Patent Description:
The present invention relates to a method for measurement of three-dimensional welding torch orientation for manual arc welding process as defined in the preamble of claim <NUM>. Such a method is known from <CIT> disclosing a welding torch comprising a gyro sensor and a position sensor. <CIT> discloses a system for calibrating an inertial measurement unit (IMU) that has one or more sensors, said system comprising a calibration fixture, said calibration fixture being sized and configured to limit relative movement of the IMU with respect to said calibration fixture, said calibration fixture being configured to allow for linear movement and to allow for angular positioning of the IMU at various angles; and a computer system receiving signals from the one or more sensors, and calculating calibration values for compensating signals from the one or more sensors from a calibration model. <NPL> further describes an IMU calibration.

Arc welding has been developed and refined for years, as one of the most widely used material joining technologies. High-quality welds are critical for many applications, such as automobile manufacturing, refineries and ship building. The torch orientation is defined as the torch posture throughout a welding process. It is one of the most important welding parameters, and is directly contingent upon the weld quality and appearance. Optimal quality welds can only be guaranteed if the torch orientation is well adjusted. Inappropriate torch manipulations cause various weld defects and discontinuities, such as poor penetration, undercuts, porosity and different types of cracks. Therefore, detailed torch orientations for almost every welding process have been recommended by various bodies and organizations.

Limitations and disadvantages of conventional approaches to manual welding will become apparent to one of skill in the art, through comparison of such approaches with some aspects of the present method and system set forth in the remainder of this disclosure with reference to the drawings.

According to the present invention, a method is provided as defined in claim <NUM>.

An optional embodiment is further defined in dependent claim <NUM>.

Different welding processes may have various parameters such as the welding current, voltage, torch traveling speed, wire feed speed if applicable and the number of weld passes. The recommended torch orientation manipulations can differ accordingly. Typical recommended torch postures are shown in <FIG> and <FIG> for the two widely used welding processes which have torch orientation requirements: gas tungsten arc welding (GTAW) and gas metal arc welding (GMAW), in <FIG> and <FIG>, respectively. Four different fit-up types for each process are illustrated in the two figures. For the GTAW process of <FIG>, there is shown torch <NUM>, electrode <NUM>, seam <NUM>, and weld bead <NUM> for each of the fit-up types. For the GMAW process of <FIG>, there is shown torch <NUM>, seam <NUM>, weld bead <NUM>, and wire <NUM> for each of the fit-up types. Moreover, four different torch swing patterns <NUM> are adopted for the four fit-up types in <FIG>, besides the diversities in torch orientation.

Mastering the torch manipulation is challenging in a manual arc welding process. To ensure weld quality, a human welder is required to maintain a recommended torch posture while moving the torch smoothly along the weld seam, possibly with one particular swing pattern. Due to various disturbances in the welding field, the torch is required to be adjusted accordingly to guard against the effects of the disturbances to the weld quality. The capability of proper torch orientation manipulation depends on the welder's skill level and his/her physiological conditions. The major problem is that a welder cannot master the torch adjusting maneuver without countless hours of practice through acquired rule-of-thumb techniques, and this makes the welder training cycle intolerably long. In addition, the needed concentration from the welder is always required but can never be assured.

Torch orientation measurement can be used to accelerate the welding training process. A database of welding experts' performance can be established using the torch manipulation data combined with other critical welding parameters. With the database, the operations of a welding trainee can be compared with the expert's performance throughout the practice by detecting the torch orientation in real-time, and incorrect or unfavorable operations from the trainee can be identified immediately. Audio or visual indications can thus be provided to the trainee as instant performance feedback throughout the training practice. It has been found that welding skills increase significantly with this feedback.

Detecting the torch manipulation may also open the door to better understanding of the intelligent welding operations of skilled welders. Given that a skilled welder's torch maneuvers are detected, the dynamics of the torch orientation related to the weld quality control can be obtained. The mathematical formulation of the experts' welding skills, which make an experienced welder better than an unskilled welder in delivering quality weld, can be further established. Applying the formulated skill to automatic welding will build the foundation for the next generation of intelligent welding robots that possess disturbance-resistant capabilities comparable to a skilled human welder. Another possibility is to compensate the error in torch orientation manipulation by adjusting other welding parameters that can be changed by the welding power supply.

Aspects of the methods and systems disclosed herein provide an accurate three-dimensional (3D) torch orientation measurement scheme that can be conveniently used in a real manual arc welding process or a welder training system. The embodiment is based on a miniature inertial measurement unit (IMU), and uses a quaternion-based unscented Kalman filter (UKF) and an auto-nulling algorithm. The UKF is designed to estimate the 3D orientation with the rotation quaternion included in its state vector. An innovative auto-nulling algorithm described herein captures and compensates the gyro drift based on the gyro's own output without requiring extra information from an accelerometer. The UKF incorporated with the auto-nulling algorithm provides a complete 3D estimation with a reasonable accuracy, without the aid of a magnetometer whose function may be affected during welding. The detection of human welders' torch manipulation is the foundation of studying their experienced behavior during the arc welding process, which has been extensively studied by the inventors. It is the core to understanding the difference between skilled and unskilled welders and can be utilized in accelerating the welder training process and developing next generation of intelligent welding robots. By simulations and experimental validation with torch motion signals captured from the real arc welding process, improvements in the accuracy of orientation estimation are demonstrated herein as compared with other orientation estimation counterparts.

