Image Processing Reference

In-Depth Information

2.2.1.
Estimation and calculation of a law
a posteriori

In the context of mobile robotics, for which the general concepts of fusion will be

described in Chapter 4, the navigation of a mobile robot is a basic problem for a fusion

system. It is well-known today that the solution to this problem is obtained from the

competition between two sub-systems [ABI 92, STE 95]:

- an almost continuous navigation, using dead reckoning, based on a behavioral

model and on data provided by different proprioceptive sensors;

- a retiming operation at regular intervals based on the observation of checkpoints

or control points located near the mobile robot.

Dead reckoning uses sensors such as a gyrometer, an accelerometer, a steering

wheel angle measurements, a pedometer and an odometer (based on an angular encod-

er connected to a wheel). The exclusive use of dead reckoning works through the

integration of data using a dynamic model and cannot prevent the estimated trajec-

tory from straying from the actual trajectory. It is therefore necessary to observe the

real world at regular intervals, using sensors such as cameras, distance measurements,

acoustic or optical barriers, GPS (Global Positioning System) in order to register the

estimated trajectory with the real world. The most commonly used fusion mechanism

consists of combining various elements of information through an extended Kalman

filter that works in three phases: the first phase is a short-term prediction based on

dead reckoning navigation by proprioceptive data integration
1
; when exteroceptive
2

data is accessible, the second phase consists of providing an estimate of its own loca-

tion based on this data; the final phase of this iterative process is a fusion categorized

as a revision or an update, which is conducted using a weighted interpolation of the

distributions between the position predicted from the proprioceptive data and the posi-

tion estimated from the exteroceptive data (see Figure 2.1, as well as section 4.2.2).

The use of an adequate Kalman filter [CHU 91] provides an optimal estimate of

the internal state involving the moving object's navigation, in the context of stochastic

dynamic systems theory [GEL 84, GOP 93]. The predicted and estimated positions

are provided by one, two or three-dimensional probability density distributions. The

greatest difficulty lies not in predicting the moving object's future position, which

can be modeled very reliably, but in the mechanism for estimating the position that

depends on the environment and the final accuracy desired. The environment can be

completely structured (in other words filled with markers leading to a precise recon-

struction of the position), partly structured (there are a certain number of markers that

can be used for regular retiming, the difficulty being to find them and use them to infer

1. Proprioceptive: able to measure an attribute involving its own state.

2. Exteroceptive: able to measure an attribute involving an external object that is present.

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