The present invention relates to transfer of payloads between two locations, more particularly to such transfer implementing a trolley in a manner suitable for carrying payloads between ships in underway replenishment operations at sea.
For many years the United States Navy has routinely engaged in “underway replenishment” (“UNREP”) for ships at sea. Equipment and procedures for underway replenishment have changed little since World War II. Currently more than thirty UNREP ships are operated by the Military Sealift Command (MSC) Naval Fleet Auxiliary Force to supply/resupply the U.S. Navy's combatant fleet at sea; the UNREP ships deliver items including food, fuel, ammunition, and spare parts. U.S. Navy UNREP procedures are described by “Underway Replenishment,” Naval Warfare Publication NWP 4-01.4, Department of the Navy, Office of the Chief of Naval Operations.
“Connected UNREP” typically involves use of payload transfer apparatus physically connecting two side-by-side marine vessels. Even today, “connected UNREP” tends to require excessive time and manpower. For instance, up to twenty-five sailors may be needed to handle each line from a supply vessel; therefore, with two cargo and two refueling rigs, up to a hundred people on a warship can be involved in a single UNREP operation. The U.S. Navy performs dry cargo transfer between ships in a skin-to-skin configuration up to Sea State Two, albeit it is theoretically possible to moor tankers and transfer liquid cargoes in Sea States as high as Six. The Navy wishes to develop technologies permitting UNREP operations that are safer and that necessitate fewer people and less “alongside” time. See Otto, C, “Logistics Takes Higher Priority in Navy Planning,” Sea Power, May 2001.
More specifically, it is desirable to increase the maximum weight of a highline transfer to 12,000 pounds, which is more than double the current load limit. This could greatly reduce the time required for replenishment, leaving more time for combat operations. Further, it is desirable to be able to transfer 20-foot commercial standardized containers. Further, it is desirable to permit a wider separation between replenishment ships (e.g., more than 150 feet at twelve knots), thereby increasing the safety margin in rough seas and strong winds during UNREP operations. Further, it is desirable that the UNREP systems be able to carry the load and move it to the required position as fast and accurately as possible, with the smallest amount of load swing (pendulation).
Notably difficult for computer-controlled operation of UNREP systems is the simultaneous control of the swing and the end-point positioning of the payload. Because of the nature of a traditional ship-to-ship replenishment configuration, there is no direct control over the position of the payload; this makes it difficult to control the payload, especially insofar as reducing the swing of the payload. According to manual operation, a human operator attempts to maneuver the load to minimize the load swing. However, according to computer-controlled operation, the payload-control problem is significant due to complexity of the system model, difficulties in measuring the payload motion, and unknown disturbances due to sea waves. Pendulation control of UNREP systems has been a subject of considerable research and development for over thirty years. Described immediately hereinbelow by way of background are some efforts that have been made in this regard.
The High-Capacity Alongside Sea Base Sustainment (HiCASS) intends to address the feasibility issues related to a substantial through-put rate capability and reliable delivery of material in up to Sea State Five. See S. Kery et al., “Achieving High Container Through-Put Rates between Vessels in High Seas (a Vision of HiCASS),” Proceedings of MTS/IEEE, 2005, Oceans, Volume 1, pages 454-459.
Rolls-Royce proposed to develop an integrated technology solution for HiCASS in heavy seas using advanced sensing and measuring technologies. See Rolls-Royce, “Coming Alongside Speeds up String at Sea,” In-Department, Issue 7, 2000.
Oceaneering International, Inc. proposed a technology demonstration that integrated innovations in ship motion prediction measured wave fields, fendering, crane configurations and actuation methods, controls, sensors, and simulation technologies. See Oceaneering Technologies (OTECH), “High Capacity Alongside Sea Base Sustainment (HiCASS),” http://www.oceaneering.com/brochures/Pdfs/hicass.pdf.
Lockheed Martin demonstrated in a virtual simulation environment a HiCASS capability employing enabling technologies to ensure safe and expeditious ship approach, connection of ships, minimization of relative motion between the ships, dynamic handling of the moored-ship assembly, and separation of the ships in open ocean environment and in sea states up to and including Sea State Five.
A simple Proportional-plus-Derivative (PD) type output feedback control has been proposed for a rotary crane described by a nonlinear model. See B. Kiss, “A Simple Output Feedback PD Controller for Nonlinear Cranes,” IEEE Conference on Decision Control, 2000.
