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A computational algorithm is developed for estimating accurately the attitude of a robotic arm which moves along a predetermined path. This algorithm requires preliminary input data obtained in the static mode to yield phase observables for the precise, 3-axis attitude determination of a swinging manipulator in the dynamic mode. Measurements are recorded simultaneously by three GPS L1 receivers and then processed in several steps to accomplish this task. First, artkconv batch executable converts GPS receiver readings into RINEX format to generate GPS observables and ephemeris for multiple satellites. Then baseline vectors determination is carried out by baseline constrained Least-Squares Ambiguity Decorrelation (LAMBDA) method that uses double difference carrier phase estimates as input to calculate integer solution for each baseline. Finally, attitude determination is made by employing alternatively Least-squares attitude determination (LSAD) in the static mode and extended Kalman filter in the dynamic mode. The algorithm presented in this paper is applied to recorded data on Mitsubishi RV-M1 robotic arm in order to produce attitude estimates. These results are confirmed by another set of Euler angles independently evaluated from robotic arm postures obtained along the predefined trajectory.
d beforehand on Movemaster EX Simulator as shown in Figs 2–4 Just before starting of these three dynamic tests, corresponding experiments in static modes were carried out to provide the initial attitude angles which were used in the verification analysis afterward Based on the simulation models described above, and the dynamic experiments were conducted, such that the rotation of antennas was controlled by the robotic arm In this experiment, the platform mounted with antennas rotated with a constant angular rate The GPS data was collected at Hz sampling rate The LSAD and the EKF were used for static and dynamic modes accordingly to calculate the yaw, roll and pitch angles Integer 339 ambiguities were computed as a result of static experiments which were used as input to the algorithm for dynamic attitude determination The following parameters were used to tune the extended Kalman filter The standard deviation of carrier phase noise was mm The matrix R was calculated based on the satellite geometry and the position of the master antenna at the starting epoch The yaw, roll, and pitch estimates were initialized using the LSAD results at the first epoch The initial angular rates were calculated by averaging the between-epoch variations of yaw, roll, and pitch angles during the entire static observation session Software design A piece of software on MATLAB has been implemented to process the data from the mounted GPS antennas This software is used for post-processing of the RINEX data, which was obtained by converting corresponding navigational files output by the GPS receivers Attitude determination starts with the data synchronization The GPS measurements from all three antennas at the same receipt epoch are processed to carry out the data synchronization The position of the master antenna should be calculated prior to performing the differential positioning If there is no available ground base station for differential correction, the position of the master antenna can be computed by single-point positioning (SPP) Although the related positioning accuracy can be around several tens of meters with Selective Availability turned off, it will only Fig Computation of yaw and pitch angles in static mode Fig Verification of yaw angle determination in dynamic mode 340 A Raskaliyev et al / Journal of Advanced Research (2017) 333–341 Fig Verification of pitch angle determination in dynamic mode affect the positioning accuracy of slave antennas at millimeter level It implies that the accuracy of the attitude parameters will not be significantly degraded due to the application of SPP to the master antenna Having known the position of the master antenna, the differential positioning can be performed in order to derive the baseline vectors between antennas by making use of the LSAD method For this purpose, the integer phase ambiguities should be resolved first by employing the baseline constrained LAMBDA method In order to obtain initial values as the input of the LSAD method, the Euler angles can be firstly computed by employing the direct attitude computation method In order to apply the extended Kalman filter, the antenna body frame (ABF) should be fixed at first With two or three antennas, the ABF can be determined based on the simple geometric formulas, whereby the length of each master-slave antenna pair should be accurately measured Note that the ABF needs to be fixed only one time before the rotation along any orientation angle starts The flowchart for the data processing in a GPS-based attitude determination system is illustrated below (see Fig 5) Experimental results Good results were obtained at the first stage (static mode) in the computation of yaw and pitch angles, as shown in Fig Note that instead of extended Kalman filter, Least Squares Adjustment method was used for this case because it was not possible to utilize the dynamic model Fig presents the difference in dynamic mode between yaw angles calculated by the developed software and the corresponding verification model The model benefited a lot from the nearly constant angular rate of the platform’s rotation Fig shows a comparison between pitch angles computed by extended Kalman filter implemented in the algorithm and the verification model for the dynamic mode An increased error in attitude determination for this case might be caused by slight bending of the antenna platform during the pitch dynamic test Unfortunately, demonstrative results from the roll angle dynamic experiments were not acquired due to multiple data gaps in GPS readings from two antennas These data interruptions took place because of carrier phase cycle slips caused by the particular rotation plane of the platform that partially prevented a line of sight with navigational satellites Conclusions This paper has presented a way to resolve 3-axis attitude using three inexpensive single frequency GPS antennas, despite a dynamic environment and a low measurement sampling rate in signal reception which is Hz The 3-axis attitude estimation algorithm solves a mixed real/integer problem by taking advantage of given useful information such as baseline lengths and preliminary construction of the dynamic model The efficiency of this paper’s algorithm is demonstrated by application to a set of data from a serial robotic arm experiment with mostly rotational motion Despite some signal gaps, the raw GPS data is successfully processed by implementing baseline constrained LAMBDA method to produce accurate double differences of carrier phases and baseline vectors These baseline vectors are input to the extended Kalman filter based on the constant angular rate model that solves for the real-valued attitude solution simultaneously The results were reasonable when compared with those from a verification model constructed based on preliminarily assigned movements of the manipulator’s end effector, although there still looks to be some sort of time tagging or coordinate frame definition error The goal of this work was to develop GPS-based attitude determination algorithm based on the predefined dynamic model The performance of this technique was tested in a series of experiments by using a serial robotic arm Finally, the success rate and accuracy of this algorithm can be improved by incorporating appropriate cycle slip repair method for post-processing of the occurred data gaps Conflict of interest The authors have declared no conflict of interest Compliance with Ethics Requirments This article does not contain any studies with human or animal subjects References [1] Gong A, Zhao X, Pang C, Duan R, Wang Y GNSS single frequency, single epoch reliable attitude determination method with baseline vector constraint Passaro VMN ed Sensor (Basel Switzerland) 2015;15(12):30093–103 A Raskaliyev et al / Journal of Advanced Research (2017) 333–341 [2] Park C, Teunissen PJG Integer least squares with quadratic equality constraints and its application to GNSS 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accurately measured Note that the ABF needs to be fixed only one time before the rotation along any orientation angle starts The flowchart for the data... Kirubarajan T Estimation with applications to tracking and navigation: theory algorithms and software John Wiley & Sons; 2004 [16] Simon D Optimal state estimation: Kalman, H infinity, and nonlinear... predefined dynamic model The performance of this technique was tested in a series of experiments by using a serial robotic arm Finally, the success rate and accuracy of this algorithm can be improved