The IMU <NUM> used in the example implementation is shown in <FIG>. In an example implementation it is a Shimmer motion sensor, but other IMU sensors, either wired or wireless, may also be used without affecting the algorithms that process the signals from the sensor to compute the orientation in any ways. The size of the example IMU <NUM> used for the experiments described herein is about <NUM> ×<NUM> × <NUM>. It is an IMU with wireless capability which is composed of a tri-axial accelerometer <NUM> (Freescale MMA7260Q), a tri-axial gyro sensor (InvenSense <NUM> series) <NUM>, a microprocessor (MSP430F1611) <NUM>, and a Bluetooth transceiver <NUM>. The accelerometer <NUM> is endowed with one filter capacitor in each axis. The gyro sensor <NUM> contains three vibrating elements. The angular rate at each axis is obtained by measuring the Coriolis acceleration of the corresponding vibrating elements. The microprocessor <NUM> captures the sensor data using a <NUM>-bit analog-to-digital converter (ADC) at a pre-defined frequency. The Bluetooth transceiver <NUM> transmits the data from the IMU <NUM> to a computer. The calibration procedure for the sensors is performed according to known techniques.

Also shown in <FIG> is a host device <NUM> (e.g., desktop computer, laptop computer, tablet computer, smart phone, server, and/or the like) that comprises a CPU/chipset <NUM>, storage <NUM>, transceiver <NUM>, and user interface circuitry <NUM>. The transceiver <NUM> is configured to receive data from the transceiver <NUM> of the IMU <NUM>. The CPU/chipset <NUM> is operable to process the data from the IMU <NUM> as, for example, described below in this disclosure. The data from the IMU <NUM> may be stored in storage <NUM> before and/or after it is processed by the CPU/chipset <NUM>. The data and/or results of the processing/analysis of the data may be presented via the user interface circuitry <NUM>. The CPU/chipset <NUM> may also be operable to generate feedback/control signals based on the data. Such signals may be conveyed (e.g., via transceiver <NUM>) to the torch <NUM>, a welding power source, a welding wire feeder, and/or other welding equipment to provide feedback to the torch operator and/or automatically compensate for the orientation and/or motion of the torch <NUM>.

A torch <NUM> for the GTAW process with the attached IMU <NUM> is illustrated in <FIG>. In the example shown, the IMU <NUM> is mounted rigidly at the tail of the torch <NUM> using a plastic fixture. In other implementations it may be mounted in other places/configurations anywhere as long as the operation of the torch <NUM> is not affected. The 3D Cartesian coordinate frame, denoted as S(XYZ), in the IMU <NUM> is its internal frame. It is worth noting that during, for performing the experiments described herein, the mounting process involved holding the torch <NUM> still such that its handle was perpendicular to the gravitation direction, with aid from external calibration tools, such as a gravimeter; the IMU <NUM> was installed such that the gravitational acceleration direction coincided with the SZ axis. The coordinate frame t(XYZ) is the internal frame for the torch <NUM>. It is defined in the following manner: axis tZ coincides with the torch <NUM> head direction, axis tX coincides with axis SX. By doing this, frame t(XYZ) can be obtained by rotating frame S(XYZ) around the SX axis for an angle denoted as θst.

The orientation of the torch <NUM> is determined when the axis orientation of the coordinate frame t(XYZ) is obtained with respect to an absolute 3D Cartesian coordinate frame, denoted as frame E(XYZ). The negative direction of axis EZ is defined in coincidence with the local gravitational direction. The directions of the other two axes depend on the specific welding applications, which will be detailed below.

The torch <NUM> orientation is represented by a quaternion denoted as <MAT> where the sign ~ denotes a unit quaternion q̃ = [q<NUM>, q<NUM>, q<NUM>, q<NUM>], i.e.,
<MAT>
where q<NUM> is the scalar part and [q<NUM>, q<NUM>, q<NUM>] is the vectorial part of the quaternion, and where, for the quaternion denotation, a leading subscript denotes the reference frame and a leading superscript indicates the frame being described.

The tri-axial gyroscope <NUM> in the IMU <NUM> measures the angular velocity of frame S(XYZ) relative to frame E(XYZ). The measurement (in rad s-<NUM>) can be denoted by the <NUM>×<NUM> row vector shown in equation (<NUM>):
<MAT>.

The quaternion at instant k + <NUM> can be presented using the quaternion at instant k, angular measurement (sωk), and the time interval denoted by Ts:
<MAT>.

