Calculating the turning radius of a robot

[Mike Oliver]

Hi Everyone,
I have been working on a new wall smoothing algorithm and I've run into a
bit of an issue I cant seem to figure out. I'm trying to calculate the
turning radius of a robot given its velocity. I can get its change in
degrees per tick based on its velocity *10 - 0.75 * Math.abs(getVelocity())*,
but that doesn't really help me find the radius of its arc.

By plotting the points of my bot along its arc I was able to estimate its
radius. These values are close, but not 100% accurate. Does anyone know of
a proper formula for calculating the radius without requiring 3 sample
points along the arc?

Here are my findings: Velocity : Arc Radius

8 : 114.627
7 : 84.464
6 : 62:159
5: 45.862
4: 32.764
3: 22.186
2: 13.492
1: 6.205
0 : 0

Thanks for your time!

[Johannes Slotta]

Hi,

In theory of a continuous movement, these values should be
velocity/turning rate in radians, your values are close, the one for 6
is a bit off. Formula:
velocity / ((10-0.75*velocity)/(180/Math.PI))

In Reality, with discrete time steps, it is a bit more complicated (but
not much): velocity/2/sin(turning rate/2), or
velocity/2 / Math.sin((10-0.75*velocity)/(180*Math.PI)/2)

Values are (I used your values for first column):

measured continuous discrete
8 114.627 114.5915590262 114.6148333914
7 84.464 84.4358855982 84.4600705286
6 62.159 62.5044867415 62.5284914701
5 45.862 45.8366236105 45.8593571413
4 32.764 32.740445436 32.7608164788
3 22.186 22.1790114244 22.1959283285
2 13.492 13.4813598854 13.4937305748
1 6.205 6.1941383257 6.2008702328
0 0 0 0

HTH,
Johannes

Post by Mike Oliver
Hi Everyone,
I have been working on a new wall smoothing algorithm and I've run into a
bit of an issue I cant seem to figure out. I'm trying to calculate the
turning radius of a robot given its velocity. I can get its change in
degrees per tick based on its velocity 10 - 0.75 * Math.abs(getVelocity()),
but that doesn't really help me find the radius of its arc.
By plotting the points of my bot along its arc I was able to estimate its
radius. These values are close, but not 100% accurate. Does anyone know of
a proper formula for calculating the radius without requiring 3 sample
points along the arc?
Here are my findings: Velocity : Arc Radius
8 : 114.627
7 : 84.464
6 : 62:159
5: 45.862
4: 32.764
3: 22.186
2: 13.492
1: 6.205
0 : 0
Thanks for your time!
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[Johannes Slotta]

Should be 180/Math.PI instead of 180*Math.PI of course ;-)

Hi,
In theory of a continuous movement, these values should be velocity/turning
velocity / ((10-0.75*velocity)/(180/Math.PI))
In Reality, with discrete time steps, it is a bit more complicated (but not
much): velocity/2/sin(turning rate/2), or
velocity/2 / Math.sin((10-0.75*velocity)/(180*Math.PI)/2)
measured continuous discrete
8 114.627 114.5915590262 114.6148333914
7 84.464 84.4358855982 84.4600705286
6 62.159 62.5044867415 62.5284914701
5 45.862 45.8366236105 45.8593571413
4 32.764 32.740445436 32.7608164788
3 22.186 22.1790114244 22.1959283285
2 13.492 13.4813598854 13.4937305748
1 6.205 6.1941383257 6.2008702328
0 0 0 0
HTH,
Johannes

Post by Mike Oliver
Hi Everyone,
I have been working on a new wall smoothing algorithm and I've run into a
bit of an issue I cant seem to figure out. I'm trying to calculate the
turning radius of a robot given its velocity. I can get its change in
degrees per tick based on its velocity 10 - 0.75 *
Math.abs(getVelocity()),
but that doesn't really help me find the radius of its arc.
By plotting the points of my bot along its arc I was able to estimate its
radius. These values are close, but not 100% accurate. Does anyone know of
a proper formula for calculating the radius without requiring 3 sample
points along the arc?
Here are my findings: Velocity : Arc Radius
8 : 114.627
7 : 84.464
6 : 62:159
5: 45.862
4: 32.764
3: 22.186
2: 13.492
1: 6.205
0 : 0
Thanks for your time!
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[Mike Oliver]

Ah! Thats exactly what I was looking for, I figured there was an easier
solution to my approach. Thanks Johannes!

Post by Johannes Slotta
Should be 180/Math.PI instead of 180*Math.PI of course ;-)

Post by Johannes Slotta
Hi,
In theory of a continuous movement, these values should be

velocity/turning

Post by Johannes Slotta
rate in radians, your values are close, the one for 6 is a bit off.
velocity / ((10-0.75*velocity)/(180/Math.PI))
In Reality, with discrete time steps, it is a bit more complicated (but

not

Post by Johannes Slotta
much): velocity/2/sin(turning rate/2), or
velocity/2 / Math.sin((10-0.75*velocity)/(180*Math.PI)/2)
measured continuous discrete
8 114.627 114.5915590262 114.6148333914
7 84.464 84.4358855982 84.4600705286
6 62.159 62.5044867415 62.5284914701
5 45.862 45.8366236105 45.8593571413
4 32.764 32.740445436 32.7608164788
3 22.186 22.1790114244 22.1959283285
2 13.492 13.4813598854 13.4937305748
1 6.205 6.1941383257 6.2008702328
0 0 0 0
HTH,
Johannes

Post by Mike Oliver
Hi Everyone,
I have been working on a new wall smoothing algorithm and I've run into

a

Post by Johannes Slotta

Post by Mike Oliver
bit of an issue I cant seem to figure out. I'm trying to calculate the
turning radius of a robot given its velocity. I can get its change in
degrees per tick based on its velocity 10 - 0.75 *
Math.abs(getVelocity()),
but that doesn't really help me find the radius of its arc.
By plotting the points of my bot along its arc I was able to estimate

its

Post by Johannes Slotta

Post by Mike Oliver
radius. These values are close, but not 100% accurate. Does anyone

know

Post by Johannes Slotta

Post by Mike Oliver
of
a proper formula for calculating the radius without requiring 3 sample
points along the arc?
Here are my findings: Velocity : Arc Radius
8 : 114.627
7 : 84.464
6 : 62:159
5: 45.862
4: 32.764
3: 22.186
2: 13.492
1: 6.205
0 : 0
Thanks for your time!
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