A Lyapunov-type approach based on back-stepping method has been used to control a two-degrees-of-freedom overhead crane along a desired trajectory. See S. C. Martindale, “Approximate Nonlinear Control for a Two Degree of Freedom Overhead Crane: Theory and Experimentation”, Proceedings of the American Control Conference, June 1995.
Isidori solved the problem of controlling a nonlinear plant in order to have its output track a reference signal. See A. P. Isidori, “Output Regulation for Nonlinear System: an Overview,” International Journal of Robust Nonlinear Control, Volume 10, pages 323-337, 2000.
Vikramaditya developed a nonlinear controller for the overhead crane system using a Lyapunov function and a modified version of sliding-surface control. See B. Vikramaditya, “Nonlinear Control of a Trolley Crane System,” American Control Conference, Chicago, Ill., June 2000.
In general, for systems with flexible cables, it is important that partial differential equations be used as the system model. D'Andrea-Novel et al. used a hybrid model combining ordinary and partial differential equations to represent the trolley motion and the cable oscillations, and proved exponential stabilization under infinite dimensional settings using simple boundary feedback. See B. D'Andrea-Novel et al., “Feedback Stabilization of a Hybrid PDE-ODE System: Application to an Overhead Crane,” Mathematics of Control, Signals, and Systems, Volume 7, pages 1-22, 1994.
Conrad et al. similarly disclose strong stability results, and use a more detailed and accurate model of a trolley-cable system. See F. Conrad et al., “Strong Stability of a Model of an Overhead Crane,” Control and Cybernetics, Volume 27, pages 363-374, 1998.
Joshi et al. investigated modal analysis of cable motions, starting with a hybrid ordinary differential equation−partial differential equation model. See S. Joshi et al., “Position Control of a Flexible Cable Gantry Crane: Theory and Experiment,” Proceedings of the 1995 American Control Conference, Volume 4, pages 2820-2824, 1995.
A simple feedback control system has been presented that stabilizes several dominant modes of oscillations. Todaka et al. disclose use of H∞ control theory to provide good performance, even in the presence of modeling errors and parameter variations. See Yuji Todaka et al., “The Control System Design of a Traveling Crane Using H∞ Control Theory,” SICE 2002 Session Schedule, IEEE, 2000.
Beliveau et al. disclose a decoupling controller in which a control yoke is located at the cable support point. See Y. Beliveau et al., “Dynamic damping of Payload Motion for Cranes,” Journal of Construction Engineering and Management, Volume 119, pages 631-644, 1993. Beliveau et al.'s method is similar to that of controlling a cable using a boundary control, and minimizes the effects of disturbances.
Lau et al. investigated the effects of trolley motion trajectories on the load pendulation, and showed that a half-sine type velocity trajectory better replicated the real world manually operated trolley velocity trajectory as compared to a trapezoidal-type trajectory. See W. S. Lau et al., “Motion Analysis of a Suspended Mass Attached to a Crane,” Computers and Structures, Volume 52, pages 169-178, 1994.
Wen et al. disclose a dynamic model, using Lagrange's equation, of a shipboard crane. Wen et al.'s anti-swing control system is based on a linear quadratic regulator for minimization of load pendulation. See Bin Wen et al., “Modeling and Optimal Control Design of Shipboard Crane,” Proceedings of the American Control Conference, San Diego, pages 593-597, 1999.
Masoud et al. disclose control of load oscillations using delayed feedback for loads suspended by four cables as commonly found at shipyards. See Z. Masoud et al., “Sway reduction on Container Crane Using Delayed Feedback Controller,” ASME/ASC Structure, Structural Dynamics, and Materials Conference, Volume 1, pages 609-615, 2002.
Kimiaghalam et al. developed a feedback/feed-forward control system based on implicit description of a shipboard crane. See B. Kimiaghalam et al., “Feedback and Feedforward Control Law for a Ship Crane with Maryland Rigging System” Proceedings of the American Control Conference, 2000.
“RoboCrane” is a cable-driven manipulator that was invented by the Intelligent Systems Division of the National Institute of Standards and Technology (NIST). RoboCrane basically resembles an inverted Stewart platform, with cables serving as links, and winches serving as actuators. RoboCrane boasts six-degrees-of-freedom payload control, and improved load stability over traditional lift systems. See A. M. Lytle et al., “Development of a Robotic Structural Steel Placement System,” Proceedings of the 19th International Symposium on Automation and Robotics in Construction, Washington, D.C., Sep. 23-25, 2002.
