Excavator control architecture for generating sensor location and offset angle

Abstract

A machine is disclosed including a sensor on a limb, an implement, an architecture, and a linkage assembly (LA) including a boom and a stick. The architecture comprises one or more LA actuators and a controller that generates a sensor location and offset angle ϕ and is programmed to: pivot the limb (either the boom or stick) about a pivot point and generate a set of sensor signals. The controller is programmed to repeatedly execute an iterative process n times until exceeding a threshold, which process comprises determining a sensor location estimate .sub.n (a distance between the sensor and the pivot point) and an offset angle estimate ϕ.sub.n defined relative to a limb axis. A utilized optimization model includes the set of sensor signals and error terms.

Claims

1. An excavator comprising an excavating linkage assembly, a dynamic sensor, an excavating implement, and control architecture, wherein: the excavating linkage assembly comprises an excavator boom, an excavator stick, a boom coupling, a stick coupling, and an implement coupling; the dynamic sensor is positioned on a limb, wherein the limb is one of the excavator boom and the excavator stick; and the control architecture comprises one or more linkage assembly actuators, and an architecture controller programmed to operate as a partial function of a sensor location and an offset angle ϕ of the dynamic sensor and to execute machine readable instructions to pivot the limb on which the dynamic sensor is positioned about a pivot point, generate a set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}) at least partially derived from the dynamic sensor, the set of dynamic signals comprising an x-axis acceleration value A.sub.X, a y-axis acceleration value A.sub.Y, a measured angular rate relative to gravity {dot over (θ)}.sub.M, an estimated angular rate {dot over ({circumflex over (θ)})}, and an estimated angular position {circumflex over (θ)}, execute an iterative process comprising determining a sensor location estimate .sub.n and an offset angle estimate ϕ.sub.n, wherein (i) the sensor location estimate .sub.n is defined as a distance between the dynamic sensor and the pivot point, (ii) the offset angle estimate ϕ.sub.n of the dynamic sensor is defined relative to a limb axis, (iii) the determination comprises the use of an optimization model comprising the set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}), and (iv) the iterative process is repeated n times to generate a set of sensor location estimates (.sub.1, .sub.2, . . . , .sub.n) and a set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n) until n exceeds an iteration threshold t, and generate the sensor location and the offset angle ϕ based on the set of sensor location estimates (.sub.1, .sub.2, . . . , .sub.n) and the set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n).

2. The excavator as claimed in claim 1, wherein the iterative process further comprises: determining a total error based on the optimization model and the set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}), and comparing the total error against an optimization threshold; and executing the iterative process until the total error is less than the optimization threshold to minimize drift.

3. The excavator as claimed in claim 1, wherein the dynamic sensor comprises an inertial measurement unit (IMU), an inclinometer, an accelerometer, a gyroscope, an angular rate sensor, a rotary position sensor, a position sensing cylinder, or combinations thereof.

4. The excavator as claimed in claim 1, wherein the dynamic sensor comprises an inertial measurement unit (IMU) comprising a 3-axis accelerometer and a 3-axis gyroscope.

5. The excavator as claimed in claim 1, wherein: the set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}) are generated from a captured data set originating from the dynamic sensor; the captured data set comprises a first data section corresponding to a first sensor location .sub.1 and a first offset angle ϕ.sub.1 and a second data section corresponding to a second sensor location r.sub.2 the iterative process executed by the architecture controller comprises a validity check where sensor readings from the first data section are compared to sensor readings from the second data section to return a validity indication.

6. The excavator as claimed in claim 5, wherein: the validity indication is positive when the sensor readings from the first data section and the sensor readings from the second data section are within an acceptable difference of one another.

7. The excavator as claimed in claim 6, wherein the validity indication is negative when the sensor readings from the first data section and the sensor readings from the second data section are outside the acceptable difference.

8. The excavator as claimed in claim 7, wherein the architecture controller is programmed to calibrate the dynamic sensor when the validity indication is negative.

9. The excavator as claimed in claim 6, wherein the architecture controller is programmed to generate the sensor location and the offset angle ϕ when the validity indication is positive.

10. The excavator as claimed in claim 5, wherein the captured data set represents pivoting the limb on which the dynamic sensor is positioned for a period of time in a range of from about 10 seconds to about 30 seconds.

