Disclosure of Invention
The invention aims to solve the technical problem of providing a swing control method of a rocket and the rocket, and solves the problem that 9 engines are distributed on the rocket and the blank of the swing control method thereof.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a swing control method of rocket is applied to a flight control computer and comprises the following steps:
acquiring flight state information of a rocket at the current moment;
according to the flight state information, determining the swing angles of the rocket target in at least three axial directions;
according to the rocket target swing angle, determining the swing angle of each engine in at least five engines; the rocket comprises a central engine and eight engines symmetrically arranged around the central engine, wherein the at least five engines comprise the central engine and at least four engines in the eight engines;
and controlling the at least five engines to move according to the swing angle.
Optionally, determining, according to the flight state information, a rocket target swing angle of the rocket in at least three axial directions includes:
determining control target moments of the rocket in at least three axial directions; the control target torque includes: pitch control moment, yaw control moment, and roll control moment;
according to the control target moment, calculating to obtain a rocket target swing angle; the rocket target swing angle comprises: rocket pitch angle, rocket yaw angle, and rocket roll angle.
Optionally, according to the control target moment, calculating to obtain a rocket target swing angle, including at least one of the following:
by the formulaDetermining a rocket pitching angle;
by the formula delta ψ =asin(M yb /(P·X kz ) Determining a rocket yaw angle;
by the formula delta γ =asin(M xb /(P·Z kz ) Determining the rocket rolling swing angle;
wherein, the liquid crystal display device comprises a liquid crystal display device,is rocket pitching angle delta ψ Is the yaw angle delta of rocket γ For rocket roll-to-roll swing angle, M zb For pitch control moment, M yb For yaw control moment, M xb Is the rolling control moment, P is the engine thrust, X kz For controlling arm of force, Z, for pitch and yaw kz The arm of force is controlled for roll.
Optionally, determining the swing angle of each engine of the at least five engines according to the rocket target swing angle includes:
by the formulaCalculating the swing angle of each engine in the first axial direction and the second axial direction of at least five engines;
wherein delta A1 A first target swing angle delta of the central engine B1 For a second target pivot angle, delta, of the central engine A2 A third target swing angle delta of the first engine B2 A fourth target swing angle delta of the first engine A4 A fifth target pivot angle delta of the third engine B4 A sixth target pivot angle delta of the third engine A6 A seventh target pivot angle delta for the fifth engine B6 An eighth target pivot angle delta of the fifth engine A8 A ninth target pivot angle, delta, for the seventh engine B8 For the tenth target pivot angle of the seventh engine,is rocket pitching angle delta ψ Is the yaw angle delta of rocket γ Is the rocket roll swing angle.
Optionally, controlling the at least five motors to move according to the swing angle includes at least one of the following:
controlling the central engine to move along a first axial direction according to a first target swing angle and along a second axial direction according to a second target swing angle;
controlling the first engine to move along a third axial direction according to a third target swing angle and along a fourth axial direction according to a fourth target swing angle;
controlling the third engine to move along a fifth axial direction according to a fifth target swing angle and along a sixth axial direction according to a sixth target swing angle;
controlling the fifth engine to move along the seventh axial direction according to a seventh target swing angle and along the eighth axial direction according to an eighth target swing angle;
and controlling the seventh engine to move along the ninth axial direction according to the ninth target swing angle and along the tenth axial direction according to the tenth target swing angle.
Optionally, the first axial direction is the same as the third axial direction, and the second axial direction is the same as the fourth axial direction;
the fifth axial direction, the seventh axial direction and the ninth axial direction are all obtained by rotating the first axial direction by a first preset angle according to a preset rotating direction;
the sixth axial direction, the eighth axial direction and the tenth axial direction are all obtained by rotating the first axial direction by a second preset angle according to a preset rotating direction.
