicle. In the current robotic systems these quantities are obtained by the use of inertial sensing systems. Inertial sensing systems involve drift errors which can be significant even after the vehicle has traversed only short distances on the terrain. A different approach is suggested here which guarantees accurate, drift-free sensing of the angular position and rates of the vehicle body. A camera system consisting of two cameras in fixed relationship to one another is made to continuously track two stationary objects (stars or the sun). The camera system is mounted on the vehicle body through an actuated three-degree-of-freedom joint. The angular positions and rates of these joints can be used to evaluate the angular positions and rates of the vehicle body. An estimate of the absolute position of the vehicle on the terrain can also be obtained from this sensing system. This can serve as the primary system for estimating the position of a vehicle on a planet, or as an inexpensive alternative/backup to a more accurate Global Positioning System (GPS) for estimating the position of a vehicle on earth.

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11

W Hunstead, Richard. "Position and Flux Density Calibration at Molonglo." Australian Journal of Physics 44, no. 6 (1991): 743. http://dx.doi.org/10.1071/ph910743.

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When the Molonglo Cross was brought into full operation its higher angular resolution and greater pointing accuracy posed special problems for position calibration. The development of a southern radio calibration grid is described, together with its extension for the MOST. The techniques developed in this program have found wide applicability in radio-source identification searches at other observatories. Calibration in flux density was based on absolute measurements at 408 MHz and transferred via secondary standards; at 843 MHz, the flux density calibration was based partly on absolute measurements and partly on the earlier 408 MHz data. The collection of data spanning several years led to the discovery of significant time variability at 408 MHz.

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12

Layne, John, Michael Land, and Jochen Zeil. "Fiddler Crabs Use the Visual Horizon to Distinguish Predators from Conspecifics: A Review of the Evidence." Journal of the Marine Biological Association of the United Kingdom 77, no. 1 (February 1997): 43–54. http://dx.doi.org/10.1017/s0025315400033774.

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Male fiddler crabs, Uca pugilator (Crustacea: Decapoda), respond to conspecifics by claw waving, and to predators by freezing or escape. In field experiments it was found that this distinction was not made on the basis of angular size and speed, nor was shape important. The remaining possibilities were either the absolute size of the stimulus, determined from angular size and distance, or the position of the stimulus relative to the horizon. To distinguish between these, a crab was placed in a glass dish, and moved black stimuli on a white background, at a distance of 22 cm. Stimuli below the crab's horizon hardly ever evoked escape. However, identical stimuli partially or wholly above the crab's horizon produced escape responses whose frequency varied with the angular size of the stimulus. Halving the distance of the stimulus showed that it was angular and not absolute size that determines escape frequency; and experiments with a tilted horizon showed that it is the position of the stimulus relative to the eye equator that is important, rather than the geographical horizon itself. It has been concluded that crabs categorize stimuli as dangerous or otherwise by their position relative to the crabs’ visual horizon.

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13

Chen, Yuan-Liu, Yuki Shimizu, Jun Tamada, Kazuki Nakamura, Hiraku Matsukuma, Xiuguo Chen, and Wei Gao. "Laser autocollimation based on an optical frequency comb for absolute angular position measurement." Precision Engineering 54 (October 2018): 284–93. http://dx.doi.org/10.1016/j.precisioneng.2018.06.005.

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14

Luo, Pinggui, Qifu Tang, Huan Jing, and Xihou Chen. "Design and Development of a Self-Calibration- Based Inductive Absolute Angular Position Sensor." IEEE Sensors Journal 19, no. 14 (July 15, 2019): 5446–53. http://dx.doi.org/10.1109/jsen.2019.2908927.

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15

Kim, Jong-Ahn, Jae Wan Kim, Chu-Shik Kang, Jae Yong Lee, and Jonghan Jin. "On-machine calibration of angular position and runout of a precision rotation stage using two absolute position sensors." Measurement 153 (March 2020): 107399. http://dx.doi.org/10.1016/j.measurement.2019.107399.

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16

Xiujun Li, G. C. M. Meijer, G. W. de Jong, and J. W. Spronck. "An accurate low-cost capacitive absolute angular-position sensor with a full-circle range." IEEE Transactions on Instrumentation and Measurement 45, no. 2 (April 1996): 516–20. http://dx.doi.org/10.1109/19.492778.

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17

Nakajima, Hajime, Kazuhiko Sumi, and Hiroshi Inujima. "High-Precision Absolute Rotary Angular Measurement by Using a Multielectrode Circular Position-Sensitive Detector." IEEE Transactions on Instrumentation and Measurement 59, no. 11 (November 2010): 3041–48. http://dx.doi.org/10.1109/tim.2010.2047125.

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18

Pu, Hongji, Hewen Wang, Xiaokang Liu, Zhicheng Yu, and Kai Peng. "A High-Precision Absolute Angular Position Sensor With Vernier Capacitive Arrays Based on Time Grating." IEEE Sensors Journal 19, no. 19 (October 1, 2019): 8626–34. http://dx.doi.org/10.1109/jsen.2019.2921479.

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19

Zangl, H., B. Brandstatter, S. P. Cermak, G. Brasseur, and P. L. Fulmek. "Simulation and Robustness Analysis for a Novel Capacitive/Magnetic Full-Turn Absolute Angular Position Sensor." IEEE Transactions on Instrumentation and Measurement 54, no. 1 (February 2005): 436–41. http://dx.doi.org/10.1109/tim.2004.840246.