11. The excavator as claimed in claim 1, wherein the optimization model is a function of gravitational acceleration g, an estimation error e, a tangential acceleration A.sub.T of the dynamic sensor, a dynamic angular acceleration of the dynamic sensor over time {umlaut over ({circumflex over (θ)})}, a dynamic angular rate of the dynamic sensor over time {dot over ({circumflex over (θ)})}, and an initial start angle θ between the terminal pivot points A and B of the excavator boom and the excavator stick relative to horizontal.

12. The excavator as claimed in claim 11, wherein the optimization model comprises a first equation for {umlaut over ({circumflex over (θ)})} comprising a first term $\frac{g}{}\left(A_T+\sin \left(\theta \right)\right)$ and one or more error terms, and the optimization model further comprises the following additional equations:
{circumflex over (θ)}=∫{dot over (θ)}.sub.m+θ.sub.IC
{dot over ({circumflex over (θ)})}=∫{umlaut over ({circumflex over (θ)})}+{dot over (θ)}.sub.IC and
A.sub.T=A.sub.x cos(ϕ)−A.sub.y sin(ϕ) where
e={dot over (θ)}.sub.m−{dot over ({circumflex over (θ)})}, for which {dot over (θ)}.sub.m is a dynamic angular rate of the dynamic sensor as measured by a gyroscope of the dynamic sensor.

13. The excavator as claimed in claim 11, wherein the optimization model further comprises the following set of equations: $A_{R,M}=A_x\sin \left(\varphi \right)+A_y\cos \left(\varphi \right)$ $\mathrm{and}$ $=\frac{g}{}{\stackrel{.}{\theta }}^2-\cos \left(\theta \right)$ where A.sub.R,M is a measured radial acceleration of the dynamic sensor, is an expected radial acceleration based on the optimization model, and A.sub.R,M is equivalent to .

14. The excavator as claimed in claim 11, wherein the optimization model comprises an error based on a following equation: $\mathrm{Error}=.Math.{\left(\frac{g}{}{\widehat{\stackrel{.}{\theta }}}^2-\cos \left(\hat{\theta }\right)-A_{R,M}\right)}^2+.Math.{\left({\stackrel{.}{\theta }}_m-\widehat{\stackrel{.}{\theta }}\right)}^2.$

15. The excavator as claimed in claim 1, wherein the control architecture comprises a non-transitory computer-readable storage medium comprising the machine readable instructions.

16. The excavator as claimed in claim 1, wherein the one or more linkage assembly actuators facilitate movement of the excavating linkage assembly.

17. The excavator as claimed in claim 16, wherein the one or more linkage assembly actuators comprise a hydraulic cylinder actuator, a pneumatic cylinder actuator, an electrical actuator, a mechanical actuator, or combinations thereof.

18. The excavator as claimed in claim 1, wherein the excavator boom comprises a variable-angle excavator boom.

19. An earthmoving machine comprising a dynamic sensor, an earthmoving implement, and control architecture, wherein: the dynamic sensor is positioned on a limb of the earthmoving machine; and the control architecture comprises one or more linkage assembly actuators, and an architecture controller programmed to operate as a partial function of a sensor location and an offset angle ϕ of the dynamic sensor and to execute machine readable instructions to pivot the limb on which the dynamic sensor is positioned about a pivot point, generate a set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}) at least partially derived from the dynamic sensor, the set of dynamic signals comprising an x-axis acceleration value A.sub.X, a y-axis acceleration value A.sub.Y, a measured angular rate {dot over (θ)}.sub.M, an estimated angular rate {dot over ({circumflex over (θ)})}, and an estimated angular position {circumflex over (θ)}, and execute an iterative process comprising determining a sensor location estimate .sub.n and an offset angle estimate ϕ.sub.n, wherein (i) the sensor location estimate .sub.n is defined as a distance between the dynamic sensor and the pivot point, (ii) the offset angle estimate ϕ.sub.n of the dynamic sensor is defined relative to a limb axis, (iii) the determination comprises the use of an optimization model comprising the set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}), and (iv) the iterative process is repeated n times to generate a set of sensor location estimates (.sub.1, .sub.2, . . . , .sub.n) and a set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n) until n exceeds an iteration threshold t, and generate the sensor location and the offset angle ϕ based on the set of sensor location estimates (.sub.1, .sub.2, . . . , .sub.n) and the set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n).

