Photogrammetry system and method for determining relative motion between two bodies
First Claim
1. A method of determining the relative position of first and second bodies, the method comprising:
- providing the first body with at least first and second imaging devices at known imaging device locations relative to the first body in a coordinate system defined by the first body;
providing the second body with at least three non-collinear targets;
providing a known first target location relative to the first body for each of the at least three targets at a first time, wherein the known first target locations are defined in the coordinate system;
utilizing the imaging devices to generate a plurality of unit vectors corresponding to a line-of-sight from the imaging devices to each of the at least three targets at a series of later times that are after the first time, wherein the imaging devices have non-overlapping fields-of-view in at least one of the later times whereby the lines-of-sight of the first imaging device are not to any targets for which the second imaging device has lines-of-sight to;
generating a plurality of equations in matrix form for each of the later times, whereby, for each of the later times, a matrix of known quantities is multiplied by a vector of unknown positions that are a function of time, and subtracting a matrix including the known imaging device locations from the product of the matrix of known quantities and the vector of unknown positions, and setting the result equal to a residual error vector, wherein the matrix of known quantities includes the known first target locations and the unit vectors, and wherein the vector of unknown positions includes three unknown Euler angles, three translations of the targets on the first body relative to the second body, and distances from the imaging devices to the targets;
determining a criteria defining an acceptable residual error vector; and
iterating the equations to converge upon a best solution whereby the residual error vector is minimized to within the criteria.
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Abstract
A photogrammetry system and method provide for determining the relative position between two objects. The system utilizes one or more imaging devices, such as high speed cameras, that are mounted on a first body, and three or more photogrammetry targets of a known location on a second body. The system and method can be utilized with cameras having fish-eye, hyperbolic, omnidirectional, or other lenses. The system and method do not require overlapping fields-of-view if two or more cameras are utilized. The system and method derive relative orientation by equally weighting information from an arbitrary number of heterogeneous cameras, all with non-overlapping fields-of-view. Furthermore, the system can make the measurements with arbitrary wide-angle lenses on the cameras.
45 Citations
20 Claims
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1. A method of determining the relative position of first and second bodies, the method comprising:
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providing the first body with at least first and second imaging devices at known imaging device locations relative to the first body in a coordinate system defined by the first body; providing the second body with at least three non-collinear targets; providing a known first target location relative to the first body for each of the at least three targets at a first time, wherein the known first target locations are defined in the coordinate system; utilizing the imaging devices to generate a plurality of unit vectors corresponding to a line-of-sight from the imaging devices to each of the at least three targets at a series of later times that are after the first time, wherein the imaging devices have non-overlapping fields-of-view in at least one of the later times whereby the lines-of-sight of the first imaging device are not to any targets for which the second imaging device has lines-of-sight to; generating a plurality of equations in matrix form for each of the later times, whereby, for each of the later times, a matrix of known quantities is multiplied by a vector of unknown positions that are a function of time, and subtracting a matrix including the known imaging device locations from the product of the matrix of known quantities and the vector of unknown positions, and setting the result equal to a residual error vector, wherein the matrix of known quantities includes the known first target locations and the unit vectors, and wherein the vector of unknown positions includes three unknown Euler angles, three translations of the targets on the first body relative to the second body, and distances from the imaging devices to the targets; determining a criteria defining an acceptable residual error vector; and iterating the equations to converge upon a best solution whereby the residual error vector is minimized to within the criteria. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A method of determining the relative position of first and second rigid bodies, the method comprising:
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mounting at least two cameras on a first rigid body defining a coordinate system, wherein at least one of the cameras has a wide-angle lens, the wide-angle lens defining a center and a field-of-view, and wherein the wide-angle lens has a three-dimensional projection pattern with significant curvature about the center of the wide-angle lens, and wherein the fields-of-view of the at least two cameras do not overlap; providing a second rigid body with at least three targets that can be utilized by the cameras to form discrete images on image planes of the cameras; calibrating the cameras; determining the locations and orientations of the cameras in the coordinate system of the first rigid body; generating a target database comprising first positions of the at least three targets relative to the first rigid body at a first time; utilizing the cameras to form a plurality of images corresponding to the targets in a series of frames that are generated at a plurality of later time increments that are after the first time; determining the locations of the targets in the images to generate known lines-of-sight from the cameras to the targets for the later time increments; tracking the images from frame to frame; associating images with the first positions of the targets utilizing the target database; generating a plurality of equations that can be expressed in matrix form as Ax(t)−
b=e, wherein A comprises the known lines-of-sight and the first positions of the targets, t comprises a vector of unknown positions of the targets relative to the first positions of the targets at the later time increments, the vector including three unknown Euler angles corresponding to rotation of the second rigid body relative to the first rigid body, three unknown translations of the second rigid body relative to the first rigid body, and unknown distances of the targets relative to the centers of the lenses, x(t) comprises a function of a shorter vector t of the unknown positions, wherein x( ) returns a longer vector x, b comprises the positions of the cameras in the coordinate system of the first rigid body, and e comprises a residual error vector; anditerating the plurality of equations over t to converge upon a best solution whereby the residual error vector e is minimized. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
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Specification