Pose determination in parallel kinematics systems with reference markers
A parallel kinematic system comprises mutually distinguishable markings which are attached in a marking region to the parallel kinematic system. The marking region is a region of the kinematic system that moves along with the pose of the kinematic system. The markings can be attached in a direction at a distance that ensures that n markings are always fully visible in the direction, and the pose of the parallel kinematic system can be determined based on an image that is captured by the camera and contains at least n markings in the direction. The markings can be attached in a direction at a distance that ensures that n or more markings are fully visible in the direction, the markings are attached in different planes, and the pose of the parallel kinematic system can be determined based on an image that is captured by the camera and contains at least any n markings in the direction.
1 . An arrangement with a parallel kinematic system and means for determining the pose of the parallel kinematic system comprising:
a camera and a marking region with mutually distinguishable markings, wherein the camera is configured to observe the marking region in different poses of the parallel kinematic system, wherein
the means for determining the pose of the parallel kinematic system are configured to determine the pose of the parallel kinematic system based only on images of the marking region captured by the camera if one of the images contains at least a number n of any of the markings in a direction, wherein n is greater than or equal to 1, where
a distance, D, between any two markings that are adjacent in the direction satisfies the following formula:
F
O
V
min
-
(
n
+
2
)
*
t
m
n
+
1
<
D
≤
F
O
V
min
-
(
n
+
1
)
*
t
m
n
,
wherein
t m is the length of one of the markings,
FOV min is a length of the section of the marking region which falls into the field of view of the camera at a minimum distance of the camera from the marking region, wherein
the minimum distance is a minimum distance among the distances that the marking region can be away from the camera due to pose changes.
2 . The parallel kinematic system according to claim 1 , wherein
the length FOV min satisfies the following equation:
FOV
min
=
(
g
min
f
-
1
)
l
S
e
n
s
o
r
,
g min is the minimum distance, l sensor is a length of the sensor of the camera and f is a focal distance of the camera.
3 . The parallel kinematic system according to claim 1 , wherein
the markings are arranged in the marking region according to a regular arrangement pattern.
4 . The parallel kinematic system according to claim 1 , wherein
the marking region is attached to an underside of a work platform of the parallel kinematic system and the camera is attached in or on a base of the parallel kinematic system and is directed towards the underside of the work platform, or
the marking region is attached in or on the base of the parallel kinematic system and the camera is attached to an underside of the work platform and is directed towards the base of the parallel kinematic system.
5 . The parallel kinematic system according to claim 1 , wherein
the length t m of a marking satisfies the following equation:
t
m
≥
p
x
*
p
*
t
b
*
(
g
max
f
-
1
)
,
wherein
p is a value that is dependent upon the camera greater than or equal to 2 and less than or equal to 5,
px is the length that corresponds to a sampling value of the camera,
g max is a maximum distance among the distances that the marking region can be away from the camera due to pose changes,
f is a focal distance of the camera, and
t b is the number of information units of the marking.
6 . The parallel kinematic system according to claim 1 , wherein
the markings are reference markings selected from ARToolKit markings, ArUco markings, QR codes, and AprilTag markings.
7 . The parallel kinematic system according to claim 1 , wherein
each of the markings consists of several squares, wherein
the squares correspond to the information units and a bit can be encoded in each square.
8 . A method for attaching mutually distinguishable markings to a parallel kinematic system of an arrangement according to claim 1 in a marking region so that the pose of the parallel kinematic system can be determined based only on images of the marking region captured by a camera if one of the images contains at least a predetermined number, n, of markings in a direction, wherein nis greater than or equal to 1, the method comprising:
determining a distance, D, between any two markings that are adjacent in the direction according to the following formula:
F
O
V
min
-
(
n
+
2
)
*
t
m
n
+
1
<
D
≤
F
O
V
min
-
(
n
+
1
)
*
t
m
n
,
wherein
t m is the length of one of the markings,
FOV min is a length of the section of the marking region which falls into the field of view of the camera at a minimum distance of the camera from the marking region, wherein
the minimum distance is a minimum distance among the distances that the marking region can be away from the camera due to pose changes, and
attaching respectively adjacent markings at the determined distance.
9 . An arrangement with a parallel kinematic system and means for determining the pose of the parallel kinematic system comprising:
a camera and a marking region with mutually distinguishable markings, wherein the camera is configured to observe the marking region in different poses of the parallel kinematic system, wherein
a distance, D, between any two markings that are adjacent in a direction satisfies the following formula:
D
≤
F
O
V
min
-
(
n
+
1
)
*
t
m
n
,
wherein
t m is the length of one of the markings,
FOV min is a length of the section of the marking region which falls into the field of view of the camera at a minimum distance of the camera from the marking region, wherein
the minimum distance is a minimum distance among the distances that the marking region can be away from the camera due to pose changes,
the markings are disposed in different planes, and
the means for determining the pose of the parallel kinematic system are configured to determine the pose of the parallel kinematic system based only on images of the marking region captured by the camera if one of the images contains at least a number, n, of any of the markings in a direction, wherein n is greater than or equal to 2.
10 . A method for attaching mutually distinguishable markings to a parallel kinematic system of an arrangement according to claim 9 in a marking region so that the pose of the parallel kinematic system can be determined based only on images of the marking region captured by a camera if one of the images contains at least a predetermined number, n, of markings in a direction, wherein n is greater than or equal to 2, the method comprising:
determining a distance, D, between any two markings that are adjacent in the direction according to the following formula:
D
≤
F
O
V
min
-
(
n
+
1
)
*
t
m
n
,
wherein
t m is the length of one of the markings,
FOV min is a length of the section of the marking region which falls into the field of view of the camera at a minimum distance of the camera from the marking region, wherein
the minimum distance is a minimum distance among the distances that the marking region can be away from the camera due to pose changes, and
attaching any markings that are adjacent in the direction at the determined distance, where
the markings are attached such that they are disposed in different planes.