20. A method of generating a sensor location and an offset angle ϕ of a dynamic sensor on and with respect to a limb of an earthmoving machine, the method comprising: pivoting, via an architecture controller, the limb on which the dynamic sensor is positioned about a pivot point; generating a set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}) at least partially derived from the dynamic sensor, the set of dynamic signals comprising an x-axis acceleration value A.sub.X, a y-axis acceleration value A.sub.Y, a measured angular rate {dot over (θ)}.sub.M, an estimated angular rate {dot over ({circumflex over (θ)})}, and an estimated angular position {circumflex over (θ)}; executing an iterative process comprising determining a sensor location estimate .sub.n and an offset angle estimate ϕ.sub.n, wherein (i) the sensor location estimate .sub.n is defined as a distance between the dynamic sensor and the pivot point, (ii) the offset angle estimate ϕ.sub.n of the dynamic sensor is defined relative to a limb axis, and (iii) the determination comprises the use of an optimization model comprising the set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}); repeating the iterative process n times to generate a set of sensor location estimates (.sub.1, .sub.2, . . . , r.sub.n) and a set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n) until n exceeds an iteration threshold t; and generating, via the architecture controller, the sensor location and the offset angle ϕ based on the set of sensor location estimates (.sub.1, .sub.2, . . . , .sub.n) and the set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n).

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) The following detailed description of specific embodiments of the present disclosure can be best understood when read in conjunction with the following drawings, where like structure is indicated with like reference numerals and in which:

(2) FIG. 1 illustrates an excavator incorporating aspects of the present disclosure;

(3) FIG. 2 is a side view of an excavator incorporating aspects of the present disclosure;

(4) FIG. 3 is an isometric view of a dynamic sensor, which can be disposed on a linkage of the excavator of FIG. 2;

(5) FIG. 4 is a side elevation view of a linkage assembly of the excavator of FIG. 2; and

(6) FIG. 5 is a flow chart illustrating an optimization process that may be used to determine a sensor radius estimation and a sensor offset angle with respect to a linkage axis according to aspects of the present disclosure.

DETAILED DESCRIPTION

(7) The present disclosure relates to earthmoving machines and, more particularly, to earthmoving machines such as excavators including components subject to control. For example, and not by way of limitation, many types of excavators typically have a hydraulically controlled earthmoving implement that can be manipulated by a joystick or other means in an operator control station of the machine, and is also subject to partially or fully automated control. The user of the machine may control the lift, tilt, angle, and pitch of the implement. In addition, one or more of these variables may also be subject to partially or fully automated control based on information sensed or received by an adaptive environmental sensor of the machine. In the embodiments described herein, an excavator calibration utilizes a control architecture to determine a location of a dynamic sensor positioned on an excavator limb and a sensor offset of the sensor disposed on the limb, as described in greater detail further below. Such determined values may be utilized by an excavator control to operate the excavator.

(8) Referring initially to FIGS. 1-2, an excavator 100 comprising a machine chassis 102, an excavating linkage assembly 104, a dynamic sensor 120, an excavating implement 114, and control architecture 106. The excavating linkage assembly 104 comprises an excavator boom 108, an excavator stick 110, a boom coupling 112A, a stick coupling 112B, and an implement coupling 112C. The dynamic sensor 120 is positioned on a limb, wherein the limb is one of the excavator boom 108 and the excavator stick 110.

(9) In embodiments, and referring to FIGS. 2-4, the dynamic sensor 120 comprises an inertial measurement unit (IMU), an inclinometer, an accelerometer, a gyroscope, an angular rate sensor, a rotary position sensor, a position sensing cylinder, or combinations thereof. For example, the dynamic sensor 120 may comprise an IMU comprising a 3-axis accelerometer and a 3-axis gyroscope. As shown in FIG. 3, the dynamic sensor 120 includes accelerations A.sub.x, A.sub.y, and A.sub.z, respectively representing x-axis, y-axis-, and z-axis acceleration values.