The invention also provides a rocket, comprising:
an arrow body;
the flight control computer is arranged on the rocket body and is used for executing the swing control method of the rocket;
the arrow body bottom bracket is fixedly connected with one end of the arrow body;
the central engine is fixedly connected to the center of the arrow body bottom bracket;
eight engines are symmetrically arranged around the central engine, and the eight engines are fixedly connected with the bracket at the bottom of the rocket body.
Optionally, the eight engines form four groups of symmetrical engine units;
the first symmetrical engine unit comprises a first engine and a fifth engine, the second symmetrical engine unit comprises a second engine and a sixth engine, the third symmetrical engine unit comprises a third engine and a seventh engine, and the fourth symmetrical engine unit comprises a fourth engine and an eighth engine.
Optionally, the first engine, the second engine, the third engine, the fourth engine, the fifth engine, the sixth engine, the seventh engine, and the eighth engine are evenly distributed around the central engine.
Optionally, servo control devices are installed on the central engine, the first engine, the third engine, the fifth engine and the seventh engine; and/or the center engine, the second engine, the sixth engine, the fourth engine and the eighth engine are provided with servo control equipment;
wherein the servo control device is used for controlling the movement of the engine.
The scheme of the invention at least comprises the following beneficial effects:
according to the scheme, flight state information of the rocket at the current moment is obtained; according to the flight state information, determining the swing angles of the rocket target in at least three axial directions; according to the rocket target swing angle, determining the swing angle of each engine in at least five engines; the rocket comprises a central engine and eight engines symmetrically arranged around the central engine, wherein the at least five engines comprise the central engine and at least four engines in the eight engines; controlling the at least five engines to move according to the swing angle; the method solves the blank of layout of 9 engines on the rocket and the swing control method thereof, effectively simplifies the rocket control method, reduces the complexity of control calculation and improves the calculation efficiency.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
As shown in fig. 1, an embodiment of the present invention provides a swing control method of a rocket, which is applied to a flight control computer, and includes:
step 11, acquiring flight state information of a rocket at the current moment;
step 12, according to the flight state information, determining the swing angles of the rocket target in at least three axial directions;
step 13, determining the swing angle of each engine in at least five engines according to the swing angle of the rocket target; wherein the rocket comprises a central engine 11 and eight engines symmetrically arranged around the central engine 11, and the at least five engines comprise at least four engines of the central engine 11 and eight engines;
and 14, controlling the at least five motors to move according to the swing angle.
In the embodiment, the rocket is provided with 9 engines, wherein the 9 engines comprise a central engine 11 and eight engines symmetrically arranged around the central engine 11, the central engine 11 is arranged at the center of the rocket body bottom bracket 2, the eight engines form four groups of symmetrical engine units, each group of symmetrical engine units comprises two engines, the two engines in each group are centrally symmetrical about the central engine 11, and based on the nine-engine layout mode, the attitude control of the rocket can be realized by only controlling the central engine 11 and the two groups of non-adjacent symmetrical engine units, so that the number of servo control equipment is reduced, and the hardware cost of the rocket is reduced; determining at least three axial rocket target swing angles required by swinging the rocket to a target attitude based on flight state information of the rocket at the current moment, and determining the swing angle of each engine in at least five engines according to the rocket target swing angles; controlling the rocket to move to a target attitude according to the swing angle of each engine in at least five engines; the rocket control method is effectively simplified, the complexity of control calculation is reduced, and the calculation efficiency is improved.