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20

Krasnov, Ivan Yurievich, Sergey Vladimirovich Langraf, and Stepan Ivanovich Chobanov. "A Sensorless Initial Rotor Position Estimation for Permanent Magnet Synchronous Machines." Applied Mechanics and Materials 792 (September 2015): 83–89. http://dx.doi.org/10.4028/www.scientific.net/amm.792.83.

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Permanent magnet synchronous motors for the effective start requires information about an initial position of a rotor. In this regard, most systems use position sensors, which substantially increase a cost of an electrical drive entirely [1-3]. The aim of this article is to develop new method, allowing to determine the absolute angular position of the rotor of the permanent magnet synchronous motors [4,5]. With a certain voltage pulses, in series applied to the motor, stator is magnetized by currents leakage in the windings. This allows, using a special algorithm, to calculate the absolute position of the rotor without using any motor parameters [6]. Simulation results prove the simplicity and efficiency of this method for determining an initial position of the rotor of the permanent magnet synchronous motors. Thus, this method can be widely used in the electrical industry.

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Brodet, Eyal. "Absolute Hidden Symmetry in Time and Absolute Asymmetry in Mass and Velocity between a Particle and Its Anti-Particle." Applied Physics Research 11, no. 2 (March 12, 2019): 43. http://dx.doi.org/10.5539/apr.v11n2p43.

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In this paper we will the discuss possible hidden symmetry in time and the possible asymmetry in mass and velocity between a particle and its anti-particle. Possible hidden symmetry in time between a particle and its anti-particle manifested in their corresponding possible hidden variables in time, fr and -fr  was first discussed in Brodet (2017b). In this paper we will extend the discussion and discuss how the above possible hidden symmetry in time and its corresponding possible symmetry in absolute position, energy and momentum, may yield an asymmetry in mass and velocity of a particle and its corresponding anti-particle. We will deconstruct the particle’s and anti-particle’s absolute position, into three complex number describing the particle/anti-particle time, velocity and mass. The particle/anti-particle symmetry and asymmetry of the above complex numbers will be discussed in the context of parity violation and the known asymmetry in angular production of particles and anti-particles. Moreover, the possible mass asymmetry will be used to explain the CP violation in the neutral kaon system. Finally, experimental ways to investigate and test the above are presented.

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Pisani, Marco, Milena Astrua, Pierre-Alix Carles, Stefan Kubsky, Thanh-Liêm Nguyên, and Olivier Acher. "Characterization of Angle Accuracy and Precision of 3-Degree-of-Freedom Absolute Encoder Based on NanoGPS OxyO Technology." Sensors 20, no. 12 (June 19, 2020): 3462. http://dx.doi.org/10.3390/s20123462.

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An absolute encoder based on vision system nanoGPS OxyO was developed by HORIBA France. This encoder provides three types of position information, namely, two inplane co-ordinates and inplane angular orientation. This paper focuses on the characterization of its angular performance. To this aim, the nanoGPS OxyO system was compared with the national angle standard of the National Metrology Institute of Italy (INRIM) that had evaluated accuracy of about 0.1 µrad. The effect of image size and illumination conditions on angular measurements was studied. Precision better than 10 µrad and accuracy better than 63 µrad over 2π rotation were demonstrated. Moreover, the application of nanoGPS OxyO to the characterization of rotation bearing is presented. Small deviations from pure rotational behavior were evidenced that would have not been possible using laser interferometers. As a consequence of its accuracy and versatility, the nanoGPS OxyO encoder is expected to be useful for laboratory experiments and quality-control tasks.

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Krklješ, Damir, Dragana Vasiljević, and Goran Stojanović. "A capacitive angular sensor with flexible digitated electrodes." Sensor Review 34, no. 4 (August 26, 2014): 382–88. http://dx.doi.org/10.1108/sr-11-2012-683.

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Purpose – This paper aims to present a prototype of a capacitive angular-position sensor which exploits advantages of flexible/printed electronics. The novelty of the sensor is that the capacitor structure is placed at the circumference of the rotor and stator, that it posses two channels (capacitor structures) electrically shifted for p/4 and that the rotor is common for both channels. The electrodes of the sensing capacitor are digitated, providing a triangular transfer function. Design/methodology/approach – This sensor prototype consists of two flexible inkjet-printed silver electrodes forming a cylindrical capacitor structure. One of them is wrapped around the stator and another is wrapped around the rotor part of a simple mechanical platform used to precisely adjust the angular displacement. Findings – The capacitance as a function of angular position was measured using an inductance capacitance impedance (LCZ) Meter, and results are presented for a full-turn measurement range. The experimental results are compared with analytical ones and very good agreement has been achieved. Originality/value – The proposed capacitive sensor structure can be used as an absolute or an incremental encoder with different resolutions, and it can be applied in automotive industry or robotics.

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Bevan, L., P. Cordo, L. Carlton, and M. Carlton. "Proprioceptive coordination of movement sequences: discrimination of joint angle versus angular distance." Journal of Neurophysiology 71, no. 5 (May 1, 1994): 1862–72. http://dx.doi.org/10.1152/jn.1994.71.5.1862.

