# Forward Kinematics Kernel for Improved Proxy Collision Checking

arXiv: https://arxiv.org/abs/1910.06451 · HTML: https://mlsanity.com/paper/1910.06451/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [DiffCo: Auto-Differentiable Proxy Collision Detection with Multi-class Labels for Safety-Aware Trajectory Optimization](https://mlsanity.com/paper/2102.07413/) (2021)
- [Composing Diffusion Policies for Few-shot Learning of Movement Trajectories](https://mlsanity.com/paper/2410.17479/) (2024)
- [Direct Robot Configuration Space Construction using Convolutional Encoder-Decoders](https://mlsanity.com/paper/2303.05653/) (2023)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models](https://mlsanity.com/paper/2604.07084/) (2026)

## Abstract (arXiv)

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.