Method and apparatus for determining remote object orientation and position
First Claim
1. An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:
- a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a source reference coordinate frame;
a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another;
a plurality of receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having independent components for detecting each of said transmitted electromagnetic fields and defining a sensor reference coordinate frame; and
analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position and orientation relative to said source reference coordinate frame, said analyzing means including processing means for processing the components of said electromagnetic fields into remote object orientation using quaternions and blending means for blending a prior solution for said orientation into a new solution for said orientation.
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Accused Products
Abstract
A method and apparatus is provided for determining remote object orientation and position with an electromagnetic coupling. A plurality of radiating antennas are provided for radiating electromagnetic energy. Each of the radiating antennas have independent components for defining a source reference coordinate frame. A transmitter is provided for applying electrical signals to the radiating antennas for generating a plurality of electromagnetic fields. The signals are multiplexed so that the fields are distinguishable from one another. A plurality of receiving antennas are disposed on a remote object for receiving the transmitted electromagnetic fields. The receiving antennas have a plurality of independent components for detecting the transmitted electromagnetic fields and defining a sensor reference coordinate frame. An analyzer is provided for receiving the output of the receiving antennas and converting the components of the transmitted electromagnetic fields into remote object position and orientation relative to the source reference coordinate frame. The analyzing means includes means for processing the components of the electromagnetic fields independently into remote object position in cartesian coordinates and remote object orientation using a quaternion processing strategy. The processing technique provides an uncoupled, noniterative, closed form solution for both position and orientation which is fast and continuous. Further, in the case where dipole antennas are used and the size of the antennas is significant relative to the separation distance between the radiating and receiving antennas, an aperture compensation technique is provided for compensating for distortion in the dipole fields. Still further, the processing technique provides an arrangement for smoothing or filtering the solution for position and orientation by blending previous solutions into the current solution.
527 Citations
19 Claims
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1. An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:
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a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a source reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; a plurality of receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having independent components for detecting each of said transmitted electromagnetic fields and defining a sensor reference coordinate frame; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position and orientation relative to said source reference coordinate frame, said analyzing means including processing means for processing the components of said electromagnetic fields into remote object orientation using quaternions and blending means for blending a prior solution for said orientation into a new solution for said orientation. - View Dependent Claims (2, 3, 4, 19)
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5. A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:
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providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame, receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; processing the components of said electromagnetic fields into remote object orientation using quaternions; and blending a prior solution for orientation into a new solution for said orientation. - View Dependent Claims (6, 7, 8)
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9. A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:
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providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame, receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing the components of said electromagnetic fields into remote object position and orientation by; establishing a signal matrix S representative of the received components of said electromagnetic fields; finding ST S and normalizing to determine the position unit vector r; forming PH-1 PT ; post multiplying the signal matrix S by said PH-1 PT and building a 4×
4 matrix Q;finding v=Qqt-1 where q is a quaternion representing orientation and qt-1 is the last computed quaternion; normalizing said v to determine the orientation vector; and determining range r from ##EQU39## - View Dependent Claims (10, 11)
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12. An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:
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a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a source reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of electromagnetic fields, said electromagnetic fields being distinguishable from one another; a plurality of receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having independent components for detecting each of said transmitted electromagnetic fields and defining a sensor reference coordinate frame; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position vector r, orientation vector v and range value r relative to said source reference coordinate frame, said analyzing means including means for establishing a signal matrix S representative of the received components of said electromagnetic fields, means for determining ST S and normalizing to determine said position vector r, means for forming PH-1 PT, means for post multiplying the signal matrix S by said PH-1 PT and building a 4×
4 matrix Q,means for determining v=Qqt-1 were q is a quaternion representing orientation and qt-1 is the last computed quaternion, means for normalizing v to determine said orientation vector v and means for determining said range value r according to ##EQU40##
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- 13. The apparatus of claim 13 further comprising means for introducing a smoothing factor for said position vector r.
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15. A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:
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providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame, receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing the components of said electromagnetic fields into remote object position and orientation by; establishing a signal matrix S representative of the received components of said electromagnetic fields, finding ST S and normalizing to determine the position unit vector r, forming PH-1 PT, post multiplying the signal matrix S by said PH-1 PT to form a matrix X=SPH-1 PT, forming Δ
A=At-1T X,where A is a matrix representing orientation and At-1 is the last computed orientation matrix, extracting Δ
q from Δ
A where q is a quaternion,determining the current quaternion representation of orientation qt =Δ
qqt-1 where qt-1 is the last computed quaternion, andnormalizing qt to determine orientation.
