  In robotics motion is often described from an external perspective, i.e., we
give information on the obstacle motion in a mathematical manner with respect
to a specific (often inertial) reference frame. In the current work, we propose
to describe the robotic motion with respect to the robot itself. Similar to how
we give instructions to each other (go straight, and then after multiple meters
move left, and then a sharp turn right.), we give the instructions to a robot
as a relative rotation. We first introduce an obstacle avoidance framework that
allows avoiding star-shaped obstacles while trying to stay close to an initial
(linear or nonlinear) dynamical system. The framework of the local rotation is
extended to motion learning. Automated clustering defines regions of local
stability, for which the precise dynamics are individually learned. The
framework has been applied to the LASA-handwriting dataset and shows promising
results.