(10) The excavating linkage assembly 104 may be configured to define a linkage assembly heading {circumflex over (N)} and to swing with, or relative to, the machine chassis 102 about a swing axis S of the excavator 100. The excavator stick 110 is configured to curl relative to the excavator boom 108. For example, the excavator stick 110 may be configured to curl relative to the excavator boom 108 about a curl axis C of the excavator 100. The excavator boom 108 and excavator stick 110 of the excavator 100 illustrated in FIG. 1 are linked by a simple mechanical coupling that permits movement of the excavator stick 110 in one degree of rotational freedom relative to the excavator boom 108. In these types of excavators, the linkage assembly heading {circumflex over (N)} will correspond to the heading of the excavator boom 108. However, the present disclosure also contemplates the use of excavators equipped with offset booms where the excavator boom 108 and excavator stick 110 are linked by a multidirectional coupling that permits movement in more than one rotational degree of freedom. See, for example, the excavator illustrated in U.S. Pat. No. 7,869,923 (“Slewing Controller, Slewing Control Method, and Construction Machine”). In the case of an excavator with an offset boom, the linkage assembly heading {circumflex over (N)} will correspond to the heading of the excavator stick 110. In embodiments, the excavator boom 108 comprises a variable-angle excavator boom.

(11) Referring to FIG. 2, the excavator stick 110 is mechanically coupled to a terminal pivot point B of the excavator boom 108 via the stick coupling 112B. The machine chassis 102 is mechanically coupled to a terminal pivot point A of the excavator boom 108 via the boom coupling 112A. The excavating implement 114 is mechanically coupled to the excavator stick 110. For example, the excavating implement 114 is mechanically coupled to a terminal point G of the excavator stick 110 via the implement coupling 112C.

(12) Referring to FIG. 1, the excavating implement 114 may be mechanically coupled to the excavator stick 110 via the implement coupling 112 and configured to rotate about a rotary axis R. In an embodiment, the rotary axis R may be defined by the implement coupling 112 joining the excavator stick 110 and the rotary excavating implement 114. In an alternative embodiment, the rotary axis R may be defined by a multidirectional, stick coupling joining the excavator boom 108 and the excavator stick 110 along the plane P such that the excavator stick 110 is configured to rotate about the rotary axis R. Rotation of the excavator stick 110 about the rotary axis R defined by the stick coupling may result in a corresponding rotation of the rotary excavating implement 114, which is coupled to the excavator stick 110, about the rotary axis R defined by the stick coupling.

(13) The control architecture 106 comprises one or more linkage assembly actuators, and an architecture controller. The one or more linkage assembly actuators facilitate movement of the excavating linkage assembly 104. The one or more linkage assembly actuators may comprise a hydraulic cylinder actuator, a pneumatic cylinder actuator, an electrical actuator, a mechanical actuator, or combinations thereof.

(14) The architecture controller is programmed to operate as a partial function of a sensor location and an offset angle ϕ of the dynamic sensor 120 and to execute machine readable instructions. The control architecture 106 may comprise a non-transitory computer-readable storage medium comprising the machine readable instructions.

(15) As shown in control scheme 200 of FIG. 5, the machine readable instructions comprise instructions to pivot the limb on which the dynamic sensor 120 is positioned about a pivot point. In embodiments, an operator pivots the limb. The pivot point comprises the terminal pivot point A when the limb is the excavator boom 108 and the terminal pivot point B when the limb is the excavator stick 110. For example, in step 202, the excavator 100, which may include a component thereof, is pivoted.

(16) The machine readable instructions further comprising instructions to generate a set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}) at least partially derived from the dynamic sensor 120. The set of dynamic signals comprises an x-axis acceleration value A.sub.X, a y-axis acceleration value A.sub.Y, a measured angular rate {dot over (θ)}.sub.M, an estimated angular rate {dot over ({circumflex over (θ)})}, and an estimated angular position {circumflex over (θ)}.