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1. The purpose of these experiments was to determine the accuracy with which human subjects could discriminate proprioceptive (nonretinotopic) targets during movement. The targets were located at either a specified angle in joint space, or a specified angular distance from an initial joint angle. 2. In these experiments the right elbows of normal human subjects were passively extended from either predictable or unpredictable starting angles. The subjects were instructed to open the right hand to indicate that the elbow was passing through a target joint angle or a target angular distance. The subjects were not given visual information about the location of the elbow, so they had to rely on proprioceptive input to perform this task. The target (criterion joint angle or angular distance) was learned by the use of proprioception during 8-15 practice trials. 3. Four experiments were conducted. In three experiments the target was located at a constant joint angle, and in the fourth experiment the target was located at a constant angular distance from the starting angle. The starting angle in all four experiments was pseudorandomly varied from trial to trial. 4. On the basis of an analysis of constant errors, subjects were more accurate at discriminating angular distance than joint angle. The slope of the relationship between the starting position and the constant errors was dictated by the task requirement. 5. In the distance discrimination experiment, when the starting angle was more flexed than the intermediate (i.e., central) position, the subjects slightly overshot the target distance. Conversely, when the starting angle was more extended than the intermediate position, the subjects slightly undershot the target distance. 6. In the joint angle discrimination experiments, the opposite results were obtained. Subjects overshot the target when the starting position of the elbow was more extended than the intermediate starting position, and they undershot the target when the starting position was more flexed than the intermediate starting position. The amplitude of these systematic errors increased when the subjects were unaware that the initial angle of their elbow was variable. 7. It is concluded that, in kinesthetic tasks of this type, the discrimination of angular distance is more accurate than the discrimination of joint angle. We hypothesize that the nervous system extracts kinematic information related to both joint angle and angular distance from proprioceptors, and that the encoding and or decoding of angular distance is more accurate than that of absolute joint angle.(ABSTRACT TRUNCATED AT 400 WORDS)

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Wang, Hewen, Kai Peng, Xiaokang Liu, Zhicheng Yu, and Ziran Chen. "Design and Realization of a Compact High-Precision Capacitive Absolute Angular Position Sensor Based on Time Grating." IEEE Transactions on Industrial Electronics 68, no. 4 (April 2021): 3548–57. http://dx.doi.org/10.1109/tie.2020.2977540.

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Loudon, Janice K. "Measurement of Knee-Joint-Position Sense in Women with Genu Recurvatum." Journal of Sport Rehabilitation 9, no. 1 (February 2000): 15–25. http://dx.doi.org/10.1123/jsr.9.1.15.

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Context:Proprioception of the knee joint.Objective:To determine the difference in knee-joint-angle reproduction in women with and without genu recurvatum (GR).Design:Between-subjects.Setting:Clinic.Subjects:Twenty-four women divided into 2 groups according to their standing knee-extension angle.Main Outcome Measures:Each subject's ability to actively reproduce active positioning of 3 knee angles (10, 30, and 60°) was measured. Pearson correlation coefficients were calculated to determine correlation values for standing GR angle and absolute angular error (AAE). A1 -way repeated-measures MANOVA was computed to evaluate differences in group, angle, limb, and trial.Results:Standing GR angle correlated significantly to the AAE angle at 10° (r= .48). The high-recurvatum group consistently scored worse, with the highest error rate occurring at 10°.Conclusion:Individuals with GR might have diminished proprioceptive sense at end-range extension that could potentially lead to knee injury.

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Seo, Woojin, and Kwang-Ryul Baek. "Indoor Dead Reckoning Localization Using Ultrasonic Anemometer with IMU." Journal of Sensors 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/3542354.

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Dead reckoning is an important aspect of estimating the instantaneous position of a mobile robot. An inertial measurement unit (IMU) is generally used for dead reckoning because it measures triaxis acceleration and triaxis angular velocities in order to estimate the position of the mobile robot. Positioning with inertial data is reasonable for a short period of time. However, the velocity, position, and attitude errors increase over time. Much research has been conducted in ways to reduce these errors. To position a mobile robot, an absolute positioning method can be combined with dead reckoning. The performance of a combined positioning method can be improved based on improvement in dead reckoning. In this paper, an ultrasonic anemometer is used to improve the performance of dead reckoning when indoors. A new approach to the equation of an ultrasonic anemometer is proposed. The ultrasonic anemometer prevents divergence of the mobile robot’s velocity. To position a mobile robot indoors, the ultrasonic anemometer measures the relative movement of air while the robot moves through static air. Velocity data from the ultrasonic anemometer and the acceleration and angular velocity data from the IMU are combined via Kalman filter. Finally we show that the proposed method has the performance with a positioning method using encoders on a good floor condition.

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Jovanović, Jelena, Dragan Denić, and Uglješa Jovanović. "An Improved Linearization Circuit Used for Optical Rotary Encoders." Measurement Science Review 17, no. 5 (October 1, 2017): 241–49. http://dx.doi.org/10.1515/msr-2017-0029.

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Abstract Optical rotary encoders generate nonlinear sine and cosine signals in response to a change of angular position that is being measured. Due to the nonlinear shape of encoder output signals, encoder sensitivity to very small changes of angular position is low, causing a poor measurement accuracy level. To improve the optical encoder sensitivity and to increase its accuracy, an improved linearization circuit based on pseudo-linear signal generation and its further linearization with the two-stage piecewise linear analog-to-digital converter is presented in this paper. The proposed linearization circuit is composed of a mixed-signal circuit, which generates analog pseudo-linear signal and determines the first four bits of the final digital result, and the two-stage piecewise linear analog-to-digital converter, which performs simultaneous linearization and digitalization of the pseudo-linear signal. As a result, the maximal value of the absolute measurement error equals to 3.77168·10−5 [rad] (0.00216°) over the full measurement range of 2π [rad].

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Forster, J. R., and J. L. Caswell. "Relationship of OH and H2O Masers." Symposium - International Astronomical Union 115 (1987): 174–75. http://dx.doi.org/10.1017/s0074180900095334.