In view of the foregoing, it is an object of the present invention to provide an improved methodology for transferring payloads between ships at sea.
The present invention is typically embodied as a transport system suitable for use between ships at sea. The inventive transport system includes two highlines, a trolley, two trolley-movement cables, four hoisting cables, two trolley-movement winches, four hoisting winches, a trolley-movement-control computer, and a hoisting-control computer.
The two highlines (a left highline and a right highline) are tensioned and generally parallel, and extend between a first location (e.g., onboard a first ship) and a second location (e.g., onboard a second ship). The trolley is situated upon and movable along the highlines. The trolley has a trolley body, a left front wheel, a right front wheel, a left back wheel, a right back wheel, a front trolley end, and a back trolley end. The left front wheel and the left back wheel each rotatably engage the left highline. The right front wheel and the right back wheel each rotatably engage the right highline.
The two trolley-movement winches are respectively situated at the first location and the second location. The two trolley-movement cables are respectively associated with the trolley-control winches and are respectively connected at the front trolley end and the back trolley end. Each trolley-movement winch, together with its associated trolley-movement cable, is capable of exerting a pulling force on the trolley. The trolley-movement winches, together with their respectively associated trolley-movement cables, cooperatively act to propel the trolley along the highlines. The trolley-movement-control computer is connected to the trolley-movement winches, and is configured to execute trolley-movement-control computer program logic that, when executed, is capable of controllably motivating the trolley, in either direction, along the highlines.
The four hoisting cables are connected to the trolley body for hoisting a payload. The payload includes a container suspended from the trolley via the hoisting cables. The hoisting cables are respectively associated with the hoisting winches. Each hoisting winch, together with its associated hoisting cable, is capable of exerting a pulling force on the container. The hoisting-control computer is connected to the hoisting winches, and is configured to execute hoisting computer program logic that, when executed, is capable of controllably reducing pendulation of the payload.
The present invention, as typically embodied, provides a plural-highlines trolley-payload inter-ship transfer system. United States Navy UNREP systems are among the diverse potential applications of the present invention. For the Navy, inventive practice can represent a new and superior dynamic system for effecting ISO container transfer, doing so with greater stability than conventional transfer systems in the face of uncertain platform motion and other disruptive factors. Ship-to-ship replenishment and heavy lifting will remain important aspects of sea-basing for the foreseeable future. The present invention provides for automation and control of ship-to-ship replenishment whereby the payload remains in a stable state during transport. Positive pendulation control during UNREP cargo transfer under adverse sea conditions is becoming increasingly important in UNREP operations.
Other potential benefits of inventive practice include the following: reduced workload; increased safety (e.g., reduced risk to sailors); increased operational efficiency; obviation of sailor tag-line pulling; ship-to-ship replenishment capabilities under High Sea States; uninterrupted ship-to-ship replenishment to mission critical areas; increased fleet supportability; increased equipment reliability; increased survivability; improved wartime effectiveness.
A typical algorithm implemented in inventive practice includes two main algorithmic components, viz., (i) a payload anti-swing automation control component, and (ii) a payload position automation control component. An inventively practiced central computer can spearhead highly efficient logistic system throughput, as the central computer can perform, in short time periods, large amounts of work directed to both main algorithmic components. The present invention is typically embodied so as to afford, for instance during underway replenishment, what may be described in principle as active stabilization of a highlines-suspended “inverted Stewart platform” payload.
Various approaches to exercising trolley-movement control and hoisting control are not elaborated upon herein but have been considered by the present inventors and may be worthy of further investigation. For instance, inventive control can use predictive control strategies based on estimated arrival times of sea waves to the ship. As another example, sensor technologies can be implemented to measure wave heights and propagation velocities.
