We consider the problem of learning to follow a desired trajectory
when given a small number of demonstrations from a sub-optimal expert.
We present an algorithm that (i) extracts the---initially
unknown---desired trajectory from the sub-optimal expert's
demonstrations and (ii) learns a local model suitable for control
along the learned trajectory. We apply our algorithm to the problem
of autonomous helicopter flight. In all cases, the autonomous
helicopter's performance exceeds that of our expert helicopter pilot's
demonstrations. Even stronger, our results significantly extend the
state-of-the-art in autonomous helicopter aerobatics. In particular,
our results include the first autonomous tic-tocs, loops and
hurricane, vastly superior performance on previously performed
aerobatic maneuvers (such as in-place flips and rolls), and a complete
airshow, which requires autonomous transitions between these and
various other maneuvers.
The videos below show the results from our algorithm.
- Recorded demonstrations videos show visualizations of the
recorded pilot demonstrations for each maneuver.
demonstrations videos show visualizations of the aligned
demonstration trajectories, along with the inferred ideal trajectory
(shown as a white helicopter).
- Flight performance video shows a
comparison of the actual helicopter trajectory (black helicopter)
along with the desired ideal trajectory (white helicopter), as
displayed by our software during an autonomous flight on the real
- Autonomous flight videos show the real autonomous
flight of the helicopter.