Sensor-based Trajectory Deformation: Application to Reactive Navigation of Nonholonomic Robots - Visual Servoing via Advanced Numerical Methods - page 318

Fig. 17.5 Example of the
docking configuration. The
robot scans the environment
using a 2D laser scanner,
from the current config-
uration along the current
trajectory. Extracted straight
line segments are matched
with the docking pattern
to define the docking con-
figuration. The trajectory
is progressively deformed
in order to make the final
configuration tend toward
the docking configuration

robot is at the docking configuration is called a docking pattern . Figure 17.4 presents
such docking patterns . On each image, the docking configuration is represented
relatively to the docking pattern. Thus a docking task takes as input:

• a collision free trajectory planned within a model of the environment;

• a set of landmarks relative to the docking configuration: the docking patterns .

17.5.2 Computation of the Docking Configuration

In the absence of any additional information, the docking configuration is the last
configuration of the planned trajectory. Otherwise, the comparison between docking
patterns and sensor perceptions can be used to compute the docking configuration:
i.e. the robot configuration where sensor perceptions best match docking patterns .
We borrow ideas from localization and use a classical extended Kalman filter ap-
proach to integrate this information.

17.5.2.1 Probabilistic Framework

The main steps of the computation of the docking configuration are the following.
First, the robot extract features from sensor readings and predicts from the current
position of the robot how these features would be seen from the final configuration
of the current trajectory. We call those the predicted features .
Sensor readings are modeled as Gaussian variables centered on the perfect read-
ing for given robot and landmark positions. The predicted features are matched with
the features of the docking pattern using a criterion based on the Mahalanobis dis-
tance corresponding to the Gaussian noise associated to the sensors.
The docking pattern is built from a Gaussian random configuration centered on
the final configuration of the current trajectory q rand by evaluating the expected
valued conditionally to the predicted features.