# Week #11 20/04 - 24/04

## Velocity error study

Posted by Rui Costa on April 26, 2020

This week I've work on trying to understand how badly the velocity error, explained last week, would influence my results. A lot of the time spent this week was researching articles and books regarding the velocity model of a moving vehicle. My goal was to try to theoritically understand how a static target would be perceived as a moving one while the Atlascar was rotating, for example while making a 90 degree turn, and then compare to the bagfile information recorded. In order to better understand the theory behind this issue it is best to demonstrate it with an example of the worst case scenario. Imagine the Atlascar making a left turn at 5 km/h (1.39 m/s), the radius of said curve is 4.5 meters, stated in the Atlascar manual as the minimum radius (it is not stated from where it was measured so I assumed it was from the front inner wheel to the center of the circle), a static target is detected at 9 meters to the left from the Atlascar at t0 time (as seen on image 1). The publish frequency of the targets topic from the GNN node is approximatly 19 hz, 0.05 seconds, so we can assume that the Atlascar is travelling at approximatly 0.0731 meters per scan. Using the arc length formula (Arc length = pi * turning radius *(theta/180)) being the arc length the distance travelled by the Atlascar in a scan time interval, we get the angle rate per scan of 0.9307 degrees, wich is essencially the angular velocity per scan of the Atlascar turning. Since the data collected is referenced to the Atlascar and the target is static the same distance travelled by the target is expected, meaning that instead of moving the car we move the target, the travelled distance of the target should be the same. Using the same angle as of the Atlascar but now with the distance D in the same arc lenght formula as before we get the distance travelled by targets. We can se that due to the higher distance between the target and the center of the turn (D) the arc length is also higher. Hence the error of the velocity while turning, since if the distance travelled by the target is higher so will be its velocity wich supposedly should be the same 5 km/h because the target is static. Just think about if the target was in the center of the turn, the distance D would have been 0, and the arc length also would have been 0, therefore the relative velocity between the Atlascar and the target would again be 0 wich is not true since the Atlascar is travelling at a speed of 5 km/h.