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Detailed maps of 70 OH and H2O masers associated with star-forming regions have been made with the VLA at an angular resolution of ∼2″ arc. The absolute position accuracy is 0″.5 for both the OH and H2O observations, and the relative position accuracy of maser spots within a group is 0″.1 for each species. For about half of the sources compact H II regions are detected at 22 GHz with 0″.1 positional accuracy relative to the strongest H2O maser. Preliminary results are presented, with emphasis on the spatial relationship between the OH and H2O masers and compact H II regions.

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Zhang, Shuang. "Mobile robot positioning algorithm based on Kalman filtering method in network environment." MATEC Web of Conferences 327 (2020): 03005. http://dx.doi.org/10.1051/matecconf/202032703005.

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Positioning is the basic link in a multi-mobile robot control system, and is also a problem that must be solved before completing a specified task. The positioning method can be generally divided into relative positioning and absolute positioning. Absolute positioning method refers to that the robot calculates its current position by acquiring the reference information of some known positions in the outside world, calculating the relationship between itself and the reference information. Absolute positioning generally adopts methods based on beacons, environment map matching, and visual positioning. The relative positioning method mainly uses the inertial navigation system INS. The inertial navigation system directly fixes the inertial measurement unit composed of the gyroscope and the accelerometer to the target device, and uses the inertial devices such as the gyroscope and the accelerometer to measure the triaxial angular velocity and The three-axis acceleration information is measured and integrated, and the mobile robot coordinates are updated in real time. Combined with the initial inertial information of the target device, navigation information such as the attitude, speed, and position of the target device is obtained through integral operation [1-2]. The inertial navigation system does not depend on external information when it is working, and is not easily damaged by interference. As an autonomous navigation system, it has the advantages of high data update rate and high short-term positioning accuracy [3]. However, under the long-term operation of inertial navigation, due to the cumulative error of integration, the positioning accuracy is seriously degraded, so it is necessary to seek an external positioning method to correct its position information [4]

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Alam, Md Moktadir, Soichi Ibaraki, and Koki Fukuda. "Kinematic Modeling of Six-Axis Industrial Robot and its Parameter Identification: A Tutorial." International Journal of Automation Technology 15, no. 5 (September 5, 2021): 599–610. http://dx.doi.org/10.20965/ijat.2021.p0599.

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In advanced industrial applications, like machining, the absolute positioning accuracy of a six-axis robot is indispensable. To improve the absolute positioning accuracy of an industrial robot, numerical compensation based on positioning error prediction by the Denavit and Hartenberg (D-H) model has been investigated extensively. The main objective of this study is to review the kinematic modeling theory for a six-axis industrial robot. In the form of a tutorial, this paper defines a local coordinate system based on the position and orientation of the rotary axis average lines, as well as the derivation of the kinematic model based on the coordinate transformation theory. Although the present model is equivalent to the classical D-H model, this study shows that a different kinematic model can be derived using a different definition of the local coordinate systems. Subsequently, an algorithm is presented to identify the error sources included in the kinematic model based on a set of measured end-effector positions. The identification of the classical D-H parameters indicates a practical engineering application of the kinematic model for improving a robot’s positioning accuracy. Furthermore, this paper presents an extension of the present model, including the angular positioning deviation of each rotary axis. The angular positioning deviation of each rotary axis is formed as a function of the axis’ command angles and the direction of its rotation to model the effect of the rotary axis backlash. The identification of the angular positioning deviation of each rotary axis and its numerical compensation are presented, along with their experimental demonstration. This paper provides an essential theoretical basis for the error source diagnosis and error compensation of a six-axis robot.

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Reshmin, S. "Threshold absolute value of relay control for the fastest possible reduction of a satellite to the desired angular position." Известия Российской академии наук. Теория и системы управления, no. 5 (October 2018): 30–41. http://dx.doi.org/10.31857/s000233880002843-6.

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Ranganathan, Shivakumar I. "A novel finite element model incorporating rotary inertia in thin circular rods." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 10 (December 14, 2012): 2386–90. http://dx.doi.org/10.1177/0954406212471754.

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In this article, we extend the finite element formulation proposed by Buckham et al.2 to include the effects of rotary inertia in isotropic circular rods (or cables). In developing our model, we first express the angular velocities in terms of the time derivatives of the Frenet frame and use this definition to determine the contributions of rotary inertia. A salient feature of this model is that only six variables representing the absolute position vectors are used as nodal coordinates. Galerkin’s weighted residual approach is used to complete the discretization.

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Qin, Haoye, and Zhong Wu. "Angle Tracking Observer with Improved Accuracy for Resolver-to-Digital Conversion." Symmetry 11, no. 11 (November 1, 2019): 1347. http://dx.doi.org/10.3390/sym11111347.

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A resolver is an absolute shaft sensor which outputs pair signals with ortho-symmetric amplitudes. Ideally, they are sinusoidal and cosinusoidal functions of the shaft angle. In order to demodulate angular position and velocity from resolver signals, resolver-to-digital conversion (RDC) is necessary. In software-based RDC, most algorithms mainly employ a phase-locked loop (PLL)-based angle tracking observer (ATO) to form a type-II system. PLL can track the detected angle by regulating the phase error from the phase detector which depends on the feature of orthogonal symmetry in the resolver outputs. However, a type-II system will result in either steady-state errors or cumulative errors in the estimation of angular position with constant accelerations. Although type-III ATOs can suppress these errors, they are still vulnerable to high-order acceleration signals. In this paper, an improved PLL-based ATO with a compensation model is proposed. By using dynamic compensation, the proposed ATO becomes a type-IV system and can reduce position estimation errors for high-order acceleration signals. In addition, the parameters of ATO can be tuned according to the bandwidth, noise level and capability of error suppression. Simulation and experimental results demonstrate the effectiveness of the proposed method.

