Learning Orbitally Stable Systems for Diagrammatic Teaching
Keywords: Learning from demonstration, Policy learning, Dynamical systems
Abstract: 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 introduce 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 follow the user-specified sketch. This is achieved by
applying a 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
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.
Submission Number: 7
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