Here, the layout of 7 engines on a rocket will be described by way of specific examples:
as shown in FIG. 2, in one particular embodiment, the rocket body coordinate system of the rocket is defined by O b X b Y b Z b The body coordinate system of each engine is represented by O i X i Y i Z i Where i is the number of the engine, i=1 is the central engine 11, i=2 is the first engine 12, i=3 is the second engine 13, and so on;
the 9 engines are arranged on the arrow body bottom bracket 2, the center engine 11 is arranged at the center of the arrow body bottom bracket 2, the rest 8 engines are uniformly distributed on the outer circumference of the center engine 11, the 8 engines are respectively a first engine 12, a second engine 13, a third engine 14, a fourth engine 15, a fifth engine 16, a sixth engine 17, a seventh engine 18 and an eighth engine 19 which are clockwise distributed around the center engine 11, and the centers of the 8 engines are positioned on the same dividing circle;
the rocket body bottom bracket 2 is arranged on a rocket coordinate system (O b -X b Y b Z b ) In the rocket body, the center of the rocket body bottom bracket 2 and the origin O of the rocket coordinate system b Coinciding, the engine coordinate system of the central engine 11 coincides with the rocket coordinate system;
origin O in the engine coordinate system of the first engine 12 2 Through the origin O of the central engine 11 1 Translating along quadrant I of the rocket coordinate system, wherein the translation distance is line segment O 1 O 2 Coordinate axis Y of engine coordinate system of first engine 12 2 Is directed to the central engine 11 coordinate axis Y of engine coordinate system 1 The same;
the engine coordinate system of the second engine 13 is defined by the engine coordinate system of the first engine 12 along the distance line segment O 1 O 2 Clockwise rotation by a first preset angle, preferably 45 °;
same reasonThe third engine 14, the fourth engine 15, the fifth engine 16, the sixth engine 17, the seventh engine 18, and the eighth engine 19 are each along a distance line segment O by the engine coordinate system of the first engine 12 1 O 2 Clockwise rotating a first preset angle to obtain;
y of first engine 12, second engine 13, third engine 14, fourth engine 15, fifth engine 16, sixth engine 17, seventh engine 18, and eighth engine 19 i The axes all point to the origin of the rocket coordinate system;
the installation directions of the 8 engines except the center engine 11 are circumferentially symmetrical, the first engine 12 with the number 2 and the fifth engine 16 with the number 7 form a first symmetrical engine group, the second engine 13 with the number 3 and the sixth engine 17 with the number 6 form a second symmetrical engine group, the third engine 14 with the number 4 and the seventh engine 18 with the number 8 form a third symmetrical engine group, and the fourth engine 15 with the number 5 and the eighth engine 19 with the number 9 form a fourth symmetrical engine group;
+O of body coordinate system of each engine i Y i The axis pointing to the rocket center O b ,+O i Z i The axis pointing in a counter-clockwise direction, where counter-clockwise refers to +O when looking at the engine from the bottom of the rocket body to the top of the rocket body i Z i The orientation of the axis;
as shown in fig. 3, at least five engines are provided with servo control equipment, and the servo control equipment can control the swing of a spray pipe of the engine; the spray pipe of each engine can be along the rocket system + -O b Y b Direction and + -O b Z b To make bidirectional swinging, the swinging angle delta Ai 、δ Bi Wherein A, B is the code number of the oscillating passage of the spray pipe, i is the engine number, delta Ai The spray pipe swings towards the center of the rocket as positive, delta Bi The spray pipe swings to the anticlockwise direction, servo control equipment is not installed on the other 4 engines, and the spray pipe does not swing;
the layout mode and the swing control mode of the 9 engines not only fill the design blank, but also reduce the number of servo control equipment and reduce the hardware cost of the rocket.
In an alternative embodiment of the present invention, step 12 includes:
step 121, determining control target moments of the rocket in at least three axial directions; the control target torque includes: pitch control moment, yaw control moment, and roll control moment;
step 122, calculating a rocket target swing angle according to the control target moment; the rocket target swing angle comprises: rocket pitch angle, rocket yaw angle, and rocket roll angle.
According to the embodiment of the invention, according to the flight state information of the rocket and the target gesture to which the rocket is to run, the control target moment of the rocket body of the rocket in at least three axial directions is determined; the target swing angle of the rocket can be obtained through calculation; the calculated rocket target swing angle is the swing angle required by the rocket body for realizing the movement to the target gesture, and further, the swing angle required by each engine can be determined according to the numerical value of the rocket target swing angle required by the rocket body, namely, the swing angles of a plurality of engines are controlled to jointly realize the rocket target swing angle.