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Oh, Kyung Chul, Jee-Hwan Kim, Chang-Woo Woo, and Hong Seok Moon. "Accuracy of Customized Prefabricated Screw-Type Immediate Provisional Restorations after Single-Implant Placement." Journal of Clinical Medicine 8, no. 4 (April 11, 2019): 490. http://dx.doi.org/10.3390/jcm8040490.

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Limited evidence is available comparing the differences between pre-operative and post-operative 3D implant positions from the viewpoint of prosthetics. We aimed to investigate the differences between preplanned positions of virtual provisional restorations and their actual positions following fully guided single-implant placement. Ten maxillary typodonts with missing right central incisors were imaged using cone-beam computed tomography, and digital impressions were obtained using an intraoral scanner. These data were imported into implant-planning software, following which the provisional restorations were designed. After data superimposition, an appropriate implant position was determined, and a computer-assisted implant surgical guide was designed for each typodont. Orders generated from the implant-planning software were imported into relevant computer-aided design software to design the custom abutments. The abutments, provisional restorations, and surgical guides were fabricated, and each restoration was cemented to the corresponding abutments, generating a screw-type immediate provisional restoration. The implants were placed using the surgical guides, and the screw-type provisional restorations were engaged to the implants. The typodonts were then rescanned using the intraoral scanner. The restorations designed at the treatment planning stage were compared with those in the post-operative scan using metrology software. The angular deviation around the central axis of the implant was measured, and the differences in the crown position were converted to root mean square (RMS) values. The post-operative provisional restorations exhibited an absolute angular deviation of 6.94 ± 5.78° and an RMS value of 85.8 ± 20.2 µm when compared with their positions in the pre-operative stage. Within the limitations of the present in vitro study, the results highlight the potential application of customized prefabricated immediate provisional restorations after single-implant placement.

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Paredes, Ferran, Cristian Herrojo, and Ferran Martín. "Position Sensors for Industrial Applications Based on Electromagnetic Encoders." Sensors 21, no. 8 (April 13, 2021): 2738. http://dx.doi.org/10.3390/s21082738.

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Optical and magnetic linear/rotary encoders are well-known systems traditionally used in industry for the accurate measurement of linear/angular displacements and velocities. Recently, a different approach for the implementation of linear/rotary encoders has been proposed. Such an approach uses electromagnetic signals, and the working principle of these electromagnetic encoders is very similar to the one of optical encoders, i.e., pulse counting. Specifically, a transmission line based structure fed by a harmonic signal tuned to a certain frequency, the stator, is perturbed by encoder motion. Such encoder consists in a linear or circular chain (or chains) of inclusions (metallic, dielectric, or apertures) on a dielectric substrate, rigid or flexible, and made of different materials, including plastics, organic materials, rubber, etc. The harmonic signal is amplitude modulated by the encoder chain, and the envelope function contains the information relative to the position and velocity. The paper mainly focuses on linear encoders based on metallic and dielectric inclusions. Moreover, it is shown that synchronous electromagnetic encoders, able to provide the quasi-absolute position (plus the velocity and direction of motion in some cases), can be implemented. Several prototype examples are reviewed in the paper, including encoders implemented by means of additive process, such as 3D printed and screen-printed encoders.

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Lee, Sang-Jeong, Ji-Yong Yoo, Sang-Yoon Woo, Hoon Joo Yang, Jo-eun Kim, Kyung-Hoe Huh, Sam-Sun Lee, Min-Suk Heo, Soon Jung Hwang, and Won-Jin Yi. "A Complete Digital Workflow for Planning, Simulation, and Evaluation in Orthognathic Surgery." Journal of Clinical Medicine 10, no. 17 (September 3, 2021): 4000. http://dx.doi.org/10.3390/jcm10174000.

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The purpose of this study was to develop a complete digital workflow for planning, simulation, and evaluation for orthognathic surgery based on 3D digital natural head position reproduction, a cloud-based collaboration platform, and 3D landmark-based evaluation. We included 24 patients who underwent bimaxillary orthognathic surgery. Surgeons and engineers could share the massive image data immediately and conveniently and collaborate closely in surgical planning and simulation using a cloud-based platform. The digital surgical splint could be optimized for a specific patient before or after the physical fabrication of 3D printing splints through close collaboration. The surgical accuracy was evaluated comprehensively via the translational (linear) and rotational (angular) discrepancies between identical 3D landmarks on the simulation and postoperative computed tomography (CT) models. The means of the absolute linear discrepancy at eight tooth landmarks were 0.61 ± 0.55, 0.86 ± 0.68, and 1.00 ± 0.79 mm in left–right, advance–setback, and impaction–elongation directions, respectively, and 1.67 mm in the root mean square direction. The linear discrepancy in the left–right direction was significantly different from the other two directions as shown by analysis of variance (ANOVA, p < 0.05). The means of the absolute angular discrepancies were 1.43 ± 1.06°, 0.50 ± 0.31°, and 0.58 ± 0.41° in the pitch, roll, and yaw orientations, respectively. The angular discrepancy in the pitch orientation was significantly different from the other two orientations (ANOVA, p < 0.05). The complete digital workflow that we developed for orthognathic patients provides efficient and streamlined procedures for orthognathic surgery and shows high surgical accuracy with efficient image data sharing and close collaboration.

