# Effects of distance between wheels on differential line following robots

I have been working on a line following robot for a line tracing competition. It has 7 IR sensors for line detection and the robot size is limited based on the competition rules. The robot structure is similar to the one shown in this question Length and Width of a Line Following Robot.

My questions is, given a fixed robot length and fixed distance between the wheels and the caster wheel, should be distance between the differential wheels be as big as possible or as small as possible, if there are sharp turns (90 degrees and more) in the competition map?

I watched this youtube video Control of Mobile Robots- 2.2 Differential Drive Robotsand it says the car turning speed is $$R*(v_l-v_r)/L$$ where $$R$$ is the wheel radius, $$L$$ is distance between wheels, $$v_l$$ and $$v_r$$ are angular speed of left and right wheels. From this equation, it seems the $$L$$ should be as small as possible, and $$R$$ should be as big as possible, to allow fast turning. However, I saw so many designs with big $$L$$ and very small $$R$$, like the one showing below. So I am not sure if I understood the equation correctly or I missed something. • cut a model out of cardboard and slide it around a track on a table ... see how the sensors and lines interact – jsotola Aug 14 '19 at 6:45
• @jsotola, I am not sure I understand what you were trying to say. How to use cardboard to simulate different width between wheels? – roTor-roTor Aug 14 '19 at 22:30

## 1 Answer

Huge R, Small L can be the theoretic optimum, but you want to build a physical robot with real motors. If your robot is turning very fast, you have to be able to control the motor very accurately otherwise you robot will rotate very fast, but most likely not into the direction you want it to face. Large L also improves the weight distribution between the wheels so that at least the slip is similar for both wheels.

• I am not saying we have to push the turning speed to the limit. I just want to figure out the reason why some really fast cars in line following competition chose to use small R and big L, which is the opposite to the theory. Other than balanced slip, what other factors we have to consider beyond the math equation. – roTor-roTor Aug 14 '19 at 23:16