(17) The machine readable instructions further comprise instructions to execute an iterative process. The iterative process comprises determining a sensor location estimate .sub.n and an offset angle estimate ϕ.sub.n. The sensor location estimate .sub.n is defined as a distance between the dynamic sensor and the pivot point, and the offset angle estimate ϕ.sub.n of the dynamic sensor is defined relative to a limb axis. The determination comprises the use of an optimization model comprising the set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}) and one or more error minimization terms. For example, in step 204, such set of dynamic signals are sensor data read by the architecture controller. The iterative process, as illustrated by at least steps 206-208 and 212-214, is repeated n times to generate a set of sensor location estimates (.sub.1, .sub.2, . . . , .sub.n) and a set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n) until n exceeds an iteration threshold t, and the architecture controller generates (in step 220, for example) the sensor location and the offset angle ϕ based on the set of sensor location estimates (.sub.1, .sub.2, . . . , .sub.n), the set of angle offset estimates (ϕ.sub.1, ϕ.sub.2, . . . , ϕ.sub.n), and the one or more error minimization terms.

(18) In embodiments, the iterative process further comprises steps 210, 216, and 218 of FIG. 5, including determining a total error based on the optimization model and the set of dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}), and comparing the total error against an optimization threshold. For example, in step 210, a total error equation may be updated to generate an error based on an optimization estimate determined in step 208 and the sensor data read in step 204. If n is above a threshold in step 212 but the error is not less than an optimizer threshold to minimize drift, the iterative process returns to step 206. If, however, n is above the threshold in step 212 and the error is less than the optimizer threshold in step 216, the control scheme may continue to step 220 and generate final values for the sensor location and the offset angle ϕ. Thus, the iterative process may be executed until the total error is less than the optimization threshold to minimize drift.

(19) In embodiments, the dynamic signals (A.sub.X, A.sub.Y, {dot over (θ)}.sub.M, {dot over ({circumflex over (θ)})}, {circumflex over (θ)}) are generated from a captured data set originating from the dynamic sensor 120. The captured data set comprises a first data section corresponding to a first sensor location .sub.1 and a first offset angle ϕ.sub.1 and a second data section corresponding to a second sensor location .sub.2 and a second offset angle ϕ.sub.2. In embodiments, the captured data set represents pivoting the limb on which the dynamic sensor 120 is positioned for a period of time in a range of from about 10 seconds to about 30 seconds.

(20) Further, the iterative process executed by the architecture controller comprises a validity check where sensor readings from the first data section are compared to sensor readings from the second data section to return a validity indication. For example, the validity indication is positive when the sensor readings from the first data section and the sensor readings from the second data section are within an acceptable difference of one another. The validity indication is negative when the sensor readings from the first data section and the sensor readings from the second data section are outside the acceptable difference. Further, the architecture controller may be programmed to calibrate the dynamic sensor when the validity indication is negative. Additionally or alternatively, the architecture controller may be programmed to generate the sensor location and the offset angle ϕ in step 220 of FIG. 5, for example, when the validity indication is positive.

(21) The optimization model of step 208, for example, may be a function of gravitational acceleration g, an estimation error e, a tangential acceleration A.sub.T of the dynamic sensor, a dynamic angular acceleration of the dynamic sensor over time {umlaut over ({circumflex over (θ)})}, a dynamic angular rate of the dynamic sensor over time {dot over ({circumflex over (θ)})}, and an initial start velocity {dot over (θ)}.sub.IC from the dynamic sensor and an initial start angle θ.sub.IC between terminal pivot points A and B of the excavator boom 108 and the excavator stick 110 relative to horizontal. The optimization model may further comprise the following set of equations:

(22) $\begin{array}{cc}\widehat{\stackrel{\mathrm{.Math.}}{\theta }}=\frac{g}{}\left(A_T+\sin \left(\theta \right)\right)+K_{P}e+K_D\stackrel{.}{e}+K_I\int e\hat{\theta }=\int {\stackrel{.}{\theta }}_m+{\theta }_{\mathrm{IC}},\widehat{\stackrel{.}{\theta }}=\int \widehat{\stackrel{\mathrm{.Math.}}{\theta }}+{\stackrel{.}{\theta }}_{\mathrm{IC}},\mathrm{and}{A}_T=A_x\cos \left(\varphi \right)-A_y\sin \left(\varphi \right)& \left(\mathrm{Equations}1\text{-}4\right)\end{array}$

(23) where K.sub.P is a proportional term coefficient, where K.sub.D is a derivative term coefficient, and K.sub.I is an integral term coefficient, and where
e={dot over (θ)}.sub.m−{dot over ({circumflex over (θ)})}  (Equation 5)

(24) for which {dot over (θ)}.sub.m is a dynamic angular rate of the dynamic sensor as measured by a gyroscope of the dynamic sensor.

