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BACKGROUND OF THE INVENTION
I. Field of the Invention
This invention relates to an object locating or tracking system or process
in which a vector field which is caused to nutate about an axis called the
pointing vector, is used to locate or track a remote object. More
particularly, the invention relates to such a system or process which is
capable of transforming error components of translation and of angular
orientation of a remote object from one coordinate frame into another
coordinate frame.
II. Description of the Prior Art
The use of orthogonal coils for generating and sensing magnetic fields is
well known and has been used in locating and tracking remote objects. For
example, U.S. Pat. No. 3,644,825 teaches generating and sensing coils
which move with respect to each other. Alternatively, the magnetic field
can be made to rotate as taught in Kalmus, "A New Guiding and Tracking
System", IRE Transactions on Aerospace and Navigational Electronics, March
1962, pages 7 through 10.
The use of coordinate transformers to determine the orientation of a first
coordinate system with respect to a second coordinate system is well
known. For example, U.S. Pat. Nos. 3,474,241 and 3,660,648 disclose
transformers which transform angular rates or angular errors measured in a
first coordinate frame into angular rates defined about the axes of an
intermediate coordinate frame about whose axes the angular rotations or
rates are defined and then integrate to determine the angles defining the
angle-axis sequence which defines the orientation of the first coordinate
frame with respect to a second coordinate frame through the use of Euler
angles.
There still remains a need for a way to determine continuously the three
errors in the angular orientation of and the two errors in the pointing
angles to a remote object in a manner suitable for directly correcting the
presumed values of the five angles in addition just to locating or
tracking the object. Further, there is a need for a coordinate transformer
capable of transforming error components of a translation displacement, as
well as an angular orientation displacement, of a remote object from one
coordinate frame into another coordinate frame. Such coordinate
transformation is not only useful in providing accurate tracking and
orientation determination of the remote object but is necessary for
providing accurately sensed error information about the pointing to and
the orientation of the object relative to a useful coordinate frame,
regardless of the attitude assumed by the object.
SUMMARY OF THE INVENTION
Mutually orthogonal radiating coils, defining a reference coordinate frame,
emit a magnetic field which nutates about a pointing vector. The magnetic
field is detected by mutually orthogonal sense coils defining a sense
coordinate frame. A pointing frame is defined as having its x-axis
coincident with the pointing vector and its orthogonal y-axis in the x-y
plane of the reference frame. Signals are generated or detected in the
sense coils. These signals are used to adjust the currents in the
radiating coils so the pointing vector points at the sense coils.
Simultaneously, these signals are used to adjust the three Euler angles
which determine the orientation of the sense coils relative to the
orientation of the reference coils. This invention recognizes the fact
that coordinate transformer apparatus are useful in controlling the
direction of an electrically generated pointing vector which desirably
connects the origin of the reference frame and the origin of the sensor
frame. The detected signals on the sense coils relate to the errors in the
location and orientation of the sense frame as measured in the pointing
frame. However, such information concerning the errors in the angular
displacement and translation displacement of the sense frame is not
typically desired or suitable. Typically, it is more advantageous to
obtain the error information representing the correction in the angular
and translation displacement of the sense frame not in the pointing frame
but with respect to an intermediate frame having axes about which the
angular rotation must occur. As a result, the error information is used to
correct the presumed, to provide the actual, translation and orientation
displacement of the sense frame with respect to the reference frame.
Accordingly, it is an object of this invention to provide a system and
process capable of determining both relative translation and relative
orientation of remote objects through the use of a vector field.
It is also an object of this invention to recognize a need for coordinate
transformation of the error signals detected after processing of the
signals generated in the sense coils before corrections are applied to the
coils of the radiator in the reference frame.
It is a further object of the invention to provide a system and process for
transforming a movement of the sense frame with respect to the pointing
frame to a movement of the sense frame with respect to the reference
frame.
