Graphics Reference
In-Depth Information
4.3.6 Motion Planning Strategies
When the low-level controller executes the planned waypoints, different real-world
considerations require specific execution strategies.
First, our planner is designed to maintain a safety invariance while the vehicle is
flying [
54
] by adapting vehicle velocities such that the vehicle can come to a hover
from the current state without collision. Note, that hovering is an invariant state of
the quadrotor—once the vehicle is in a hover state, it can theoretically remain in
hover without collision indefinitely in a static environment. Second, paths planned a
certain distance behind a perceived obstacle are considered as feasible, which allows
to plan into potentially free space behind obstacles. The maintained safety invariance
ensures an early replanning should this space not be free. Space with no available
data is treated similarly, since we expect that obstacles will have enough surface
texture to be captured in the collision checking process.
Third, the predicted trajectory and the actual trajectory flown are generally
close [
32
]. To account for nonzero prediction errors and changes in the environments,
the planner repropagates the latest states and changes the trajectory accordingly to
ensure collision-free flight from the current position.
Last, if the collision checker rejects a trajectory because it ends in occluded space
or outside the field of view, we retain the feasible portion of such a trajectory in the
tree, so that RRT can quickly connect future samples and grow trees from it.
4.3.7 Experimental Results
To evaluate our approach, we implemented our navigation algorithm both in a
simulation environment (Fig.
4.13
) and on a Asctec Pelican quadrotor system
(Fig.
4.6
). The simulation environment mimics a quadrotor within a virtual 3D world
that is composed of cuboids.
At the beginning of a simulated flight, the quadrotor is placed at a starting position
above the ground and the planner is executed a few seconds ahead of the controller to
allow the construction of an initial tree of decent size. Figure
4.13
gives an example
of such a step, where the stationary vehicle has planned trajectories toward the goal
at the top of the scene. When the controller is started, the vehicle begins to execute
the planned trajectory, replanning simultaneously during flight. As the position of the
vehicle changes, new parts of the scene come into view, and trajectories are updated
accordingly, until the goal is reached. To verify the robustness of our approach, we
repeatedly executed a simulated flight for several example scenes. One standard
scenario for performance evaluation of planning stability is the flight through a
vertical opening in a wall (Figs.
4.14
and
4.15
), which we use to measure the influence
of a corrupted pose on the planning approach. In a Monte Carlo simulation, we
commanded the vehicle to pass the vertical opening with noise added to the pose
estimate and recorded the flown flight paths for 100 flights for each experiment.