The gyroscope <NUM> and the accelerometer <NUM> in the IMU <NUM> measure the angular velocity and the acceleration of the sensor, respectively. Besides the true values, Sωtrue and Satrue there are several main error sources affecting the IMU <NUM> measurement including the bias, scale-factor instability, non-orthogonality of axes and the measurement noise. To this regard, the IMU <NUM> measurements are expressed in equations (<NUM>) and (<NUM>):
<MAT>
<MAT>
where Sω and Sa are the scale-factor matrices; Tω and Ta are the non-orthogonality factor matrices; bω and ba are the bias; and vω and va are the measurement noises. This is a simplified sensor model. Some minor error sources are not considered, such as the cross-sensitivity and gravity-sensitivity, other embodiments may account for these error sources.

Measurement noises vω and va are normally considered as uncorrelated white Gaussian noises, with a null mean and <NUM>×<NUM> covariance matrices <MAT> and <MAT>, respectively. The covariance matrix of sensor model R is
<MAT>.

The true acceleration measurement includes two components: the sensor acceleration and the gravitation acceleration, as expressed by equation (<NUM>):
<MAT>
where sg is the gravitational acceleration in the sensor frame, which can be obtained using equation (<NUM>):
<MAT>.

The torch <NUM> should be moved smoothly along the seam <NUM> with unnoticeable accelerations (including "decelerations") throughout the arc welding process, given that the skilled welder is well motivated. Thereby, in the example implementation, sasensor is insignificant compared with the gravitational acceleration and thus may be considered as a disturbance. Henceforth, equation (<NUM>) can be expressed by equation (<NUM>):
<MAT>
Normalized gravity may be used to eliminate the measurement error caused by localized gravity differences.

The bias and the scale factors, in equations (<NUM>) and (<NUM>), depend on non-idealities of the IMU <NUM> and the working field. The typical bias of the gyro <NUM> is <NUM>-<NUM> rad h-<NUM> and the acceleration bias is about <NUM>-<NUM>µg for tactical grade. In particular, the ambient temperature significantly affects the bias of the gyro <NUM>. In the example implementation, the IMU <NUM> is employed near the welding arc which is a strong heat source. Hence, the bias of the gyro <NUM> might not be constant throughout an arc welding process. In an example implementation of this disclosure, an auto-nulling algorithm is used to compensate the drift of the gyro <NUM> in-line to guard the effect of the drift variation over temperature to the estimation accuracy.

The influence of temperature on the bias of the accelerometer <NUM> is much less intense. The in-line calibration of the accelerometer <NUM> may require the vector output of the accelerometer <NUM> to remain in a quasi-static equilibrium for several different orientations. That is, require the accelerometer <NUM> to be not accelerating or decelerating at more than a determined threshold. The threshold may be set to any value greater than or equal to <NUM>. In an example implementation, the vector output of the accelerometer <NUM> may be lower than a determined threshold when the accelerometer <NUM> is in quasi-static equilibrium. However, in a typical application, the torch <NUM> should be held in one certain orientation, as shown in <FIG> and <FIG>, throughout the arc welding process. Therefore, there will not be enough orientations for in-line calibration. Accordingly, in the example implementation, the bias of the accelerometer <NUM> is assumed to be constant, and compensated for by calibration before use.

The scale-factor drifts of IMU <NUM> are known to affect the measurement accuracy to a much smaller extent than the bias drifts. The drift variation over temperature is also negligible. Therefore, in the example implementation, the scale factors are considered to be subjected to small variations around their average values throughout the welding process. Their nominal values may be determined through the sensor calibration before use.

The capture of the drift of the gyro <NUM> may require keeping the gyro <NUM> from rotation. The basic principle is called the zero attitude update (ZAU), also referred as auto-nulling, i.e., when no rotation occurs to the gyro <NUM>, its output can be considered as the drift caused by the bias and other error sources. The drift can then be periodically captured and compensated for. In the example implementation, a new auto-nulling algorithm is used in which the quasi-static equilibrium status is detected using information from the gyro's own output.

The mean and deviation of the output of the gyro <NUM> obtained in a small time interval when the IMU <NUM> is set still can be used to determine whether in quasi-static equilibrium. The two variables are defined by
<MAT>
<MAT>
where M is the number of samples. To record the data for calculating µS and σS, a quasi-static equilibrium data acquisition process may be conducted where the IMU <NUM> is set still at room temperature (about <NUM>). Before recording valid data from the gyro <NUM>, the IMU <NUM> is allowed to power up for a few minutes until it reaches thermal stability.

For an arbitrary angular velocity Sωi recorded by the gyro <NUM>, the corresponding mean and deviation are defined in equations (<NUM>) and (<NUM>)
<MAT>
<MAT>
where i > N, and N is the number of samples of the gyroscope output gathered in a small interval Tau right before Sωi is recorded. In the example implementation, Tau = <NUM>.

If the mean and the deviation of the output of the gyro <NUM> within the interval Tau are close (within a determined threshold) to µS and σS, then the torch <NUM> and IMU <NUM> are considered to be in quasi-static equilibrium. Other methods for detecting quasi-static equilibrium are of course possible. According to the ZAU principle, the mean value, µ(i), can be thus thought of as a drift. In the example implementation, the possible ambient temperature variation caused by the welding arc is in a comparatively low rate due to the thermal latency. Therefore, the data from the gyro <NUM> in the time vicinity of the quasi-static equilibrium interval can be compensated using the drift obtained in the quasi-static equilibrium interval. If the IMU <NUM> is in a dynamic period (µ(i) or σ(i) are much larger than µS and σS), then compensation can be accomplished by the mean value from the nearest quasi-static equilibrium interval.