It is another object of the invention to determine relative translation and
orientation of remote objects through use of a field in a continuous
manner, so that translation and orientation may be tracked and therefor
determined continuously, regardless of pointing and orientation angles.
It is still another object of the invention to provide a system and process
for locating an object precisely relative to a reference coordinate frame
of the vector field generating means.
It is yet still another object of the invention to provide a system in
which a pointing vector defined by a modulated field is used to track an
object very precisely.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 describes the geometry of a simple coordinate transformation called
a rotation;
FIG. 2 is the block diagram representation of a single rotation operator,
as in FIG. 1, called a Resolver;
FIG. 3a shows the pointing angles defined for three-dimensional pointing;
FIG. 3b illustrates the circuit corresponding to the pointing angles of
FIG. 3a;
FIG. 4 is a schematic representation of a system in accordance with the
invention which will track the location or direction and the relative
angular orientation of an object free to move in three-dimensions.
FIG. 5 is a schematic representation of a translation coordinate
transformer with two resolvers in accordance with an embodiment of this
invention; and
FIG. 6 is a schematic representation of an orientation coordinate
transformer with five resolvers in accordance with an embodiment of this
invention.
DETAILED DESCRIPTION OF THE INVENTION
This invention includes an object tracking and orientation determination
means, system and process. Such a means, system and process is disclosed
in allowed application, Ser. No. 383,688, filed July 30, 1973, now U.S.
Pat. No. 3,868,565, issued Feb. 25, 1975 the disclosure of which is
incorporated by reference herein. To aid in the logical explanation of an
embodiment of this invention portions of the disclosure are repeated or
summarized herein.
Apparatus in accordance with an embodiment of this invention for generating
a directable, nutating, magnetic field along a pointing vector includes
three orthogonally positioned coils through which excitation currents can
be passed. The mutually orthogonal coils define a reference coordinate
frame. An orthogonal pointing coordinate frame is defined as having the
x-axis coincident with the pointing vector and the y-axis in the x-y plane
of the reference frame but orthogonal to this x-axis. The z-axis is
mutually orthogonal to the above mentioned x and y axes, sensed according
to the right hand rule. With all pointing and orientation angles equal to
zero, the pointing frame, the reference frame and the sense frame are all
coincident. The nutation desirably describes a conical motion about the
pointing vector of the field, the conical apex at the intersection of the
radiator or excitor coils. Such a nutating field can be generated by the
combination of a DC signal in one of the coils, an AC signal in a second
coil, and another AC signal having a phase in quadrature with the phase of
the first AC signal, passed through the third coil, all three coils being
mutually, spacially orthogonal. The pointing vector is fixed to the
direction of the axis of the DC field. To make this nutating field
directable, a signal processing means known as a coordinate transformation
circuit must operate on the reference AC and DC excitation signals in
order to point the nutating field in the desired direction. A brief
discussion of the coordinate transformation known as a rotation is
presented as background in order to properly teach the principles
underlying the techniques employed in this invention.
A vector transformed by pure rotation from one coordinate frame into
another coordinate frame is also said to be resolved from the one into the
other coordinate frame. Resolve and resolution in this context are
synonyms for transform and transformation. The operator which transforms
the components of a given vector in one coordinate frame into its
components in another coordinate frame where the two coordinate frames are
related by a simple angular rotation is defined as a resolver. The
equations governing this transformation are:
x.sub.2 = x.sub.1 cosA + y.sub.1 sinA
y.sub.2 = y.sub.1 cosA - x.sub.1 sinA
z.sub.2 = z.sub.1
where in this case the z.sub.1 axis is the axis of rotation. The equations
are readily verified from the geometry illustrated in FIG. 1. Note that
when the two components operated on by the resolver are ordered positively
(zxyzxy . . . ) then the first component of the positively ordered pair
always has the positive sine term when the angle of rotation is positive.
If the angle of rotation is negative then the sign of the sine terms
reverses. A convenient notation for a resolver is the block shown in FIG.