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Romero-Franco, Natalia, Juan Antonio Montaño-Munuera, Juan Carlos Fernández-Domínguez, and Pedro Jiménez-Reyes. "Validity and Reliability of a Digital Inclinometer to Assess Knee Joint Position Sense in an Open Kinetic Chain." Journal of Sport Rehabilitation 28, no. 4 (May 1, 2019): 332–38. http://dx.doi.org/10.1123/jsr.2017-0221.

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Context: New methods are being validated to easily evaluate the knee joint position sense (JPS) due to its role in the sports movement and the risk of injury. However, no studies to date have considered the open kinetic chain (OKC) technique, despite the biomechanical differences compared with closed kinetic chain movements. Objective: To analyze the validity and reliability of a digital inclinometer to measure the knee JPS in the OKC movement. Design: The validity and intertester and intratester reliability of a digital inclinometer for measuring knee JPS were evaluated. Setting: Sports research laboratory. Participants: A total of 18 athletes (11 males and 7 females; 28.4 [6.6] y; 71.9 [14.0] kg; 1.77 [0.09] m; 22.8 [3.2] kg/m2) voluntary participated in this study. Main Outcomes Measures: Absolute angular error (AAE), relative angular error (RAE), and variable angular error (VAE) of knee JPS in an OKC. Results: Intraclass correlation coefficient (ICC) and standard error of the mean (SEM) were calculated to determine the validity and reliability of the inclinometer. Data showed excellent validity of the inclinometer to obtain proprioceptive errors compared with the video analysis in JPS tasks (AAE: ICC = .981, SEM = 0.08; RAE: ICC = .974, SEM = 0.12; VAE: ICC = .973, SEM = 0.07). Intertester reliability was also excellent for all the proprioceptive errors (AAE: ICC = .967, SEM = 0.04; RAE: ICC = .974, SEM = 0.03; VAE: ICC = .939, SEM = 0.08). Similar results were obtained for intratester reliability (AAE: ICC = .861, SEM = 0.1; RAE: ICC = .894, SEM = 0.1; VAE: ICC = .700, SEM = 0.2). Conclusions: The digital inclinometer is a valid and reliable method to assess the knee JPS in OKC. Sport professionals may evaluate the knee JPS to monitor its deterioration during training or improvements throughout the rehabilitation process.

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LaPointe, Stephan J., Charles Peebles, Aprajita Nakra, and Howard Hillstrom. "The Reliability of Clinical and Caliper-Based Calcaneal Bisection Measurements." Journal of the American Podiatric Medical Association 91, no. 3 (March 1, 2001): 121–26. http://dx.doi.org/10.7547/87507315-91-3-121.

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The measurements of subtalar joint neutral position and hindfoot range of motion have been shown to be unreliable. The first step in making these measurements is to determine the calcaneal bisection. This study examines the reliability of bisecting the calcaneus with digital linear calipers. Five trials on each of six cadavers resulted in a mean absolute angular difference of 0.60° (SD ±1.17°). These results were then compared with results from the typical visual method used clinically. Three raters each performed five trials on six cadavers. Visual bisection was more variable, with a mean absolute error of 3.61° (±3.13°). A mean error of 6° (±1°) is certainly possible when the heel is visually bisected. It was determined that the caliper bisection was a valid technique for bisection of the heel, but that clinical visual bisection was not. (J Am Podiatr Med Assoc 91(3): 121-126, 2001)

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Reich, Wolfgang, and Patricia Reich. "Measuring and calibrating galactic synchrotron emission." Proceedings of the International Astronomical Union 4, S259 (November 2008): 603–12. http://dx.doi.org/10.1017/s1743921309031433.

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AbstractOur position inside the Galaxy requires all-sky surveys to reveal its large-scale properties. The zero-level calibration of all-sky surveys differs from standard ‘relative’ measurements, where a source is measured in respect to its surroundings. All-sky surveys aim to include emission structures of all angular scales exceeding their angular resolution including isotropic emission components. Synchrotron radiation is the dominating emission process in the Galaxy up to frequencies of a few GHz, where numerous ground based surveys of the total intensity up to 1.4 GHz exist. Its polarization properties were just recently mapped for the entire sky at 1.4 GHz. All-sky total intensity and linear polarization maps from WMAP for frequencies of 23 GHz and higher became available and complement existing sky maps. Galactic plane surveys have higher angular resolution using large single-dish or synthesis telescopes. Polarized diffuse emission shows structures with no relation to total intensity emission resulting from Faraday rotation effects in the interstellar medium. The interpretation of these polarization structures critically depends on a correct setting of the absolute zero-level in Stokes U and Q.

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Surpi, G. C., D. D. Harari, and J. A. Frieman. "Effects Of Large-Scale Structure Upon The Determination Of Ho From Time Delays." Symposium - International Astronomical Union 173 (1996): 91–92. http://dx.doi.org/10.1017/s0074180900230994.

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We have analyzed the effects of both large-scale inhomogeneities in the mass distribution and cosmological gravitational waves upon the time delay between two images in a gravitational lens system. We have shown that their leading order effect, which could potentially bias the determination of the Hubble parameter, is indistinguishable from a change in the relative angle between the source and the lens axis. Since the absolute angular position of the source is not directly measurable, nor does it enter the relationship between the Hubble parameter and the lens observables, the determination of Ho from gravitational lens time delays follows in the usual way, as if the metric perturbations were absent.