The flight state information can be used for calculating the control moment of adjusting the rocket to the target attitude; the rocket's flight status information includes at least one of: quality; a centroid; moment of inertia; a location; a speed; acceleration; attitude angle; angular velocity; angular acceleration.
In an alternative embodiment of the present invention, step 122 includes at least one of:
by the formulaDetermining a rocket pitching angle;
by the formula delta ψ =asin(M yb /(P·X kz ) Determining a rocket yaw angle;
by the formula delta γ =asin(M xb /(P·Z kz ) Determining the rocket rolling swing angle;
wherein, the liquid crystal display device comprises a liquid crystal display device,is rocket pitching angle delta ψ Is the yaw angle delta of rocket γ For rocket roll-to-roll swing angle, M zb For pitch control moment, M yb For yaw control moment, M xb Is the rolling control moment, P is the engine thrust, X kz For controlling arm of force, Z, for pitch and yaw kz For roll control moment arm, asin (·) is an arcsine function.
In the embodiment of the invention, the pitch control moment, the yaw control moment and the roll control moment in the control target moment are determined based on a rocket body coordinate system, and the rocket target swing angles corresponding to the control target moments can be calculated respectively;
based on the pitching control moment, the formula is adoptedDetermining the rocket pitch angle, based on yaw control moment, by the formula +.>Determining rocket yaw angle based on roll control moment by formula +.>Determining the roll swing angle of the rocket; wherein P is the thrust of the engine, and P refers to the thrust of an engine; in order to control the motion of the rocket body by controlling the least number of engines, preferably, each engine in the 9 engines is an engine of the same model, and the thrust generated during the ignition and starting work is the same; thus, only the center engine 11 of the 9 engines and at least 4 engines which are not adjacent to each other need to be controlled, so that the rocket can be controlled.
In an alternative embodiment of the present invention, step 13 includes:
step 131, by formulaCalculating the swing angle of each engine in the first axial direction and the second axial direction of at least five engines;
wherein delta A1 Is the first target pivot angle, delta, of the center engine 11 B1 For a second target pivot angle, delta, of the central engine 11 A2 Is the third target yaw angle, delta, of the first engine 12 B2 Is the fourth target yaw angle, delta, of the first engine 12 A4 Is the fifth target pivot angle, delta, of the third engine 14 B4 Is the sixth target tilt angle, delta, of the third engine 14 A6 A seventh target pivot angle, δ, for the fifth engine 16 B6 An eighth target pivot angle δ for the fifth engine 16 A8 A ninth target pivot angle, δ, for the seventh engine 18 B8 For the tenth target pivot angle of the seventh engine 18,is rocket pitching angle delta ψ Is the yaw angle delta of rocket γ Is the rocket roll swing angle.
As shown in fig. 3, in the embodiment of the present invention, the swing angle of each engine can be calculated by using the relationship between the swing angles of the five engines and the swing angle of the rocket target in fig. 3, and as can be seen from the above equation, the swing angle calculation results of the 5 engines have unique solutions, and the calculation formulas are concise and have no coupling therebetween, so that the complexity of control calculation is reduced and the control calculation efficiency is improved.
In an alternative embodiment of the present invention, step 14 includes at least one of:
controlling the center motor 11 to move along a first axial direction according to a first target swing angle and along a second axial direction according to a second target swing angle;
controlling the first motor 12 to move in a third axial direction according to a third target pivot angle and in a fourth axial direction according to a fourth target pivot angle;
controlling the third motor 14 to move in a fifth axial direction according to a fifth target pivot angle and in a sixth axial direction according to a sixth target pivot angle;
controlling the fifth motor 16 to move in the seventh axial direction according to the seventh target pivot angle and in the eighth axial direction according to the eighth target pivot angle:
the seventh motor 18 is controlled to move in the ninth axial direction at the ninth target pivot angle and in the tenth axial direction at the tenth target pivot angle.