To some extent, the present invention has built upon and evolved from previous work by the present inventors, such as indicated by the following pertinent papers, each of which is hereby incorporated herein by reference: Qing Dong, Albert Ortiz, Saroj Biswas, and Donald Longo, “UNREP with Minimum Payload Pendulation in Random Sea States,” ASNE, Automation and Controls (ACS) 2007 Proceedings, American Society of Naval Engineers (ASNE), Biloxi, Mississippi, 10-11 Dec. 2007; Qing Dong and Saroj Biswas, “Feedback Stabilization Control of a Dual-Cable Ropeway System,” Intelligent Ships Symposium VIII (Innovating Naval Ship Operation) Proceedings, American Society of Naval Engineers (ASNE), Drexel University, Philadelphia, Pa., 20-21 May 2009; Qing Dong and Saroj Biswas, “Nonlinear Feedback Control of a Dual-Cable Ropeway System,” Naval Engineers Journal, American Society of Naval Engineers (ASNE), Technical Paper, pages 21-27, 2011.
Other objects, advantages, and features of the present invention will become apparent from the following detailed description of the present invention when considered in conjunction with the accompanying drawings.
The present invention will now be described by way of example with reference to the accompanying drawings, wherein like numbers indicate same or similar parts or components, and wherein:
Referring now to
The terms “source ship” and “destination ship” are used herein to conveniently distinguish the two ships participating in the transfer; nevertheless, it is to be understood that inventive practice provides for bidirectional transfer of objects, i.e., either from source ship 600a's deck 601 to destination ship 600b's deck 601, or from destination ship 600b's deck 601 to source ship 600a's deck 601.
Although four hoist lines are shown herein in some figures and six hoist lines are shown herein in others, it is emphasized that practically any number of hoist lines greater than two can be used in inventive practice. Typically, inventive practice will balance the attachment points of the hoist lines about a geometric center (or geometric vertical axis). For instance, three hoist lines can be inventively utilized efficaciously whereby they are spaced apart 120 degrees in an equiangular (equilateral) triangular configuration.
Trolley 100 includes a trolley body 145 and four wheels 150. Trolley body 145 includes two longitudinal trolley sections 101 and two transverse trolley sections 102. Trolley body 145 is characterized by an approximately rectangular plan profile and four trolley corners 123. Frequent inventive practice provides a square geometric plan shape of trolley body 145, such as square s shown in
The number of wheels 150 is variable in inventive practice. Further, the number of highlines 200 is variable in inventive practice. For instance,
As illustrated in
Two separate haul (pull) lines 300, viz., 300a and 300b, are respectively attached at opposite (front and back) ends of trolley 100, each haul line 300 serving to pull in the direction of the ship deck 601 with which it is connected. Some inventive embodiments provide for a continuous bidirectional haul line 300′ (incl. 300a and 300b) such as shown in
Haul winching mechanisms 325a includes a haul line 325a and a haul line winch 350a. Haul winching mechanisms 325b includes a haul line 325b and a haul line winch 350b. Haul line winch 350a is situated on deck 601 of ship 600a. Haul line winch 350b is situated on deck 601 of ship 600b. As viewed in
The present invention is frequently practiced whereby payload 500 includes a container 501 and cargo 502, inside container 501. The skilled artisan who reads the instant disclosure understands that the present invention can be practiced in association with a variety of payloads.
Electrical connections between computer control components and inter-ship transfer components, in accordance with the present invention, are shown by way of example in
Inventive practice admits of implementation of a central computer 934, which houses, contains, or incorporates the two computers 390 and 490; however, collocation or sharing of computer means (e.g., sharing the same computer hardware) for the various forms of inventive control is not necessary in inventive practice. The skilled artisan who reads the instant disclosure understands that haul-control computer 390 and hoist-control computer 490 can share the same computer hardware, or can correspond to different computer hardware at the same or different locations. The semantic distinction herein between “haul-control computer 390” and “hoist-control computer 490” primarily conveys that a first computer means is directed to executing haul-control computer program logic 391, and that a second computer means—same as, connected to, disconnected from, or different from the first computer means—is directed to executing hoist-control computer program logic 491.
Haul winches 450, together with their respectively associated haul cable 300, cooperatively act to propel trolley 100 along highlines 200 between two locations, either: (i) away from the first location (e.g., ship 600a) and toward the second location (e.g., ship 600b); or, (ii) away from the second location (e.g., ship 600b) and toward the first location (e.g., ship 600a). Haul-control computer 390 is configured to execute haul-control computer program logic 391 that, when executed, is capable of controllably motivating trolley 100 along highlines 200 between the first location and the second location.
