IEEE Robotics & Automation Magazine - September 2017 - 67

Objective
The main goal of our application is to optimize both the accuracy of the estimated position and its integrity (e.g., the probability that this estimation is true has to be greater than 95%).
The position of our vehicle is represented by coordinates
^ x, y h in the Cartesian plane and the orientation i , so, at each
time k, the robot position is modeled by a state vector
X k (x, y, i) and a covariance matrix C k . We first define the
accuracy objective, which is an area in the state space where
we would like to be sure the mobile robot belongs.
For example, the accuracy objective can be 10 cm on x,
2 cm on y, and 1c on i with independence between these
values. To explain that, let us consider the case with only one
dimension x. In this case, the objective is an interval I. At
each time k, the accuracy of the estimated position can be
represented by a Gaussian curve (p (X k) = N (Xt k, C k) . So
the probability Pp to reach the precision objective is given by
Pp =

# N (Xt k, C k) dX,
I

BN
Map
Objectives

Action Selection

Update

Perception

EKF
Sensors

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where Pp represents the area under the Gaussian curve in the
interval I; it is the desired objective uncertainty. The calculation of Pp is detailed in [6].
Now, let us consider the reliability of our estimation. Two
terms are used: integrity (already defined in the "Absolute
Localization" section) and confidence. Confidence is the
probability that the integrity of estimation is respected. A confidence objective noted Pc is fixed. Finally, we have multiple
objectives: both the accuracy and the confidence are important. For example, saying the robot is on Earth with a confidence of 1 is not sufficient. On the contrary, saying it is at a
given position ^x, y h with a 10 -5 cm uncertainty but with a
confidence of 0.01 (so it has 1% of chance to really be located
at this position) is also useless. The objective is to maximize
both terms Pp and Pc .
Selection of Action
To reach the objective previously defined, we must choose
at each time the best action to perform. Each time, this
algorithm must choose the best perceptive triplet [18] composed of landmark l i (e.g., a tree, wall, sidewalk) to detect
from the map, the sensor S i (a camera, lidar) to use to detect this feature, and the associated detector D i (several
detectors can be chosen to detect same landmark). The
perceptive triplet includes much more information than
only a landmark.
Illustration of the Process with an Example
Figure 2 shows an illustration of the perceptive triplet
principle. A vehicle is positioned at point O with a position uncertainty represented by the red ellipse. Various
landmarks (points A-E) are also placed. The vehicle is
oriented to the right and has a sensor that allows a plus or
minus 90° sight angle (then it sees anything that is in front
of it). The first step aims at choosing the triplet Ti, leading
more efficiently to the objectives. For this example and for

Figure 1. An overview of the process. In the circles, main steps,
and, in the rectangles, the main tools of our process are presented.

5
4.5

4
3.5

3
2.5
2
1.5

1
0.5

3.5

4.5

5.5

6.5

Figure 2. An example scenario. The ellipse around point O
represents the estimated position of the robot. Landmarks are
positioned to points A-E.

clarity, the vehicle has only one sensor and one detector,
so perceptive triplets can be reduced to only landmarks.
Some triplets are unattractive because they do not improve our estimation accuracy or they are ambiguous (C
and D). Point A is not observable (behind the vehicle).
Point E is the one that best improves the accuracy of the
vehicle, but it has little chance of being observable (0.5).
Finally, landmark B is the one that offers the best compromise and will be chosen by the system to be detected.
Available Perceptive Triplets
In the worst case, the number of available triplets N T will be
NT = NL # ND # NS ,
SEPTEMBER 2017

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Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2017