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McCarthy, D. W. "Infrared Speckle Interferometry: A Sensitive Technique for Physical Measurements of Unseen Companions to Nearby Stars." Symposium - International Astronomical Union 109 (1986): 309–19. http://dx.doi.org/10.1017/s0074180900076737.

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Infrared speckle interferometry combines the full resolving power of large telescopes with high photometric sensitivity over the wavelength range 2.2 to 12 microns. Despite improved atmospheric seeing at these wavelengths, seeing fluctuations limit measurement precision. Astrometric companions have been detected with angular separations ≥0.1 arcsec and magnitude differences ≤3.7 mag. Results illustrate seeing limitations and show how the usual position angle ambiguity can be overcome. These measurements yield masses and absolute magnitudes for calibrating the lower main sequence. In some cases, orbital motion is detected. A method of “shift-and-add” enables detection of substellar (0.04 to 0.08 M⊙) companions. Future improvements involving detector arrays and seeing monitors are discussed.

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Zhang, Lijun, Shan Qian, Shifeng Zhang, and Hong Cai. "Research on angles-only/SINS/CNS relative position and attitude determination algorithm for a tumbling spacecraft." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 2 (August 6, 2016): 218–28. http://dx.doi.org/10.1177/0954410016636153.

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In this paper, the relative navigation technique of final approach phase for a tumbling target spacecraft is studied and exploited. It is assumed that the tumbling target is in failure or out of control and there is no good a priori rotation rate information. The Euler’s rotational dynamics is used to propagate the target angular velocity, and the unknown inertia parameter circumstance is also considered. The chaser spacecraft is equipped with three strapdown gyros and accelerometers and a star sensor that determine the absolute motion parameters, and an optical camera that measures relative azimuth and elevation angles to the target spacecraft. On the basis of the rotational and translational motions of both spacecrafts, an angles-only/ strapdown inertial navigation system/celestial navigation system navigation filter is designed. Simulation results indicate that the proposed algorithm can accurately estimate the relative position, velocity, and attitude between two spacecrafts and compensate the biases of the gyros and accelerometers.

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Hashim, N. M., A. H. Omar, S. N. M. Ramli, K. M. Omar, and N. Din. "CADASTRAL DATABASE POSITIONAL ACCURACY IMPROVEMENT." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W5 (October 5, 2017): 91–96. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w5-91-2017.

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Positional Accuracy Improvement (PAI) is the refining process of the geometry feature in a geospatial dataset to improve its actual position. This actual position relates to the absolute position in specific coordinate system and the relation to the neighborhood features. With the growth of spatial based technology especially Geographical Information System (GIS) and Global Navigation Satellite System (GNSS), the PAI campaign is inevitable especially to the legacy cadastral database. Integration of legacy dataset and higher accuracy dataset like GNSS observation is a potential solution for improving the legacy dataset. However, by merely integrating both datasets will lead to a distortion of the relative geometry. The improved dataset should be further treated to minimize inherent errors and fitting to the new accurate dataset. The main focus of this study is to describe a method of angular based Least Square Adjustment (LSA) for PAI process of legacy dataset. The existing high accuracy dataset known as National Digital Cadastral Database (NDCDB) is then used as bench mark to validate the results. It was found that the propose technique is highly possible for positional accuracy improvement of legacy spatial datasets.

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Ashley, Steven. "Palm-Size Spy Planes." Mechanical Engineering 120, no. 02 (February 1, 1998): 74–78. http://dx.doi.org/10.1115/1.1998-feb-3.

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This article discusses that today’s squad leader must still risk troops to scout out what lies over the next hill, beyond the next tree line, or inside the next building. The Department of Defense is trying to help ground troops at the platoon, company, or brigade level with this crucial task by giving them tiny spy planes, called micro aerial vehicles (MAVs), to search the local terrain. Planners at the Defense Advanced Research Projects Agency (DARPA) envision equipping small combat units with their own “organic” intelligence assets that can locate and monitor possible threats. DARPA planners define a MAV as semiautonomous airborne vehicles, measuring less than 6 inches in any dimension and weighing about 4 ounces that can accomplish a useful military mission at an affordable cost. The most likely parameters to sense for MAV stabilization are inertial angular rate, differential and absolute pressure, acceleration, and the Earth’s magnetic and electrostatic fields; optical sensing could be used for angular position and rate stabilization. Developing useful micro aerial vehicles is going to be a severe design engineering challenge.

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Wei, Yao, Yanjun Wei, Yening Sun, Hanhong Qi, and Mengyuan Li. "An Advanced Angular Velocity Error Prediction Horizon Self-Tuning Nonlinear Model Predictive Speed Control Strategy for PMSM System." Electronics 10, no. 9 (May 10, 2021): 1123. http://dx.doi.org/10.3390/electronics10091123.

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In nonlinear model predictive control (NMPC), higher accuracy can be obtained with a shorter prediction horizon in steady-state, better dynamics can be obtained with a longer prediction horizon in a transient state, and calculation burden is proportional to the prediction horizon which is usually pre-selected as a constant according to dynamics of the system with NMPC. The minimum calculation and prediction accuracy are hard to ensure for all operating states. This can be improved by an online changing prediction horizon. A nonlinear model predictive speed control (NMPSC) with advanced angular velocity error (AAVE) prediction horizon self-tuning method has been proposed in which the prediction horizon is improved as a discrete-time integer variable and can be adjusted during each sampling period. A permanent magnet synchronous motor (PMSM) rotor position control system with the proposed strategy is accomplished. Tracking performances including rotor position Integral of Time-weighted Absolute value of the Error (ITAE), the maximal delay time, and static error are improved about 15.033%, 23.077%, and 10.294% respectively comparing with the conventional NMPSC strategy with a certain prediction horizon. Better disturbance resisting performance, lower weighting factor sensitivities, and higher servo stiffness are achieved. Simulation and experimental results are given to demonstrate the effectiveness and correctness.

