  Diagrammatic Teaching is a paradigm for robots to acquire novel skills,
whereby the user provides 2D sketches over images of the scene to shape the
robot's motion. In this work, we tackle the problem of teaching a robot to
approach a surface and then follow cyclic motion on it, where the cycle of the
motion can be arbitrarily specified by a single user-provided sketch over an
image from the robot's camera. Accordingly, we contribute the Stable
Diffeomorphic Diagrammatic Teaching (SDDT) framework. SDDT models the robot's
motion as an Orbitally Asymptotically Stable (O.A.S.) dynamical system that
learns to stablize based on a single diagrammatic sketch provided by the user.
This is achieved by applying a \emph{diffeomorphism}, i.e. a differentiable and
invertible function, to morph a known O.A.S. system. The parameterised
diffeomorphism is then optimised with respect to the Hausdorff distance between
the limit cycle of our modelled system and the sketch, to produce the desired
robot motion. We provide novel theoretical insight into the behaviour of the
optimised system and also empirically evaluate SDDT, both in simulation and on
a quadruped with a mounted 6-DOF manipulator. Results show that we can
diagrammatically teach complex cyclic motion patterns with a high degree of
accuracy.
