Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces
Zita Marinho, Byron Boots, Anca D. Dragan, Arunkumar Byravan, Geoffrey J. Gordon, Siddhartha S Srinivasa · 2016
We introduce a functional gradient descent trajectory optimization algorithm 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, since they (in theory) work by directly optimizing within a space of continuous trajectories 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 result, 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.