Furthermore, the drift of a gyro <NUM> may be sensitive to temperature, as discussed above. Therefore, in an example implementation, two thermal coefficients, ρµ and ρσ, are included in the auto-nulling algorithm to account for the temperature difference between the environment where the torch <NUM> and IMU <NUM> is used and the one where the quasi-static equilibrium experiment was conducted. For the simulations discussed below, they were set to <NUM>, since the temperature at which the quasi-static equilibrium experiment was conducted was about the same as that in which the simulations were conducted. The coefficients may be pre-set and given reasonable values based on estimation results and/or empirically chosen.

Hence, if there exist
<MAT>
then the torch <NUM> and IMU <NUM> is considered to be in quasi-static equilibrium, and µ(i) is referred to as a valid drift.

Therefore, the auto-nulling algorithm according to the present invention is expressed by
<MAT>
where µ(ξ) is the nearest valid drift for Sωi, ξ < i.

Using the auto-nulling algorithm described above, no data is required from some external sensors to compensate for the effect of drift to the orientation estimation. The effectiveness of the algorithm will be evaluated below.

In an example implementation, the state vector of the UKF is composed of the torch orientation quaternion and the angular velocity.

Using the state vector, the sensor model (equations (<NUM>) and (<NUM>)) can be rewritten as shown in equation (<NUM>):
<MAT>
where
<MAT>.

The process model represented by the state vector is
<MAT>
where <MAT> is the process noise with a covariance matrix denoted as Qk, exp(ωk) is the increment of the rotation in the kth sampling period, and exp(wq) is the process uncertainty caused by wq, which is the quaternion component of the process noise.

In the example implementation, the angular velocity is expected to be fairly small, since the torch <NUM> is required to be maintained in a recommended orientation with small adjustments for possible disturbances. Therefore, the angular velocity can be modeled as a random walk in the process model.

Because of the nonlinear nature of the process model (equation (<NUM>)) and the sensor model, the UKF approach is applied. The UKF algorithm is summarized below.

Given the estimated state vector x̂k-<NUM> and its covariance Pk-<NUM> at instant k - <NUM>, an auxiliary vector set {ψi} is defined by equation (<NUM>):
<MAT>
where <MAT> is the ith row of the matrix square root, and λ = α<NUM>(n + κ) - n, in which α and κ are two scaling parameters. A subtle detail worth noting is that the dimension of covariance Pk-<NUM> is <NUM>×<NUM>, since the degree of freedom (DOF) of the state vector is <NUM> (the unit quaternion constraint reduces one DOF). Therefore, the Ψis are <NUM>×<NUM> vectors.

UKF addresses the approximation of a nonlinear system by using a minimal set of sample points, i.e., sigma points, to capture the mean and covariance estimates. The sigma points set {(Xk-<NUM>)i} is defined by
<MAT>
as i = <NUM>, and
<MAT>
when i = <NUM>,. , <NUM>n, and ψi = [ψi|q, ψi|ω] in which ψi|q is the first three elements of ψi corresponding to the quaternion part, and ψi|ω relates to the angular velocity. The length of state vector Xk-<NUM> is <NUM>, while ψi is a six-element vector. Thereby, equation (<NUM>) performs a vector to quaternion conversion for ψi|q using the quaternion exponential in equation (<NUM>).

After the sigma points {(Xk-<NUM>)i} are obtained, the process model is used to project each point ahead in time. The propagation results are shown in equation (<NUM>), and a priori state estimate is thus obtained in equation (<NUM>):
<MAT>
<MAT>
where weights Wi(m) are defined by
<MAT>
The covariance of (χk)i is
<MAT>
where weights Wi(c) are defined in equation (<NUM>), and β is a scaling parameter used to incorporate prior knowledge about the distribution of state vector x. It should be noted that <MAT> is a <NUM>×<NUM> matrix, while (χk)i and <MAT> are seven-element vectors. A conversion is thereby performed to the right side of the equation to transform the quaternion parts into three-element rotation vectors. This quaternion-to-rotation conversion is a reverse procedure of equation (<NUM>):
<MAT>.

The results for the projected set {(χk)i} in the sensor model are expressed by
<MAT>
The measurement estimate can thus be defined in equation (<NUM>):
<MAT>
The a posteriori state estimate is computed using
<MAT>
where zk is the measurement vector from IMU <NUM>, and Kk is the Kalman gain which is defined by
<MAT>.

The cross correlation matrix Px̂kẑk and measurement estimate covariance Px̂kẑk are expressed in equations (<NUM>) and (<NUM>), respectively:
<MAT>
<MAT>.

A quaternion-to-rotation conversion is performed to the term in the second bracket of equation (<NUM>), to ensure a valid cross correlation matrix. The estimated state covariance is updated at instant k by
<MAT>.

