Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces

We introduce a functional gradient descent based trajectory optimization algorithm for robot motion planning in arbitrary Reproducing Kernel Hilbert Spaces (RKHSs). Functional gradient algorithms are a popular choice for motion planning in complex many degree-of-freedom robots. In theory, these algorithms work by directly optimizing continuous trajectories to avoid obstacles while maintaining smoothness. However, in practice, functional gradient algorithms commit to a finite parametrization of the trajectories, often as a finite set of waypoints. Such a parametrization limits expressiveness, and can fail to produce smooth trajectories despite the inclusion of smoothness in the objective. As a result, we often observe practical problems such as slow convergence and the requirement to choose an inconveniently small step size. Our work generalizes the waypoint parametrization to arbitrary RKHSs by formulating trajectory optimization as minimization of a cost functional. We derive a gra...

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Zita Marinho, Anca D. Dragan, Arunkumar Byravan, Byron Boots, Siddhartha S. Srinivasa, Geoffrey J. Gordon
• Keywords: CORR 2016, Education