  In this paper, we introduce a new probabilistically safe local steering
primitive for sampling-based motion planning in complex high-dimensional
configuration spaces. Our local steering procedure is based on a new notion of
a convex probabilistically safe corridor that is constructed around a
configuration using tangent hyperplanes of confidence ellipsoids of Gaussian
mixture models learned from prior collision history. Accordingly, we propose to
expand a random motion planning graph towards a sample goal using its
projection onto probabilistically safe corridors, which efficiently exploits
the local geometry of configuration spaces for selecting proper steering
direction and adapting steering stepsize. We observe that the proposed local
steering procedure generates effective steering motion around difficult regions
of configuration spaces, such as narrow passages, while minimizing collision
likelihood. We evaluate the proposed steering method with randomized motion
planners in a number of planning scenarios, both in simulation and on a
physical 7DoF robot arm, demonstrating the effectiveness of our safety guided
local planner over the standard straight-line planner.