2 where the rotation in this case is shown as negative about the y-axis.
The y component is therefore not affected by the transformation and this
fact is indicated in this notation by passing that component directly
through the box as shown, whereas, the resolver block representing FIG. 1
would show the z.sub.1 axis passing directly through the box. This
notation should be regarded as a signal flow or block diagram for vector
components, particularly useful in describing the computational strategy
employed in this invention.
A process in accordance with an embodiment of this invention includes the
generation of a directable, nutating field, nutating about an axis called
the pointing vector. The reference nutation excitation vector consists of
three components: a DC and two AC signals quadrature related. The pointing
vector and its entire nutating magnetic field structure are pointed in any
desired direction defined in terms of angles A and B, in this case. FIG. 3
illustrates the pointing geometry and the computational coordinate
transformation circuitry necessary for achieving the desired pointing
direction by operating on the given three reference excitation signals. A
more detailed explanation of coordinate transformations, calculations and
applications is contained in Kuipers, J., Solution and Simulation of
Certain Kinematics and Dynamics Problems Using Resolvers, Proceedings of
the Fifth Congress of the International Association for Analog
Computation, Lausanne, Switzerland, Aug. 28 - Sept. 2, 1967, pages 125 -
134, the disclosure of which is incorporated by reference herein.
The position of an object relative to the pointing vector of the field is
determined from the processed relationship between the field components
sensed in coils in each of the orthogonal axes of a sense coordinate frame
attached to the object. To track the object, the pointing vector of the
nutating field is moved until the field sensed on the axes, after
appropriate coordinate transformation processing, indicates that the
object lies along the pointing vector. This has taken place when the
processed signal resulting from the sensed nutating field is magnitude
invariant over the nutation cycle. If a pointing error exists, then the
amplitude of the modulation sensed in the pointing direction is
proportional to the angular displacement of the object from the pointing
vector.
The angular orientation of the object is specified, in general, by three
Euler (see Kuipers' referenced paper) angles measured relative to the
reference coordinate frame at the generator. Two of the error measures of
angular orientation are proportional to whatever non-zero projections of
the sensed and processed DC field component exist in the coordinate
directions of the plane perpendicular to the pointing direction. The third
angular error measure is proportional to the relative phase of the sensed
and processed nutation signals in this orthogonal plane, compared to the
nutation reference excitation at the generator means.
The above discussion explains that the error signals measured in the sense
coils are relative to the pointing vector and, in turn, to the pointing
frame. However, for locating and determining the orientation of the sense
frame, it is more desirable to have the measured errors transformed into
an intermediate coordinate frame. This is because this particular
intermediate frame is directly appropriate for making the required
corrections in the respective angles.
The orientation of the three orthogonal axes of the sense frame can be
specified with respect to the reference frame by the Euler angles.
Consequently, in accordance with an embodiment of this invention, there is
included an apparatus which can transform the orientation displacement of
the sense frame from the pointing frame into angular corrections to
previously determined Euler angles required to rotate the reference frame
into the orientation of the sense frame. There is an analogous problem in
determining the translation displacement of the sense frame from the
reference frame. The translation displacement from the pointing frame to
the sense frame can be readily determined. However, as already noted, it
would be more desirable to determine the translation displacement of the
sense frame from the pointing vector with respect to the reference frame.
It can be appreciated that when the pointing frame and the reference frame
are coincident that the aforementioned transformation is not necessary.
When this coincidence occurs, the pointing vector is along the x-axis of
the reference frame and along the x-axis of the pointing frame.