In an example implementation, for a successful UKF performance, the following parameters are required to be determined first: Qk, R, α, β, κ. Scaling parameters α, β, κ may be empirically pre-set and given reasonable values based on filter tests results. <MAT> and <MAT> account for the spectral density of the sensor signal while the sensor is lying still.

The process noise covariance Qk can be determined by
<MAT>
where Φs is a scaling parameter, Φ(τ) is an approximation to the fundamental matrix calculated by taking the Taylor series expansion of the system dynamic matrix, and Q' is the continuous process noise matrix. The covariance matrix Q' is expressed by
<MAT>
Where <MAT> and <MAT> are the covariance matrix of the quaternion part and angular velocity part of the process noise, respectively, which, in the example implementation, are assumed to be uncorrelated, zero-mean white noise.

The orientation estimation scheme was tested using the IMU <NUM> detailed above. Raw data was recorded, transmitted to a desktop, and processed in accordance with aspects of this disclosure. A welding robot (Universal Robot UR <NUM>) was used to provide reference measurements of the torch orientation. To do so, either the torch (in welding experiments) or the IMU <NUM> (in simulations) was rigidly mounted on the robot tool center, the center of the plane on the robot forearm. The orientation of the tool center was calculated by the imported accompanying software using the feedback from the robot. The obtained reference orientation was filtered by a second-order low-pass Butterworth filter (cut-off frequency: <NUM>). Initial calibration was conducted to determine the quaternion for converting the tool center orientation to the torch <NUM> and IMU <NUM> orientation. The performance of the example implementation was evaluated by comparing it with the reference measurements.

The accuracy of the reference orientation delivered by the welding robots depends on the accuracy of the orientation measurement of the robot tool center and on the robot-IMU orientation calibration. The orientation measurement error of the robot can be estimated using the data supplied by the robots manufacturer. The repeatability of the robot is ±<NUM>. The robot's shortest forearm around which the robot tool center rotates is about <NUM>. Hence, its maximum orientation error is about <NUM>°, which is acceptable as a measurement reference for an example implementation.

A reference 3D Cartesian coordinate frame E(XYZ) was defined to justify valid orientation measurements: the z-axis is defined above; the x-axis and y-axis were arbitrarily defined by the right-hand rule. The IMU <NUM> was mounted on the robot tool center such that its internal coordinate frame S(XYZ) was identical to frame E(XYZ) at the initial position.

To simulate a human hand's behavior, the welding robot was set in the teaching mode such that the robot tool center could be rotated manually and smoothly around the three axes of its internal frame. Four data sets were constructed in simulations denoted by <MAT>, where i = <NUM>, <NUM>, <NUM>, <NUM>. To evaluate the performance of the example implementation in the three dimensions separately, the IMU <NUM> was rotated around one axis in each simulation. Hence, for <MAT> to <MAT>, the robot tool center (and the IMU <NUM>) was rotated around the x-axis, y-axis and z-axis, respectively. The rotation sequence in the three data sets is identical, i.e., first rotate <NUM>° (the positive direction indicates a clockwise rotation as viewed from the negative to the positive direction of one axis), back to initial position, then rotate -<NUM>°, and back to initial position again. In each stage (at <NUM>°, -<NUM>° and the initial positions), the robot tool center stayed still for a few seconds. It should be noted that the stationary phases might not exactly be <NUM>°, -<NUM>° or <NUM>°, since the robot tool center was manually rotated. Yet, it does not affect the simulation procedure, or the estimation accuracy.

For <MAT>, the robot tool center was rotated around the three axes together with the aforementioned rotation sequence. The robot tool center was thought to be much steadier than a human hand due to a human's inherent neuro latency. To this regard, data set <MAT> was further artificially constructed by introducing two random Gaussian noises into the data from the gyro <NUM> and accelerometer <NUM> in <MAT>, respectively, in order to simulate the unsteadiness of a human hand. The variances of the noise for the data from the gyro <NUM> and accelerometer <NUM> in <MAT> were <NUM>×<NUM> -<NUM> and <NUM>×<NUM>-<NUM>.

Two UKF implementations were studied, henceforth called method A and method B. Method A incorporated the auto-nulling algorithm described above, while method B did not. Two additional trapezoidal numerical integration methods were also included as two comparisons: method C adopted the auto-nulling algorithm described above, while method D did not. Four methods were tested at three different sampling rates: <NUM>, <NUM> and <NUM>. Six repeated tests were conducted for each condition, including both methods and sampling rates.

The performance metric adopted in the example implementation is the root-mean-square error (RMSEθ) of the orientation in degree, which is defined by
<MAT>.

Two data sets of torch orientation, denoted by <MAT> and <MAT>, were obtained from welding experiments. The data set <MAT> was collected from the GTAW experiments, containing four types of welding fit-ups sequentially corresponding to the configurations in <FIG>, and the data set <MAT> was obtained from the GMAW experiments including the welding types as shown in <FIG>. Furthermore, two more data sets <MAT> and <MAT> were artificially constructed by introducing the same noise mentioned in the last section into <MAT> and <MAT>, respectively. The tested method was method A, which was the contest winner in the simulation trials. Six repeated trials were conducted for each welding type.

