Robotics: Science and Systems XII

Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces

Zita Marinho, Byron Boots, Anca Dragan, Arunkumar Byravan, Geoffrey J. Gordon, Siddhartha Srinivasa


We introduce a functional gradient descent tra- jectory optimization algorithm for robot motion planning in Reproducing Kernel Hilbert Spaces (RKHSs). Functional gra- dient algorithms are a popular choice for motion planning in complex many-degree-of-freedom robots, since they (in theory) work by directly optimizing within a space of continuous trajec- tories to avoid obstacles while maintaining geometric properties such as smoothness. However, in practice, implementations such as CHOMP and TrajOpt typically commit to a fixed, finite parametrization of trajectories, often as a sequence of waypoints. Such a parameterization can lose much of the benefit of reasoning in a continuous trajectory space: e.g., it can require taking an inconveniently small step size and large number of iterations to maintain smoothness. Our work generalizes functional gradient trajectory optimization by formulating it as minimization of a cost functional in an RKHS. This generalization lets us represent trajectories as linear combinations of kernel functions. As a re- sult, we are able to take larger steps and achieve a locally optimal trajectory in just a few iterations. 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. Our experiments 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, as compared to the standard discretized waypoint representation.



    AUTHOR    = {Zita Marinho AND Byron Boots AND Anca Dragan AND Arunkumar Byravan AND Geoffrey J. Gordon AND Siddhartha Srinivasa}, 
    TITLE     = {Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2016}, 
    ADDRESS   = {AnnArbor, Michigan}, 
    MONTH     = {June}, 
    DOI       = {10.15607/RSS.2016.XII.046}