All language subtitles for 02_odometry-modeling.en

This week we will learn about
self-localization techniques including

the particle filter.

In this first lecture,
we will consider models for

odometry as a first order
approximation to the robot's location.

As in your car, where the odometer
records how many miles you have traveled,

odometry provides a measurement
of how far the robot has moved.

Odometry is just one method of finding
the robot's location in the world.

If we look at a typical
application of localization,

car navigation,
we see several ways to find location.

Information sources include GPS,

global positioning system, cellular
networks, and Wi-Fi access points.

Each of these sources,

however, have certain levels of noise
that lead to various levels of accuracy.

Driverless cars, for instance,

will need better than 3.5 meters
of accuracy that the GPS provides.

That error is the difference between
occupying the sidewalk and the road.

The previous sources represent global
knowledge of position, exact coordinates.

Odometry and other sources of
information can augment the global

localization sources with local knowledge.

How have they changed coordinates?

These sources of information are more
precise, giving centimeter accuracy.

However, integrating sources,
like encoders and

gyroscopes, over time can lead to drift.

This is due to the accumulation
of errors in time.

Errors from slippage of the wheels
deceive the encoder for instance.

Other local sensors like
laser scanners and color and

depth cameras can help
to correct these errors.

We will see how this incorporation
happens later in the week.

Odometry updates start
with modeling the robot.

Different robots,

such as humanoids or aerial vehicles,
will require different models.

In our case, we will model
a skid steer four-wheeled robot.

The odometry measurements come
from ticks from the encoder

that measure how much the wheels
have rotated in a given timeframe.

These ticks can be mapped into translation
and rotation of the body of the robot.

First, let's explore the rotation
odometry calculation.

With a skid steer robot, the left and

right sets of wheels
are controlled independently.

When turning,
these two sides form the inner and

outer radii of circles that
share the same center.

Coupled with the knowledge of
how wide the robot vehicle is,

we can determine a change in angle
based on these encoder ticks.

First, we want to translate motor ticks
into meters traveled by the inner and

outer wheels along their respective arcs.

This conversion requires
knowledge of the wheel sizes.

Here, these measurements in
meters are denoted eo and ei.

The inner and outer arcs are known, but

they also share the same
angle of rotation.

With knowledge of the width of the robot,

we can use the difference in arcments
to calculate the shared angle data.

Next, we will consider
the translation of the robot.

Conveniently, the translation requires
knowledge of the rotation that we have

already calculated.

In measuring translation, we can form a
triangle with the known angle of rotation.

We then can average
the change in position for

both the inner and outer wheel sets to
find the change in the x direction.

The change in the y direction
requires a similar methodology.

For small movements, this is a good
approximation for the translation.

Unfortunately, the encoder measurements
can be noisy due to wheel slippage.

Angular estimates then propagate
errors into the translation estimates.

One solution to this problem
is to utilize the gyroscope

to find a more precise
measurement of angular change.

For a small number of time steps,
the gyroscope can be very accurate.

Thus, angular odometry is measured
solely by the rate of change

observed by the gyro,
integrated over time.

This measurement aids in
translation calculations as well.

This simple odometry
approach to localization

requires a frame of reference for
where the robot began its trip.

Local measurements from the encoders and
gyroscopes still provide noisy estimates.

So we want to include more
measurements to correct errors.

The next sections will discuss using
maps to aid in localization correction,

as well as ways to probabilistically
define our localization state.