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Bigazzi, Luca, Stefano Gherardini, Giacomo Innocenti, and Michele Basso. "Development of Non Expensive Technologies for Precise Maneuvering of Completely Autonomous Unmanned Aerial Vehicles." Sensors 21, no. 2 (January 8, 2021): 391. http://dx.doi.org/10.3390/s21020391.

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In this paper, solutions for precise maneuvering of an autonomous small (e.g., 350-class) Unmanned Aerial Vehicles (UAVs) are designed and implemented from smart modifications of non expensive mass market technologies. The considered class of vehicles suffers from light load, and, therefore, only a limited amount of sensors and computing devices can be installed on-board. Then, to make the prototype capable of moving autonomously along a fixed trajectory, a “cyber-pilot”, able on demand to replace the human operator, has been implemented on an embedded control board. This cyber-pilot overrides the commands thanks to a custom hardware signal mixer. The drone is able to localize itself in the environment without ground assistance by using a camera possibly mounted on a 3 Degrees Of Freedom (DOF) gimbal suspension. A computer vision system elaborates the video stream pointing out land markers with known absolute position and orientation. This information is fused with accelerations from a 6-DOF Inertial Measurement Unit (IMU) to generate a “virtual sensor” which provides refined estimates of the pose, the absolute position, the speed and the angular velocities of the drone. Due to the importance of this sensor, several fusion strategies have been investigated. The resulting data are, finally, fed to a control algorithm featuring a number of uncoupled digital PID controllers which work to bring to zero the displacement from the desired trajectory.

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Bigazzi, Luca, Stefano Gherardini, Giacomo Innocenti, and Michele Basso. "Development of Non Expensive Technologies for Precise Maneuvering of Completely Autonomous Unmanned Aerial Vehicles." Sensors 21, no. 2 (January 8, 2021): 391. http://dx.doi.org/10.3390/s21020391.

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In this paper, solutions for precise maneuvering of an autonomous small (e.g., 350-class) Unmanned Aerial Vehicles (UAVs) are designed and implemented from smart modifications of non expensive mass market technologies. The considered class of vehicles suffers from light load, and, therefore, only a limited amount of sensors and computing devices can be installed on-board. Then, to make the prototype capable of moving autonomously along a fixed trajectory, a “cyber-pilot”, able on demand to replace the human operator, has been implemented on an embedded control board. This cyber-pilot overrides the commands thanks to a custom hardware signal mixer. The drone is able to localize itself in the environment without ground assistance by using a camera possibly mounted on a 3 Degrees Of Freedom (DOF) gimbal suspension. A computer vision system elaborates the video stream pointing out land markers with known absolute position and orientation. This information is fused with accelerations from a 6-DOF Inertial Measurement Unit (IMU) to generate a “virtual sensor” which provides refined estimates of the pose, the absolute position, the speed and the angular velocities of the drone. Due to the importance of this sensor, several fusion strategies have been investigated. The resulting data are, finally, fed to a control algorithm featuring a number of uncoupled digital PID controllers which work to bring to zero the displacement from the desired trajectory.

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Friston, K. J., R. E. Passingham, J. G. Nutt, J. D. Heather, G. V. Sawle, and R. S. J. Frackowiak. "Localisation in PET Images: Direct Fitting of the Intercommissural (AC—PC) Line." Journal of Cerebral Blood Flow & Metabolism 9, no. 5 (October 1989): 690–95. http://dx.doi.org/10.1038/jcbfm.1989.97.

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A technique is described for estimating the position of the intercommisural line (AC–PC line) directly from landmarks on positron emission tomographic (PET) images, namely the ventral aspects of the anterior and posterior corpus callosum, the thalamus, and occipital pole. The relationship of this estimate to the true AC–PC line, fitted through the centres of the anterior and posterior commissures, showed minimal vertical and angular displacement when measured on magnetic resonance imaging (MRI) scans. Using regression analysis, the ease and reliability of fitting to these points was found to be high. This directly derived AC–PC line estimate was validated in terms of the assumptions used in the method of Fox et al. The ratio of distance between the AC–PC line and a line passing through the base of the inion (GI line) to total brain height was 0.21, as predicted. The technique has been further validated by localizing focal activation of the sensorimotor cortex. The technique is discussed in terms of absolute limits to localization of structures in the brain using noninvasive tomographic techniques in general and PET in particular.

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Panagia, Nino. "A Geometric Determination of the Distance to SN 1987A and the LMC." International Astronomical Union Colloquium 192 (2005): 585–92. http://dx.doi.org/10.1017/s0252921100009702.

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SummaryUsing the definitive reductions of the IUE light curves by [15] and an extensive set of HST images of SN 1987A we have repeated and improved our original analysis [8, 9] to derive a better determination of the distance to the supernova. In this way we have obtained an absolute size of the ring Rabs = (6.23 ± 0.08) × 1017 cm and an angular size R″ = 808 ± 17 mas, which give a distance to the supernova d(SN1987A) = 51.4±1.2 kpc and a distance modulus (m − M)sN1987A = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to be d(LMC) = 51.7±1.3 kpc, which corresponds to a distance modulus of (m − M)LMC = 18.56 ± 0.05.

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Journal articles on the topic 'Absolute angular position'

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