In an alternative embodiment of the present invention, the first axial direction is the same as the third axial direction, and the second axial direction is the same as the fourth axial direction;
the fifth axial direction, the seventh axial direction and the ninth axial direction are all obtained by rotating the first axial direction by a first preset angle according to a preset rotating direction;
the sixth axial direction, the eighth axial direction and the tenth axial direction are all obtained by rotating the first axial direction by a second preset angle according to a preset rotating direction.
According to the embodiment of the invention, the engine can be controlled to move according to the target swing angle through the two axial target swing angles of each engine obtained through calculation, so that the rocket can be operated to the target attitude;
the axial direction of the engine is the oscillation direction of the engine nozzle, the first axial direction and the second axial direction are the Y coordinate axis and the Z coordinate axis of the engine coordinate system of the center engine 11, the third axial direction and the fourth axial direction are the Y coordinate axis and the Z coordinate axis of the engine coordinate system of the first engine 12, the fifth axial direction and the sixth axial direction are the Y coordinate axis and the Z coordinate axis of the engine coordinate system of the third engine 14, the seventh axial direction and the eighth axial direction are the Y coordinate axis and the Z coordinate axis of the engine coordinate system of the fifth engine 16, and the ninth axial direction and the tenth axial direction are the Y coordinate axis and the Z coordinate axis of the engine coordinate system of the seventh engine 18;
the second coordinate system 13, the third engine 14, the fourth engine 15, the fifth engine 16, the sixth engine 17, the seventh engine 18, and the eighth engine 19 are all along the distance line segment O by the second engine 12 engine coordinate system 1 O 2 The clockwise rotation of the first preset angle results in the same engine coordinate system of the first engine 12 as the engine coordinate system of the central engine 11 in each axial direction, becauseThe first axial direction is the same as the third axial direction, and the second axial direction is the same as the fourth axial direction; the fifth axial direction, the seventh axial direction and the ninth axial direction are obtained by rotating the first axial direction by a first preset angle according to a preset rotating direction; the sixth axial direction, the eighth axial direction and the tenth axial direction are obtained by rotating the second shaft by a second preset angle according to a preset rotation direction, the second preset angle being preferably the same as the first preset angle.
According to the embodiment of the invention, the flight state information of the rocket at the current moment is obtained; according to the flight state information, determining the swing angles of the rocket target in at least three axial directions; according to the rocket target swing angle, determining the swing angle of each engine in at least five engines; wherein the rocket comprises a central engine 11 and eight engines symmetrically arranged around the central engine 11, and the at least five engines comprise at least four engines of the central engine 11 and eight engines; the at least five engines are controlled to move according to the swing angle, so that the blank of the layout of the 9 engines on the rocket and the swing control method thereof is solved, the rocket control method is effectively simplified, the complexity of control calculation is reduced, and the calculation efficiency is improved.
As shown in fig. 2, an embodiment of the present invention further provides a rocket including:
an arrow body;
the flight control computer is arranged on the rocket body and is used for executing the swing control method of the rocket;
the arrow body bottom bracket 2 is fixedly connected with one end of the arrow body;
a central engine 11, wherein the central engine 11 is fixedly connected to the center of the rocket body bottom bracket 2;
eight engines are symmetrically arranged around the central engine 11, and are fixedly connected with the rocket body bottom bracket 2.
In the embodiment of the invention, the rocket comprises an rocket body, an flight control computer, an rocket body bottom bracket 2, a central engine 11 and eight engines, wherein the flight control computer is arranged on the rocket body and is used for controlling the swing of the rocket, and the rocket body bottom bracket 2 is fixedly connected to the bottom of the rocket body and provides thrust far away from the bottom for the rocket body; the central engine 11 is fixedly connected to the center of the rocket body bottom bracket 2, eight engines are uniformly arranged around the central engine 11, the eight engines are fixedly connected with the rocket body bottom bracket 2, and the spray pipe of each engine can swing bidirectionally, namely, the movement axial direction of each engine is two; the 7 engines solve the blank of layout of 9 engines on the rocket and the swing control method thereof, effectively simplify the rocket control method, reduce the complexity of control calculation and improve the calculation efficiency.