Consequently, any displacement of the sense frame from the x-axis of the
pointing frame is the same as the displacement of the sense frame from the
x-axis of the reference frame. Therefore, an error defining the
displacement, translation or orientation, of the sense frame from the
pointing frame can be used directly to correct the components of electric
currents on the axes of the reference frame which generate the pointing
vector. Also, the position and orientation of the sense frame with respect
to the reference frame can be determined. It can further be appreciated
that there can be some deviation from haaving the pointing frame
coincident with the reference frame and still use errors with respect to
the pointing frame to correct the position of the pointing vector with
respect to the reference frame. However, for example, in a situation where
the x-axis of the pointing frame is coincident with the z-axis of the
reference frame, it is clear that an error about the x-axis of the
pointing frame cannot be used to provide a correction with respect to the
x-axis of the reference frame. It can be appreciated that the correction
should be made about the z-axis of the reference frame. A coordinate
transformer apparatus in accordance with an embodiment of this invention
is introduced into the orientation and tracking system to make sure that
proper corrections are made.
FIG. 4 illustrates a tracking and orientation determination system using
coordinate transformation means. The system includes mutually orthogonal
magnetic field generating coils 158, 64 and 66 and mutually orthogonal
magnetic field sensing coils 248, 52 and 54. For ease of understanding,
the three coils in each case have been shown as spacially separated. In
actuality, the magnetic axes of both the generator coils and the sensor
coils intersect in a mutually orthogonal relationship as shown by the
cartesian coordinate frames 84, 86, 160, the reference frame, and 90, 92,
170, the sense frame, respectively. Pointing frame excitation signals AC1
and AC2 are quadrature related or 90 degree phase related. They may be
considered as sinusoids of equal amplitude but 90 degrees out of phase,
although the two signals AC1 and AC2 need not necessarily be sinusoidal in
the practical embodiment of the system. Reference is again made to FIG. 3
which was related to the earlier discussion of coordinate transformation
circuitry and which shows the three dimensional pointing geometry. The
ability to point the pointing vector 180 in any direction in which the
assembly of sensing coils 52, 54 and 248 are free to move enables the
sensing coils to be tracked. The pointing excitation DC, AC1 and AC2
signals from sources 68, 70 and 140, respectively, define a conically
nutating 164 magnetic field about a pointing axis 180 which is coincident
with the axis of the DC component of the field. It should be emphasized
again that the pointing of the vector 180 is accomplished electrically by
the circuit to be described while the generating coils 64, 66 and 158
maintain a fixed orientation physically. DC source 68 and AC2 source 140
are connected by leads 142 and 144, respectively, to resolver 220, whose
output lead 148 and output lead 146 from AC1 source 70 are connected to
resolver 222. The output leads 154 and 156 provide reference frame
excitation signals from resolver 222 to generator coils 64 and 66,
respectively. Generator coil 158 is excited through connection 152 from
the output of resolver 220. The two angles A and B of resolver 222 and
220, respectively, are thus operating on the pointing frame nutating field
vector input whose components are the pointing frame excitations from
sources 68, 70 and 140, so as to provide reference frame excitations to
point the pointing vector 180 and its attendant nutating field structure
in accordance with the geometry shown in FIG. 3. The pointing vector 180
is presumed to be pointing nominally at the sensor which is fixed to the
remote object to be tracked by the system. This sensor consists of the
three mutually orthogonal sensor coils 52, 54 and 248, which are fixed to
the remote object and in the preferred embodiment are aligned to the
principal axes of the remote object, so that in the process of determining
the orientation of the sensor triad the orientation of the remote object
is therefore determined. The signals induced in the sensor coils 52, 54
and 248 depend on the orientation of their sensor coordinate frame,
defined by the mutually orthogonal coordinate axes 90, 92 and 170,
relative to the pointing axis 180 and its two orthogonal nutation
components of the nutating field. In other words, the particular mixing of
the three excitation signals DC, AC1, and AC2 from sources 68, 70 and 140,
induced in each of the three sensor coils 52, 54 and 248, depends not only
upon the two pointing angles A and B which govern the composite pointing
coordinate transformation circuit 252 but also upon the three Euler angles
defining the relative angular orientation of the remote object and which
govern the composite orientation coordinate transformation circuit 250.
