Instrumentation & Measurement Magazine 24-3 - 34
Fig. 5. Point cloud reconstruction using hand-eye calibration results. (a) A power drill and its partial point clouds. (b) Point cloud reconstruction results from
different methods.
of the hand-eye calibration results where such differences are
reflected clearly in RAE. It is noteworthy that Shah's method
[6] was originally designed for robot-world/hand-eye calibration with AX = YB formulation. The results in Table 3 only
reflect the accuracy of the X matrix. As X and Y were estimated
together in Shah's method, their errors were propagated into
each other which is why the accuracy of Shah's method was
less than the other conventional methods.
To further assess the performance of implemented methods, we applied their calibration results (i.e., GCT ) to point cloud
reconstruction for a power drill (Fig. 5). Point cloud reconstruction is the process of constructing an object's complete
point cloud by combining its partial point clouds. As shown
in Fig. 5, some partial point clouds of a power drill were obtained with different camera poses using the same system as in
Fig. 3. From GCT and BGT (computed from robot kinematics), the
34
transformation matrix from the robot base frame to the camera frame (i.e., BCT ) can be calculated as BCT BGT GCT . Using BCT ,
we can transform partial point clouds represented in different
camera frames into the robot base frame. If GCT is solved accurately, we can attain a more complete point cloud with good
quality expressed in the robot base frame. As shown in Fig. 5,
the methods with lower RAE values perform better than those
with higher RAE values.
As a conclusion, the point set matching based algorithms
can outperform conventional hand-eye calibration algorithms
when correspondence is given. The reason behind this is explained as follows. The cost function of conventional hand-eye
calibration algorithms is often similar to n1 A X XB . The X maG
trix (i.e., CT ) is solved by minimizing the cost function. As
observed in Table 3, such optimization does not minimize the
RAE values.
IEEE Instrumentation & Measurement Magazine
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Instrumentation & Measurement Magazine 24-3
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