Optionally, the eight engines form four groups of symmetrical engine units;
wherein the first set of symmetrical engine blocks comprises a first engine 12 and a fifth engine 16, the second set of symmetrical engine blocks comprises a second engine 13 and a sixth engine 17, the third set of symmetrical engine blocks comprises a third engine 14 and a seventh engine 18, and the fourth set of symmetrical engine blocks comprises a fourth engine 15 and an eighth engine 19.
Optionally, during operation of the rocket, the thrust forces generated by the central engine 11, the first engine 12, the fifth engine 16, the third engine 14 and the seventh engine 18 are all the same; and/or the number of the groups of groups,
the thrust forces generated by the center engine 11, the second engine 13, the sixth engine 17, the fourth engine 15, and the eighth engine 19 are all the same.
Optionally, the first engine 12, the second engine 13, the third engine 14, the fourth engine 15, the fifth engine 16, the sixth engine 17, the seventh engine 18 and the eighth engine 19 are evenly distributed around the central engine 11.
In the embodiment of the present invention, since the first, second, third, fourth, fifth, sixth, seventh and eighth engines 12, 13, 14, 15, 16, 17, 18 and 19 are uniformly distributed, and the engine coordinate systems of the first, fifth, sixth, seventh and eighth engines 12, 12 are rotated clockwise by the first preset angle, the rotation angles and distances between the adjacent engines are the same.
Optionally, servo control devices are mounted on the center engine 11, the first engine 12, the third engine 14, the fifth engine 16, and the seventh engine 18; and/or the center engine 11, the second engine 13, the sixth engine 17, the fourth engine 15, and the eighth engine 19 are mounted with servo control devices;
wherein the servo control device is used for controlling the movement of the engine.
It should be noted that, the rocket is a rocket corresponding to the above method, and all implementation manners in the above method embodiments are applicable to the rocket embodiments, so that the same technical effects can be achieved.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, and are not repeated herein.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus and method may be implemented in other manners. For example, the apparatus embodiments described above are merely illustrative, e.g., the division of the units is merely a logical function division, and there may be additional divisions when actually implemented, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be an indirect coupling or communication connection via some interfaces, devices or units, which may be in electrical, mechanical or other form.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a ROM, a RAM, a magnetic disk, or an optical disk, etc.
Furthermore, it should be noted that in the apparatus and method of the present invention, it is apparent that the components or steps may be disassembled and/or assembled. Such decomposition and/or recombination should be considered as equivalent aspects of the present invention. Also, the steps of performing the series of processes described above may naturally be performed in chronological order in the order of description, but are not necessarily performed in chronological order, and some steps may be performed in parallel or independently of each other. It will be appreciated by those of ordinary skill in the art that all or any of the steps or components of the methods and apparatus of the present invention may be implemented in hardware, firmware, software, or a combination thereof in any computing device (including processors, storage media, etc.) or network of computing devices, as would be apparent to one of ordinary skill in the art after reading this description of the invention.
The object of the invention can thus also be achieved by running a program or a set of programs on any computing device. The computing device may be a well-known general purpose device. The object of the invention can thus also be achieved by merely providing a program product containing program code for implementing said method or apparatus. That is, such a program product also constitutes the present invention, and a storage medium storing such a program product also constitutes the present invention. It is apparent that the storage medium may be any known storage medium or any storage medium developed in the future. It should also be noted that in the apparatus and method of the present invention, it is apparent that the components or steps may be disassembled and/or assembled. Such decomposition and/or recombination should be considered as equivalent aspects of the present invention. The steps of executing the series of processes may naturally be executed in chronological order in the order described, but are not necessarily executed in chronological order. Some steps may be performed in parallel or independently of each other.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the present invention.