To construct the data sets, the torch <NUM> with attached IMU <NUM> (as shown in <FIG>) was mounted on the tool center of the welding robot which was set in the teaching mode. A novice welder was asked to hold the robot forearm and perform the aforementioned experiments. Each welding type lasted about <NUM>. The welder took a break and set the torch <NUM> to the initial posture between every two welding trials. The welding conditions for the GTAW experiments are listed in table <NUM>. No filler metal was used in the experiments. For the GMAW experiments, not only the torch orientations were required to be maintained, but the specific torch swing patterns needed to be followed. In the experiments, the arc did not start due to the limited welding skill of the novice welder, i.e., the torch <NUM> was firmly held above and smoothly dragged along the weld seam <NUM> without the arc being established. The experimental data was transmitted to a host computer, and was processed offline using Matlab R2011.

A reference 3D Cartesian coordinate frame E'(XYZ) was defined for the experimental data. The negative direction of E'Z coincided with the gravitational direction. The positive direction of E' Y was the welding direction along the weld seam. Axis E'X was then determined using the right-hand rule. In the experiments, the spatial relation between the torch and the robot was carefully calibrated. In the initial posture, the torch head was set such that directions of the axis in E' (XYZ) coincide with those in t(XYZ), respectively.

The initial parameters for the UKF are listed in table <NUM>.

The mean and standard deviation of the output of the gyro <NUM> when the IMU <NUM> is stationary at room temperature conditions, µs and σs, were measured using equations (<NUM>) and (<NUM>). The coefficients ρµ and ρσ were chosen to be <NUM> when conducting the simulations:
<MAT>
<MAT>
The statistics of the resultant estimation of the RMSEθ are listed in table <NUM>. In table <NUM>, the estimated performance of method A is compared with the other three counterpart algorithms by the mean and the standard deviation of the RMSEθ. Table <NUM>. Orientation estimation (RMSEθ), in the form of the mean± standard deviation, obtained by the different estimation methods in the course of the Monte Carlo performance trials. The additional distance of gyro <NUM> and acceleration were artificially introduced in data set
<IMG>.

The results of the orientation estimation for the three individual axes (RMSEs [°]) are presented in table <NUM>. The evaluated data sets are <MAT> of and <MAT>, respectively.

<FIG> and <FIG> show the time functions of the Euler angles as they were measured in the simulation trials, and the reference measurements were from the welding robot. In particular, <FIG> shows the estimation of the orientation in the x-axis, y-axis and z-axis using data sets are <MAT> and <MAT>, respectively. The 3D orientation estimation is presented in <FIG>, obtained using the four algorithms with data set <MAT>. <FIG> shows the quaternion time functions obtained by method A, using the data set corresponding to <FIG>. It should be noted that each of the figures only shows one of the estimation result of the six trials for the corresponding simulation conditions.

Tables <NUM> and <NUM> show the estimation results of slow torch movement, in which the angular rate is about <NUM>° s-<NUM>. The orientation estimation results for an angular rate larger than <NUM>° s-<NUM> of the torch movement are presented in table <NUM>.

One can find from the simulation results that method A produces the best performance. The sampling rate chosen to conduct the experiments is <NUM>, since it provided a good trade-off between estimation accuracy and computation load. Table <NUM> shows the mean and standard deviation of the estimated RMSEθ obtained from the aforementioned experiments consisting of the two welding processes (GTAW and GMAW), each of which includes the four welding fit-ups.

Since the welding experiments last only about <NUM> on average, the ambient temperature is not significantly changed compared with that when the IMU <NUM> were tested for the drift while in quasi-static equilibrium. Therefore, thermal coefficients ρµ and ρσ were tuned in the range between <NUM> to <NUM> (they were set at <NUM> in the GMAW experiments).

<FIG> show the typical orientation estimation results in Euler angles. In particular, <FIG> shows the estimation results in one GTAW process with a lap joint, corresponding to the welding process shown in <FIG>. The initial posture of the torch <NUM> should be <NUM>° in all the three axes. According to the related welding type (<FIG>), the welder is expected to maintain the 3D orientation of the torch at [<NUM>°, -<NUM>°, CR], where CR denotes 'customrelated', i.e., the orientation in that particular axis depends on the welder's individual operation custom. One can see in <FIG> that the torch orientation deviated about <NUM>° from the recommended torch posture as shown in <FIG>. This is normal since the welder is a novice welder who has not mastered the torch manipulation yet. The welding processes, the results of which are shown in <FIG>, are illustrated in <FIG>(A)-(C), respectively. The recommended torch postures for the three welding types are [<NUM>° ~ <NUM>°, -<NUM>°, CR], [<NUM>°, <NUM>°, <NUM>°], and [<NUM>°, <NUM>°, <NUM>°], respectively. Similarly, the orientation deviations from the corresponding recommendations are observed in the resultant figures. Nevertheless, those deviations do not affect the estimation accuracy.

In method A, the auto-nulling algorithm is incorporated in the effort to compensate the possible time-varying gyro drift during the simulations and the welding experiments; while for the in-line self-calibration of the accelerometer, multiple postures are required. However, the torch orientation is expected to be maintained at the recommended postures throughout the welding experiments. There are thus not enough postures in a single experiment for the accelerometer to conduct the calibration.