According to computer program logic 391, if the pulling force exerted by haul winch 350b (situated at the second location) is substantially in the nature of a motivating force, then the pulling force exerted by haul winch 350a (situated at the first location) is substantially in the nature of a restraining force. If the pulling force exerted by haul winch 350a (situated at the first location) is substantially in the nature of a motivating force, then the pulling force exerted by haul winch 350b (situated at the second location) is substantially in the nature of a restraining force.
The terms “line” and “cable” are used interchangeably herein in referring to the present invention's highlines 200, haul lines 300, and hoist lines 400. The skilled artisan who reads the instant disclosure will appreciate the various types and characteristics of lines/cables that would be suitable for inventive practice.
The combination including trolley 100, hoist lines 400, and payload 500 constitute, in essence, an inverted Stewart platform. Among the features of the present invention is an “inverted Stewart platform” principle according to which positive control may be feasible to move payloads sufficiently fast and precise under adverse sea conditions. Typical inventive practice reduces payload pendulation using an inverted Stewart platform-type mechanism concurrently with a disturbance-rejecting feedback control system. Discussed herein below are various aspects of typical inventive algorithmic control, including system modeling and controllers design.
With reference to
As depicted in
A typical inventive control system includes two major control subsystems, namely: (i) a trolley-movement controller for controlling the transporting of the load from one ship to the other while minimizing payload pendulation; and, (ii) a Stewart platform controller for controlling the payload motion orientation by maintaining proper tension on each suspension cable.
The first main controller of this example of an inventive UNREP control system is the trolley trajectory controller. The trolley 100 transports the load from one ship 600 to the other. It is necessary to control the trolley 100 to counteract the randomness of ship 600 motion, as well as to “isolate” the noise from the load, in order to minimize random motion of payload 500 during UNREP operation. The design strategy for this controller will involve the regulated motion of the load by an Input-Shaping based controller, i.e. the S-curve profile.
The free body diagram of trolley 100, payload 500, and the kinematics of payload pendulation motion is shown in
It is assumed that the triad of unit vectors {î,ĵ,{circumflex over (k)}} is fixed with respect to the highline. For the mass M of the trolley, Newton's Second Law is applied by summing the forces along the x-direction.
M{umlaut over (x)}(t)=f(t)−D{dot over (x)}(t)+Fx(t) (1.1)
Similarly, summing the forces on the payload gives:
{right arrow over (F)}Y(t)+{right arrow over (F)}X(t)=mg(−{circumflex over (i)})−FX(t){circumflex over (k)} (1.2)
Let {right arrow over (V)}CMP(t) be the velocity of mass center with respect to point P, and {dot over (X)}(t){circumflex over (k)} is the velocity of point P with respect to inertial space.
XCMP(t)=l sin θ{circumflex over (k)}+(l−l cos θ)î=={dot over (X)}(t){circumflex over (k)}+{right arrow over (V)}CMP(t)=[l{dot over (θ)}(t) sin θ(t)]î+[{dot over (X)}(t)+l{dot over (θ)}(t) cos θ(t)]{circumflex over (k)} (1.3)
Differentiation of Equation (1.3) gives:
{right arrow over (a)}CMI(t)=d{right arrow over (V)}CMI(t)/dt=[l{umlaut over (θ)}(t)sin θ(t)+l{dot over (θ)}2(t)cos θ(t)]î+[{umlaut over (X)}(t)+l{umlaut over (θ)}(t)cos θ(t)−l{dot over (θ)}2(t)sin θ(t)]{circumflex over (k)} (1.4)
The sum of all moments of the pivot contact forces is
[lFX(t)cos θ(t)+lFY(t)sin θ(t)−R{dot over (θ)}(t)]ĵ (1.5)
We proceed by comparing î and {circumflex over (k)} components in (1.2) and (1.4), multiplying by m. This gives two scalar equations with respect to vector î and {circumflex over (k)}.
