Distance to ground calculation

[nakai-omer]

Hi,

I would be happy to get a little explanation on the following distance to ground calculation:

dist_to_ground_[i] = sensor_mount_height_ * sin(M_PI / 2 - delta_row_[i]) /
        cos(M_PI / 2 - delta_row_[i] - alpha);

Shouldn't the sin also decrease the alpha? If so, wouldn't it be easier to have:

dist_to_ground_[i] = sensor_mount_height_ * tan(M_PI / 2 - delta_row_[i] - alpha);

[mdrwiega]

Hi,

I think the original formula is right. Please check the below drawing for the case when $\delta$ is equal to half of FOV.

Assuming that:

• $sin(\alpha + \gamma ) = \dfrac{d}{l} \rightarrow d = l \cdot sin(\alpha + \gamma )$
• $cos(\gamma) = \dfrac{h}{l} \rightarrow l = \dfrac{h}{cos(\gamma)}$
• $\gamma=\frac{\pi}{2}-\delta$
• $h$ is the sensor_mount_height
• $\delta$ depends on the image row - variable delta_row_[i]

Then, the threshold value dist_to_ground (d) can be calculated as $$d= l \cdot sin(\alpha + \gamma ) = \dfrac{h}{cos(\gamma)} \cdot sin(\alpha + \gamma ) = h \cdot \dfrac{sin(\pi/2 - \delta + \alpha)}{cos(\pi/2 - \delta)}$$

The sign near $\delta$ was changed in the code because as I remember the sensor I used returned it with a minus.

You can find more details in the following paper: A set of depth sensor processing ROS tools for wheeled mobile robot navigation .

[nakai-omer]

@mdrwiega amazing thank you very much for the detailed answer