  In this paper, we present a novel method of motion planning for performing
complex manipulation tasks by using human demonstration and exploiting the
screw geometry of motion. We consider complex manipulation tasks where there
are constraints on the motion of the end effector of the robot. Examples of
such tasks include opening a door, opening a drawer, transferring granular
material from one container to another with a spoon, and loading dishes to a
dishwasher. Our approach consists of two steps: First, using the fact that a
motion in the task space of the robot can be approximated by using a sequence
of constant screw motions, we segment a human demonstration into a sequence of
constant screw motions. Second, we use the segmented screws to generate motion
plans via screw-linear interpolation for other instances of the same task. The
use of screw segmentation allows us to capture the invariants of the
demonstrations in a coordinate-free fashion, thus allowing us to plan for
different task instances from just one example. We present extensive
experimental results on a variety of manipulation scenarios showing that our
method can be used across a wide range of manipulation tasks.