ml[{umlaut over (θ)}(t)sin θ(t)+{dot over (θ)}2(t)cos θ(t)]=−FY(t)−mg (1.6)
m{umlaut over (X)}(t)+ml{umlaut over (θ)}(t)cos θ−ml{dot over (θ)}2(t)sin θ(t)=−FX(t) (1.7)
It is assumed that the cable is straight under high tension. Then calculation of the moments of the forces with respect to the center of payload mass, and the sum of the moments of the pivot contact forces gives
lFX(t)cos θ(t)+lFY(t)sin θ(t)−R{dot over (θ)}(t)=0 (1.8)
Equations (1.1), (1.6), (1.7), and (1.8) describe the dynamics of this crane system. Solve FX(t),FY(t) from equations (1.6) and (1.7), and substitute them into equations (1.1) and (1.8). This gives:
f(t)−D{dot over (X)}(t)+ml{dot over (θ)}2(t) sin θ(t)=(M+m){umlaut over (X)}(t)+ml cos θ(t){umlaut over (θ)}(t) (1.9)
ml2{umlaut over (θ)}(t)+ml cos θ(t){dot over (X)}(t)=−mgl sin θ(t)−R{dot over (θ)}(t) (1.10)
Linear models are good approximations as long as the pendulation angles are small and the frequencies of all present base excitations are away from the natural frequency of the cable-payload assembly. Thus, for small-angle payload motion, the inventive system model given by Equations (1.9) and (1.10) simplifies to:
(M+m){umlaut over (X)}+D{dot over (X)}+ml{umlaut over (θ)}=f(t) (1.11)
ml2{umlaut over (θ)}+ml{umlaut over (X)}+mglθ+R{dot over (θ)}=0 (1.12)
f(t)=−α3α1αx−α2α{dot over (x)}+αα1u(t) (1.13)
A typical trolley-payload system block diagram is shown in
State variables are defined thusly: x1=x; x2={dot over (x)}; x3=θ; x4={dot over (θ)}. H is the constant diffusion coefficient, and η is the external disturbance arising from wave motions. γ represents the position of the load with respect to a fixed reference point, and ξ represents the measurement noise. Then Equations (1.11), (1.12), and (1.13) can be expressed in state space form as:
Equation (1.14) can be used to design the linear stochastic controller.
The second controller of this inventive embodiment of an UNREP control system is a controller of the hoisting lines. This controller, in principle, is a kind of suspension cable tension controller for an inverted Stewart platform.
The inverted Stewart platform uses multiple point payload suspension and uses the differential between the tension forces in the various suspension cables to dampen the payload pendulation and manipulate the orientation. This design enhances stiffness of the cable-payload system, and thus it is more resistant to pendulation. This control design approach mandates a rigid body payload motion rather than a point mass. Furthermore, the multiple cable suspension inverted Stewart platform will fully control the motion orientation of the payload to mimic the prescribed container ship motion.
The coordinate systems and vectors are shown in
Equation (1.15) maps the body coordinates (x, y, z) to the spatial points (X,Y,Z).
Then the angular velocity, when resolved on the world coordinate, is
and the angular acceleration, as seen in the world coordinate, is
A vector along the kth cable is defines by the vector difference as shown in
Equation (1.18) could be normalized to give a unit vector in the same direction.
The tensions are Tk for kth cable will be
The calculation of the moment vector due to all of the tensions:
where denotes the standard cross product between two vectors.
The origin of the coordinate system fixed on the container ship, oc−xcyczc, displaces with a known motion Vcs(t). The location of the container in this coordinate system is given by a known constant vector {Rc}. Newton's second law is then applied to the motion of the center of mass of the container.
After the angular velocity and acceleration components are calculated, Euler's equations can then be used to evaluate the moments acting on the body:
Cable tension can be calculated by solving a set of simultaneous linear equation (1.23) and (1.24). Manipulation of the tension applied on each cable would mimic the container's orientation to the container ship motion.
The haul-control computer can be designed as a trajectory-following controller for minimization of cargo pendulation, and can be based on stochastic control theory, to drive the trolley. This trolley-derived controller can be implemented in state feedback linearization in conjunction with a Kalman filter. The hoist-control computer can be designed as a cable tension controller, and can be based on calculations pertaining to an inverted Stewart platform. The skilled artisan who reads the instant disclosure will understand that inventive control of trolley hauling and inventive control of payload hoisting can each be practiced in various ways in accordance with the present invention.
The present invention, which is disclosed herein, is not to be limited by the embodiments described or illustrated herein, which are given by way of example and not of limitation. Other embodiments of the present invention will be apparent to those skilled in the art from a consideration of the instant disclosure, or from practice of the present invention. Various omissions, modifications, and changes to the principles disclosed herein may be made by one skilled in the art without departing from the true scope and spirit of the present invention, which is indicated by the following claims.
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