The principal function of the two coordinate transformation circuits 250
and 252 in the overall computational strategy of the system is that the
transformation circuit 250 unmixes that part of the reference signal mix
induced in the sensor coils attributable to the relative orientation of
the remote object, and coordinate transformation circuit 252 unmixes the
remaining part of the reference signal mix that was due to the pointing
angles. If the three orientation angles defining coordinate transformation
circuit 250 and the two pointing angles defining the coordinate
transformation circuit 252 properly represent the physical relationship
between the sensor and generator coordinate frames, then the signals
sensed by the sense circuits 26 will correspond to the unmixed pointing
frame signals DC, AC1 and AC2, respectively, from sources 68, 70 and 140.
The sensor coils 54 and 248 are connected to resolver 224 by leads 168 and
172, respectively. The output of sensor coils 52 and one output from
resolver 224 connect to resolver 226 by leads 166 and 174, respectively.
One output from resolver 224 and one output from resolver 226 connect to
resolver 228 by leads 176 and 178, respectively. The two outputs from
resolver 228 are connected to resolver 230 by leads 186 and 188,
respectively. One output from resolver 226 and one output from resolver
230 connect to resolver 232 on leads 184 and 190, respectively. One output
from resolver 230 and the two outputs from resolver 232 provide the
processed signal inputs to sense circuits 26 by connections 192, 194 and
196, respectively.
Sense circuits 26 operates on the three input signals, provided by leads
194, 192 and 196, to sense deviations from their nominally correct values
which should correspond to the pointing frame excitation signal components
68, 70 and 140, respectively. The operation of sense circuits 26 is
described in the afore mentioned allowed application. Basically, sense
circuits 26 compare an input vector in the pointing frame from sources 68,
70 and 140 to an output vector in the sensing frame from inputs 192, 194
and 196. This comparison develops an error or displacement of the sense
frame from where it was expected to be. This error is expressed as five
angular errors. Accordingly, the output of sense circuits 26 are five
angular errors, two dealing with position or translation angles and three
dealing with orientation angles. To define the sense frame with respect to
the reference frame, it is desirable to convert these errors defined in
the pointing frame to errors in an intermediate coordinate frame.
Orientation angle errors transformed into this intermediate frame
correspond directly to the angular error of the respective Euler angle.
That is, the errors appearing on the x, y, and z-axes of the intermediate
frame correspond to the errors in the phi, theta, and psi Euler angles,
respectively. Translation angle errors transformed into this intermediate
frame correspond directly to the angular error of the respective pointing
angle. That is, the errors appearing on the y and z axes of the
intermediate frame correspond to the errors of the pointing angles, B and
A, respectively. Once Euler angles psi, phi and theta and pointing angles
A and B have been corrected, the translation and orientation of sense
frame is defined with respect to the reference frame.
Due to the nature of the nutating dipole vector field structure, the five
angular errors measured in the pointing frame are coupled. That is, a pure
pointing error gives a measurable error in both pointing and orientation
and vice versa. However, understanding the dipole structure of the
nutating field allows one to uncouple these errors using techniques well
known in the art. Accordingly, FIG. 4 shows five outputs 301, 302, 303,
304 and 305 from sense circuits 26 connected to a decoupler 306.
Decoupler 306 has outputs 307, 308, 309, 310 and 311 which are uncoupled
angular errors defined in the pointing frame. The uncoupled angular errors
are called e.sub.1, e.sub.2, e.sub.3, e.sub.4 and e.sub.5. As discussed,
it is desired to obtain angular error corrections for pointing angles A
and B which define the pointing vector in the reference frame. Further, it
is desired to obtain angular error corrections for presumed Euler angles
phi, theta and psi which presumably define the orientation of the sense
frame with respect to the reference frame. Accordingly, each of the
angular errors in the pointing frame is subjected to appropriate
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