The UKF parameter initialization listed in table <NUM> is found to work well after running an extensive number of simulations or experiments, even in the presence of the incorporated noises. The IMU <NUM> was calibrated before use. In addition, the auto-nulling algorithm was also incorporated in method A to compensate for the gyro drift. Hence the covariances of the measurement noise and the process noise chosen for method A are comparatively small; while the covariances in method B are selected to be larger than those in A due to the absence of the auto-nulling algorithm. The process noise may be increased to compensate for the disturbance of the inaccurate modeling and to improve the tracking ability of the filter.

The results reported in tables <NUM> and <NUM> show that the combination of the UKF and the auto-nulling algorithm give the best performance. Results for the x-axis and y-axis orientation estimations are comparable in accuracy. Yet, the z-axis estimation shows comparatively poor accuracy. It is arguable that because the accelerometer <NUM> cannot provide the torch's orientation information in the z-axis, estimations in the UKF solely rely on the accuracy of the gyro <NUM> outputs themselves. The performance is thus relatively poor without aid from the acceleration data. Another interesting observation can be found in table <NUM> by comparing the performance of method A and method B: the RMSExs and RMSEys yielded by the two methods are comparable, yet, the corresponding RMSEθ obtained using method A is significantly smaller. One can conclude from this observation: (<NUM>) the main source of RMSEθ is from the estimation for the z-axis (heading); (<NUM>) significant improvement in estimation accuracy can be obtained by applying the auto-nulling algorithm described herein to compensate for the gyro drift.

In another example implementation, data from a magnetic sensor <NUM> is fused into the UKF to improve the estimation accuracy in the z-axis. However, the existence of the strong magnetic interference from the welding machine and welding arc, poses challenges to maintaining accuracy of the orientation estimation. Fortunately, even without an extra magnetic sensor <NUM>, the 3D estimation errors reported in tables <NUM> and <NUM> may be acceptable. Furthermore, in implementations in which only accelerometers and gyroscopes are applied, cost/complexity is reduced as compared to an implementation in which magnetometers are added.

Degradations in estimation accuracy are observed in both tables <NUM> and <NUM> after injecting the noise into the gyro data and acceleration data. The auto-nulling algorithm is able to compensate for the noise in the gyro data. However, the contaminated acceleration data contains both the gravitation and the fake acceleration induced by the injected noise, while the acceleration of the IMU <NUM> is considered as a disturbance in the sensor model (equation (<NUM>)). The sensor model thus tends to be less accurate with the existence of the acceleration, and that leads to a degraded orientation estimation. Similar results can be found in table <NUM>. As the torch movement becomes faster, the accelerometer is more likely to detect the acceleration of the torch's movement. The estimation accuracy is thus degraded.

Within the limits of the analysis performed, increasing the sampling rate does improve the estimation accuracy, but its effect is not prominent. Unlike the EKF, which usually requires a high sampling rate to avoid the possible filter instability, the UKF has no such stability issue. Increasing the sampling rate is a huge computation and energy assumption burden for a battery-powered IMU <NUM>. Therefore, the sampling rate was set at <NUM> in the welding experiments.

One can find that some of the recommended torch orientations do not require specifications for the z-axis posture, such as those for the welding types in <FIG>. This is because the torch posture in the z-axis does not necessarily relate to weld quality in some welding processes. On the other hand, a proper z-axis torch posture is recommended for weld types like those shown in <FIG>, in order to perform a qualified weld. Furthermore, in the applications mentioned in section <NUM>, an accurate totally 3D orientation estimation can be highly useful.

The effect of the torch's swing motions to the torch <NUM> orientation can be found by comparing <FIG> and <FIG>: more ripples are observed in the torch orientation curves as torch swing motions are augmented. Yet, no extra errors were observed to be yielded in the orientation estimation due to the swing motions.

Methods and systems are provided herein for measuring 3D welding torch orientation, which can be conveniently adapted into a manual arc welding process or a welder training system, are described herein. An example implementation comprises a quaternion-based UKF incorporated by an auto-nulling algorithm. The UKF aims for the estimation of the 3D welding torch orientation using a miniature IMU <NUM> endowed with a tri-axis gyro and a tri-axis accelerometer. The auto-nulling algorithm serves as an in-line calibration procedure to compensate for the gyro drift, which has been verified to significantly improve the estimation accuracy in three-dimensions, especially in the heading estimation. In an example implementation, the methods and systems described herein provide an accurate orientation estimation without aid from an extra magnetometer. The accuracy of the estimation has been validated by simulation and welding experiments. Statistics show that the estimation error in an example implementation is in the order of <NUM>°.

