  Kernel functions may be used in robotics for comparing different poses of a
robot, such as in collision checking, inverse kinematics, and motion planning.
These comparisons provide distance metrics often based on joint space
measurements and are performed hundreds or thousands of times a second,
continuously for changing environments. Few examples exist in creating new
kernels, despite their significant effect on computational performance and
robustness in robot control and planning. We introduce a new kernel function
based on forward kinematics (FK) to compare robot manipulator configurations.
We integrate our new FK kernel into our proxy collision checker, Fastron, that
previously showed significant speed improvements to collision checking and
motion planning. With the new FK kernel, we realize a two-fold speedup in proxy
collision check speed, 8 times less memory, and a boost in classification
accuracy from 75% to over 95% for a 7 degrees-of-freedom robot arm compared to
the previously-used radial basis function kernel. Compared to state-of-the-art
geometric collision checkers, with the FK kernel, collision checks are now 9
times faster. To show the broadness of the approach, we apply Fastron FK in
OMPL across a wide variety of motion planners, showing unanimously faster robot
planning.
