A 6 DOF measuring system comprising:
- a tracking measurement device comprising:
- a processor;
- a camera connected to the processor;
- two rotation optical components connected to the processor, and the camera and two rotation optical components are arranged in sequence, and the boresight of the camera and the optical axis of the two rotation optical components remain coaxial, and each rotation optical component can rotate independently;
- a target mounted on the tested object, which contains at least three markers with known distance constraints, and at least one marker does not coincide with the midpoint of the line connecting any two of the remaining markers,
- the processor is configured to preform a 6 DOF measuring method, the 6 DOF measuring method comprising:
- 1) establishing a world coordinate system Ow-XwYwZw, camera coordinate system Oc-XcYcZc, target coordinate system Ot-XtYtZt and tested object coordinate system Oa-XaYaZa;
- 2) calibrating the camera to obtain the internal and external parameters of the camera;
- 3) the rotation optical components are controlled by the processor to adjust the camera boresight so that the target falls into the camera FOV;
- 4) the camera acquires images which include at least three markers, and then the image processing is carried out, and the image coordinates (Xi, Yi) (i=1˜n) of the markers are obtained;
- 6) according to a reverse ray tracing method and rotation angles of the rotation optical components, the exiting point Ki (i=1˜n) and the emergent beam vector Si(i=1˜n) of the incident beam in the rotation optical component are obtained;
- 7) three-dimensional coordinates of the markers can be obtained according to the following equation;
- {
- [
- X
- pi
- Y
- pi
- Z
- pi
- ]
- =
- [
- X
- ki
- Y
- ki
- Z
- ki
- ]
- +
- λ
- i
-
- [
- X
- si
- Y
- si
- Z
- si
- ]
- (
- X
- pi
- -
- X
- pj
- )
- 2
- +
- (
- Y
- pi
- -
- Y
- pj
- )
- 2
- +
- (
- Z
- pi
- -
- Z
- pj
- )
- 2
- =
- D
- ij
- 2
- ,
- i
- <
- j
- where, Xpi, Ypi, and Zpi are the three-dimensional coordinates of the marker i in the camera coordinate system Oc-XcYcZc of the measurement system;
- Xki, Yki, and Zki are the three-dimensional coordinates of Ki in the camera coordinate system Oc-XcYcZc of the measurement system;
- Xsi, Ysi, and Zsi are the three-dimensional coordinates of Si in the camera coordinate system Oc-XcYcZc of the measurement system, i=1˜n;
- Xpj, Ypj, Zpj are the three-dimensional coordinates of the marker j in the camera coordinate system Oc-XcYcZc of the measurement system, j=1˜n;
- Dij is the distance between the marker i and the marker j;
- and λi is the proportional coefficient of the equation i;
- 8) among the collected markers, three markers are selected and at least one of them does not coincide with the midpoint of the line connecting the other two markers;
- the normal vector of the plane where the three markers located can be solved by the following formula:
- {right arrow over (N)}={right arrow over (P1P2)}×{right arrow over (P2P3)}
- where P1 is the first marker, P2 is the second marker, P3 is the third marker, N is the normal vector of the plane where the above three markers are located;
- taking P2 as the origin and the orientation vectors of {right arrow over (P1P2)}, {right arrow over (N)}′ and as the coordinate directions, the coordinate system is established, and the target coordinate system Ot-XtYtZt coincides with this coordinate system;
- 9) an attitude matrix R of the target coordinate system Ot-XtYtZt relative to the camera coordinate system Oc-XcYcZc is solved by a directional cosine matrix;
- 10) according to the image coordinates of the three markers and based on a pinhole imaging model, a translation matrix T of the target coordinate system Ot-XtYtZt relative to the camera coordinate system Oc-XcYcZc can be solved;
- 11) the attitude matrix of the tested object relative to the world coordinate system Ow-XwYwZw can be derived as follows:
- M=M1M2M3
- where M1 is a conversion matrix of the camera relative to the world coordinate system Ow-XwYwZw,
- M
- 2
- =
- [
- R
- T
- 0
- 1
- ]
- ,
- M3 is a pose conversion matrix of the tested object coordinate system Oa-XaYaZa relative to the target coordinate system Ot-XtYtZt;
- 12) when the tested object is moving, the rotation optical components are controlled by a visual tracking algorithm to adjust the camera boresight so that the target is kept within the camera FOV, steps 4 to 11 are repeated.