In accordance withthe present invention, a system (e.g., <NUM>) receives signals from an inertial measurement unit (e.g., <NUM>) affixed to a welding torch <NUM> (or another tool such as a cutting torch, saw, etc. or a tool accessory such as gloves) and analyzes the signals to detect whether the apparatus is in quasi-static equilibrium. The system generates a gravitational acceleration vector based on a portion of the signals received while the torch is in quasi-static equilibrium (e.g., during extended periods when the operator intentionally pauses and/or during inadvertent/momentary intervals on the order of milliseconds). The system performs a real-time (e.g., during a welding or cutting operation where the apparatus is a welding or cutting torch) calibration of the inertial measurement unit based on the gravitational acceleration vector. The performance of the real-time calibration comprises a determination of the angle between an axis of a coordinate system of the inertial measurement unit (e.g., <FIG>) and the gravitational acceleration vector. The performing the real-time calibration may comprise determining a rate of angular drift. The system determines orientation of the inertial measurement unit in real-time based on the signals and based on values determined during the real-time calibration. The system processes the signals using an unscented Kalman filter and an auto-nulling algorithm as described above.

In accordance with an example implementation of this disclosure, a system (e.g., <NUM>), comprises a processor (e.g., <NUM>) and a transceiver (e.g., <NUM>). During a time interval in which an apparatus is known to be in quasi-static equilibrium (e.g., during extended periods when the operator intentionally pauses and/or during inadvertent/momentary intervals on the order of milliseconds), the transceiver receives a first set of gyroscope output samples from an inertial measurement unit e.g., <NUM>) affixed to an apparatus (e.g., a tool such as a welding torch <NUM>, a cutting torch, saw, etc. or a tool accessory such as gloves), and the processor calculates one or more metrics for the first set of gyroscope output samples. During manipulation of the apparatus (e.g., during a weld operation or cutting operation where the apparatus is a welding torch or cutting torch) the transceiver receives a second set of gyroscope output samples from the inertial measurement unit affixed to the apparatus. During manipulation of the apparatus, the processor calculates the one or more metrics for the second set of gyroscope output samples, generates a decision as to whether the apparatus is in quasi-static equilibrium based on the one or more metrics for the first set of gyroscope output samples and the one or more metrics for the second set second gyroscope output samples, and determines an angular velocity of the apparatus based on the second set of gyroscope samples and based on the decision as to whether the apparatus is in quasi-static equilibrium. The processor may determine a drift of the gyroscope based on a mean value of the first set of gyroscope output samples. The processor may use the drift of the gyroscope during the determination of the angular velocity of the apparatus. If the decision is that the apparatus is in quasi-static equilibrium, the determination of the angular velocity of the apparatus may comprise a determination of the angular velocity to be a mean value of the second set of gyroscope output samples, and if the decision is that the apparatus is not in quasi-static equilibrium, the determination of the angular velocity may include compensation for the drift. The determination of the angular velocity may include compensation for a difference between a temperature of the inertial measurement unit during generation of first set of gyroscope output samples and a temperature of the inertial measurement unit during generation of the second set of gyroscope output samples. The one or more metrics may comprise one or both of mean and standard deviation. The generation of the decision as to whether the apparatus is in quasi-static equilibrium may comprise a determination of a difference, or absolute difference, between the one or more metrics for the first set of gyroscope output samples and the one or more metrics for the second set of gyroscope output samples.

The present methods and/or systems may be realized in hardware, software, or a combination of hardware and software. A typical combination of hardware and software may be a general-purpose computing system with a program or other code that, when being loaded and executed, controls the computing system such that it carries out the methods described herein.

Claim 1:
A method for measurement of three-dimensional welding torch orientation for manual arc welding process, comprising:
- receiving by a computer system (<NUM>) signals from an inertial measurement unit IMU (<NUM>) affixed to a welding torch (<NUM>);
characterized by
- analyzing by said computer system (<NUM>) said signals to detect whether said welding torch (<NUM>) is in quasi-static equilibrium;
- generating by said computer system (<NUM>) a gravitational acceleration vector based on a portion of said signals received while said welding torch (<NUM>) is in said quasi-static equilibrium; and
- performing by said computer system (<NUM>) during welding a real-time calibration of said inertial measurement unit (<NUM>) based on said gravitational acceleration vector, wherein said performing said real-time calibration comprises determining the angle between an axis of a coordinate system of said inertial measurement unit (<NUM>) and said gravitational acceleration vector;
- determining orientation of said inertial measurement unit (<NUM>) in real-time based on said signals and based on the values determined during said real-time calibration; and
- processing said signals using a quaternion-based unscented Kalman filter and an auto-nulling algorithm, wherein the unscented Kalman filter is designed to estimate the three dimensional orientation with the rotation quaternion included in its state vector, and
wherein the auto-nulling algorithm is expressed by
<MAT>
wherein
sω is the angular velocity of the IMU sensor,
sωi is the angular velocity at ith/present sampling time, i.e., at time i which is the present time,
N is the number of the readings needed to calculate an average/mean,
µs is the estimate of the angular velocity in the initial period when the IMU is set still:
<MAT>
with sωk (k = <NUM>, ..., M) being the angular velocity reading from the still period,
µ(i) is the mean of the angular velocity at ith sampling time when the IMU is judged to be at still:
<MAT>
with N being the number of readings from the IMU after being judged to be still, and sωk (k = i - N, ...,i) being these readings, µ(ξ) is the most recently updated (at time ξ<i) drift of the IMU sensor that is available at the present time i.