All language subtitles for 03_3-2-3-handling-range-sensor.en

In this lecture, I will continue
talking about occupancy grid mapping.

We will see how to
incorporate range sensors.

In the previous lecture,

we had this example of two
sequential updates of the map.

This example, you readily localize
the robot on the global map

assuming the pose of the robot is known.

We are going to keep the assumption in
order to focus on the mapping problem.

However, we still need to
transform the sensor data

measured in the body frame
into the global map frame.

If you're familiar with coordinate
transformations between 2 different frames

and dealing with 2D arrays,
then you may skip this lecture.

Let me show what
coordinate frames we have.

This is the map and
the coordinate frame is attached to it.

The origin does not need
to be the top left corner.

This follows the MATLAB convention
represent an image array.

This is our mobile robot.

We may assign a body fix
coordinate frame as shown.

This example,

the ray from the range sensor is emitted
along the first axis of the body frame.

Let's imagine that we received
a distance measurements d.

Then, how can we tell which
cell is hit by the ray, and

which cells are observed to be free?

To answer the questions, we will first
consider a continuous version of the map.

And we turn to
the discretizedmap later.

If we know where the robot
is located on the map, and

which direction it is heading, then we
can place the robot on the map like this.

To find the coordinates of
the obstructing point,

we use the distance measurements
in the known pose of the robot.

Up to this point, we use the continuous
representation for the position.

However, the map we are going to
build should be represented as

discretized cells of a certain resolution.

Let's think about how to
express a location on the grid.

Consider a 1D case and take the example where
the grid resolution is 10 centimeters.

Any point between 0 and

10 on the continuous domain
will be mapped to the index 1.

In this example, we follow the MATLAB
convention where an index starts from 1.

A point between 10 and 20 centimeters
will be mapped to the index 2.

We can continue to obtain the index of
any point within the given line segment.

Or another example,
the grid revolution can be 7 centimeters.

In this case, any point between 0 and
7 centimeters on

the continuous domain,
will be mapped to the index 1.

A point between 7 and
14 will be mapped to the index 2.

For a given r, the index of a point x is

computed as the ceiling
integer of x over r.

To generalize, if a line segment
starts from some other value than 0,

then we just need to subtract the minimum
value from x, when we compute the index.

Getting back to our 2D map, computing
the position of the grid map does

not get more complicated than the 1D case.

Each component, X1 and X2,
can be treated independently for

the computation of the index pair,
I1 and I2.

Let me summarize how to obtain the 2D
grid indices of the occupied cell.

What is given is the distance measurement
d and the pose of the robot.

From that,
we can first compute the location of

the obstructing point on
the continuous domain.

Then, we compute the indices of the point
on the discretized map of resolution R.

Next, we will need to calculate
the indices of free empty cells.

For each, we are going to use
Bresenham's line algorithm.

We will now talk about
the algorithm itself here.

An implementation of this algorithm
will be provided as a helper function.

Basically the algorithm takes two points
as the input argument and returns a list of

cells that forms an approximation for
a line segment between the two points.

So far we have treated
a sensor as a single ray.

But in more realistic settings,

it has multiple rays emitted
in different directions.

Let's look at those cases.

Let's say the sensor emits five rays
in the indicated heading angles alphas.

With respect to the body frame.

Each ray gives the distance as shown.

If the poles of the robot
is known as before,

the position of the cells hit by the rays
can be computed in the same way.

But in this case, the direction of each
ray is taken into the computation.

You can use the Bresenham's algorithm for
individual ways to find free empty cells.

And take the union of them.

We have seen examples to learn how
to interpret range sensor readings.

Now, I suppose you are ready to start
the programming assignment for this week.

I will also continue to introduce
how 3D mapping differs from 2D

mapping in the next lecture.