(25) Further, the optimization model may comprise the following set of equations, where A.sub.R,M is a measured radial acceleration of the dynamic sensor, is an expected radial acceleration based on the model, and A.sub.R,M is equivalent to :

(26) $\begin{array}{cc}{A}_{R,M}=A_x\sin \left(\varphi \right)+A_y\cos \left(\varphi \right)=\frac{g}{}{\stackrel{.}{\theta }}^2-\cos \left(\theta \right)& \left(\mathrm{Equations}6\text{-}7\right)\end{array}$

(27) In embodiments, in step 210, one or more error minimization terms comprise an error based on the following equation, which summation is from sampling the solutions from Equations 1-5:

(28) $\begin{array}{cc}\mathrm{Error}=.Math.{\left(\frac{g}{}{\widehat{\stackrel{.}{\theta }}}^2-\cos \left(\hat{\theta }\right)-A_{R,M}\right)}^2+.Math.{\left({\stackrel{.}{\theta }}_m-\widehat{\stackrel{.}{\theta }}\right)}^2& \left(\mathrm{Equation}8\right)\end{array}$

(29) To account for drift in determining the final values of step 220, the incorporation of error terms into the optimization model of step 208, as well as the potential total error calculations and optimizer threshold, are useful to minimize model error of step 210. The final values of the sensor location and the offset angle ϕ that result in step 220 of the control scheme 200 may be used to dynamically compensate for excavator limb movement to assist with accurate determinations of limb angle and machine position.

(30) A signal may be “generated” by direct or indirect calculation or measurement, with or without the aid of a sensor.

(31) For the purposes of describing and defining the present invention, it is noted that reference herein to a variable being a “function” of (or “based on”) a parameter or another variable is not intended to denote that the variable is exclusively a function of or based on the listed parameter or variable. Rather, reference herein to a variable that is a “function” of or “based on” a listed parameter is intended to be open ended such that the variable may be a function of a single parameter or a plurality of parameters.

(32) It is also noted that recitations herein of “at least one” component, element, etc., should not be used to create an inference that the alternative use of the articles “a” or “an” should be limited to a single component, element, etc.

(33) It is noted that recitations herein of a component of the present disclosure being “configured” or “programmed” in a particular way, to embody a particular property, or to function in a particular manner, are structural recitations, as opposed to recitations of intended use. More specifically, the references herein to the manner in which a component is “configured” or “programmed” denotes an existing physical condition of the component and, as such, is to be taken as a definite recitation of the structural characteristics of the component.

(34) It is noted that terms like “preferably,” “commonly,” and “typically,” when utilized herein, are not utilized to limit the scope of the claimed invention or to imply that certain features are critical, essential, or even important to the structure or function of the claimed invention. Rather, these terms are merely intended to identify particular aspects of an embodiment of the present disclosure or to emphasize alternative or additional features that may or may not be utilized in a particular embodiment of the present disclosure.

(35) For the purposes of describing and defining the present invention it is noted that the terms “substantially” and “approximately” are utilized herein to represent the inherent degree of uncertainty that may be attributed to any quantitative comparison, value, measurement, or other representation. The terms “substantially” and “approximately” are also utilized herein to represent the degree by which a quantitative representation may vary from a stated reference without resulting in a change in the basic function of the subject matter at issue.

(36) Having described the subject matter of the present disclosure in detail and by reference to specific embodiments thereof, it is noted that the various details disclosed herein should not be taken to imply that these details relate to elements that are essential components of the various embodiments described herein, even in cases where a particular element is illustrated in each of the drawings that accompany the present description. Further, it will be apparent that modifications and variations are possible without departing from the scope of the present disclosure, including, but not limited to, embodiments defined in the appended claims. More specifically, although some aspects of the present disclosure are identified herein as preferred or particularly advantageous, it is contemplated that the present disclosure is not necessarily limited to these aspects.

(37) It is noted that one or more of the following claims utilize the term “wherein” as a transitional phrase. For the purposes of defining the present invention, it is noted that this term is introduced in the claims as an open-ended transitional phrase that is used to introduce a recitation of a series of characteristics of the structure and should be interpreted in like manner as the more commonly used open-ended preamble term “comprising.”