Robotic Motion Planning in Reproducing Kernel Hilbert Spaces

In this seminar I will present my work on trajectory optimization for robot motion planning in Reproducing Kernel Hilbert Spaces (RKHSs).
Functional gradient algorithms are a popular choice for motion planning in complex many-degree-of-freedom robots. They work by directly optimizing a continuous trajectory that avoids obstacles while maintaining geometric properties such as smoothness. We exploit this fact and propose a functional gradient based method under RKHSs.
This generalization lets us represent trajectories as linear combinations of kernel functions. Depending on the selection of kernel, we can directly optimize in spaces of trajectories that are inherently smooth in velocity, jerk, curvature, etc., and that have a low-dimensional, adaptively chosen parameterization. I will present some experiments that illustrate the effectiveness of the planner for different kernels, including Gaussian RBFs with independent and coupled interactions among robot joints, Laplacian RBFs, and B-splines.