Fusion in Robotics - Information Fusion in Signal and Image Processing - page 49

it requires, however, an assessment of the situation at a higher semantic level at times
when the strategy is changed.

4.3. Characteristics of the data in robotics

4.3.1. Calibrating and changing the frame of reference

The data that is processed in the context of robotics is, for the most part, geomet-
ric in nature. It essentially involves distances as well as their successive derivatives
(speed, acceleration, radius of curvature, etc.). We will have to localize a frame of
reference associated with the robot with respect to the frame associated with its envi-
ronment (absolute localization), or with respect to the same frame related to the robot
but with the position it was in a few moments before (relative localization). We will
also have to localize the frames associated with fixed or moving obstacles with respect
to the robot's frame.

One frame of reference at least is always assigned to the robot, only one if it is
not deformable, two or more if it is. For example, with a manipulator robot, we define
the basic frame, which does not move in the environment and the tool (or effector)
frame, which allows us to localize the operating part of the robot in the situation
where the mission could be performed. With regards to manipulator robots, we should
mention the topic by Khalil [KHA 99] which covers the basics of modeling. The same
techniques can be applied to mobile robotics.

Sensors located on the robot or in the environment also have their own frame of
reference, based on which the measurement is defined. If we want the robot to be
able to use the measurement, it has to be referenced to the frame it is associated with,
which is usually different from that of the sensor's. Using a calibration method that
is rarely trivial, the goal is to define the transformation relating the two frames, i.e.
robot and sensor. This transformation is not perfectly known, leading to measurement
errors. These errors, which are difficult to estimate, are usually neglected when the
data is used.

Figure 4.1 shows an example of a situation where a robot is located in an inside
environment. R ( k ) is the situation of the frame associated with the robot at the time
k . The robot is equipped with two sensors associated with the frames R sensor 1 and
R sensor 2 . We will assume that a map of the robot's environment is available, which
is associated with the frame R map . This environment contains two walls, the charac-
teristics of which (length, orientation) can be known, as well as their localization on
the map using the frames they are associated with, i.e. R wall 1 and R wall 2 . The entire
system can be referenced with respect to a universe frame R u . Let us assume that
we wish to localize the robot at the time k with respect to the universe frame. This
means we have to find the geometric transformation T R ( k )
R u

relating these two frames.