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16. The method of claim 16 in which said step of extracting Δ
- q from Δ
A further includes;calculating the trace of Δ
A;determining whether said trace is positive; if said trace is positive then finding Δ
q from
space="preserve" listing-type="equation">Δ
q.sub.0 =trace+ε
where ε
is 1/3 Euclidean norm of Δ
A
space="preserve" listing-type="equation">Δ
q.sub.1 =-Δ
A.sub.23 +Δ
A.sub.32
space="preserve" listing-type="equation">Δ
q.sub.2 =-Δ
A.sub.31 +Δ
A.sub.13
space="preserve" listing-type="equation">Δ
q.sub.3 =-Δ
A.sub.12 +Δ
A.sub.21;if said trace is not positive and Δ
A11 is larger than Δ
A22 and Δ
A33, then finding Δ
q from
space="preserve" listing-type="equation">Δ
q.sub.0 =-Δ
A.sub.23 +Δ
A.sub.32
space="preserve" listing-type="equation">Δ
q.sub.1 =ε
+Δ
A.sub.11 -Δ
A.sub.22 -Δ
A.sub.33
space="preserve" listing-type="equation">Δ
q.sub.2 =Δ
A.sub.12 +Δ
A.sub.21
space="preserve" listing-type="equation">Δ
q.sub.3 =Δ
A.sub.13 +Δ
A.sub.31;if said trace is not positive and Δ
A22 is larger than Δ
A11 and Δ
A33, then finding Δ
q from
space="preserve" listing-type="equation">Δ
q.sub.0 =-Δ
A.sub.31 +Δ
A.sub.13
space="preserve" listing-type="equation">Δ
q.sub.1 =Δ
A.sub.12 +Δ
A.sub.21
space="preserve" listing-type="equation">Δ
q.sub.2 =ε
-Δ
A.sub.11 +Δ
A.sub.22 -Δ
A.sub.33
space="preserve" listing-type="equation">Δ
q.sub.3 =Δ
A.sub.23 +Δ
A.sub.32 ; andif said trace is not positive and A33 is larger than A11 and A22, then finding Δ
q from
space="preserve" listing-type="equation">Δ
q.sub.0 =-Δ
A.sub.12 +Δ
A.sub.21
space="preserve" listing-type="equation">Δ
q.sub.1 =Δ
A.sub.13 +Δ
A.sub.31
space="preserve" listing-type="equation">Δ
q.sub.2 =Δ
A.sub.23 +Δ
A.sub.32
space="preserve" listing-type="equation">Δ
q.sub.3 =ε
-Δ
A.sub.11 -Δ
A.sub.22 +Δ
A.sub.33.
- q from Δ
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17. An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising:
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a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a source reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; a plurality of receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having independent components for detecting each of said transmitted electromagnetic fields and defining a sensor reference coordinate frame; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position, and orientation relative to said source reference coordinate frame, said analyzing means including means for establishing a signal matrix S representative of the received components of said electromagnetic fields, means for determining ST S and normalizing to determine said position vector r, means for forming PH-1 PT, means for post multiplying the signal matrix S by said PH-1 PT and forming a matrix X=SPH-1 PT ; means for forming Δ
A=At-1T X where A is a matrix representing orientation and At-1 is the last computed orientation matrix,extracting means for extracting Δ
q from Δ
A where q is a quaternion,means for determining the current quaternion representation of orientation qt=Δ
qqt-1 where qt-1 is the last computed quaternion, andmeans for normalizing qt to determine orientation.
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18. The apparatus in claim 18 in which said extracting means comprises:
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means for calculating the trace of Δ
A;determining means for determining if said trace is positive; calculating means responsive to said determining means for calculating Δ
q;said calculating means programmed to calculate Δ
q as
space="preserve" listing-type="equation">Δ
q.sub.0 =trace+ε
where ε
is 1/3 Euclidean norm of Δ
A,
space="preserve" listing-type="equation">Δ
q.sub.1 =-Δ
A.sub.23 +Δ
A.sub.32,
space="preserve" listing-type="equation">Δ
q.sub.2 =-Δ
A.sub.31 +Δ
A.sub.13
space="preserve" listing-type="equation">Δ
q.sub.3 =-Δ
A.sub.12 +Δ
A.sub.21 if said trace is positive;said calculating means further programmed to calculate Δ
q as
space="preserve" listing-type="equation">Δ
q.sub.0 =-Δ
A.sub.23 +Δ
A.sub.32
space="preserve" listing-type="equation">Δ
q.sub.1 =ε
+Δ
A.sub.11 -Δ
A.sub.22 -Δ
A.sub.33
space="preserve" listing-type="equation">Δ
q.sub.2 =Δ
A.sub.12 +Δ
A.sub.21
space="preserve" listing-type="equation">Δ
q.sub.3 =Δ
A.sub.13 +Δ
A.sub.31if said trace is not positive and Δ
A11 is larger than Δ
A22 and Δ
A33 ;said calculating means further programmed to calculate Δ
q as
space="preserve" listing-type="equation">Δ
q.sub.0 =-Δ
A.sub.31 +Δ
A.sub.13
space="preserve" listing-type="equation">Δ
q.sub.1 =Δ
A.sub.12 +Δ
A.sub.21
space="preserve" listing-type="equation">Δ
q.sub.2 =ε
-Δ
A.sub.11 +Δ
A.sub.22 -Δ
A.sub.33
space="preserve" listing-type="equation">Δ
q.sub.3 =Δ
A.sub.23 +Δ
A.sub.32 ;if said trace is not positive and Δ
A22 is larger than Δ
A11 and Δ
A33 ; andsaid calculating means further programmed to calculate Δ
q as
space="preserve" listing-type="equation">Δ
q.sub.0 =-Δ
A.sub.12 +Δ
A.sub.21
space="preserve" listing-type="equation">Δ
q.sub.1 =Δ
A.sub.13 +Δ
A.sub.31
space="preserve" listing-type="equation">Δ
q.sub.2 =Δ
A.sub.23 +Δ
A.sub.32
space="preserve" listing-type="equation">Δ
q.sub.3 =ε
-Δ
A.sub.11 -Δ
A.sub.22 +Δ
A.sub.33if said trace is not positive and Δ
A33 is larger than Δ
11 and Δ
22.
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Specification