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12/22/2010 Vary the joystick (or any signal which has range -1 to +1) response curve from linear (y=x) to cubic (y=x^3) or anywhere in-between.
12/27/2010 updated to 2-parameter function with tunable inverse deadband
06/05/2014 added piecewise linear gain shaping alternative, with tunable constants a b c
Attached Files
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Figure1
sensitivity adjustment.gif
download file
uploaded: 12-22-2010 10:08 AM
filetype: gif
filesize: 11.76kb
downloads: 1952
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gain adjustment
sensitivity adjustment.txt
download file
uploaded: 12-22-2010 10:10 AM
filetype: txt
filesize: 1.41kb
downloads: 1264
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12/27/2010 revised 2-parameter version with inverse deadband
2parm-b.pdf
download file
uploaded: 12-27-2010 05:55 PM
filetype: pdf
filesize: 19.56kb
downloads: 712
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piecewise linear joystick gain shaping with inverse deadband
Joystick_Gain_Shaping.png
download file
uploaded: 06-05-2014 09:23 AM
filetype: png
filesize: 27.32kb
downloads: 504
Discussion
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12-23-2010 06:24 AM
Roger
Re: paper: joystick sensitivity (gain) adjustment
I had fiddled with this off and on years before, but never really worked it out properly or had the time (or a spare robot) during build season. It's nice to see it formalized and posted here.
Just to make it clear (or correct me if I'm wrong), the X and Y are not the actual joystick numbers from the X and Y axis (eg, in y = x^3, axis x number doesn't produce axis y number), but the input and output from each direction, so really you should have two formulas:
AxisX_output = AxisX_input ^ 3
AxisY_output = AxisY_input ^ 3
The deadzone or band would be a separate calculation (at least programming-wise); a simple "if input is between -0.2 and +0.2 then Y= 0". Whilst doing it all at once would be elegant, it would be a nightmare to debug. Though looking at the graph for f(x)=x^3, in all practicallity the robot motors might not overcome robot weight at all under +/-0.3.
I wonder what the effect would be if a<0? That is, more power near zero (to overcome the robot weight) and leveling off at higher speeds.
In practice this would have to be adjusted to each individual robot; even similar robots (a prototype and competition robot for example) would have different results. Also adjust to the driver, as different drivers like different reactions. If the driver doesn't notice it, then it works!
12-23-2010 07:39 AM
Ether
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by JesseK
No dead band?
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Not sure what you mean. You can easily add additional deadband if you wish, but for values of "a" near 1, you may not need to.
12-23-2010 07:59 AM
Ether
Re: paper: joystick sensitivity (gain) adjustment
|
Originally Posted by Roger
I had fiddled with this off and on years before, but never really worked it out properly or had the time (or a spare robot) during build season. It's nice to see it formalized and posted here.
Just to make it clear (or correct me if I'm wrong), the X and Y are not the actual joystick numbers from the X and Y axis |
X' = a1*X^3 + (1-a1)*X
Y' = a2*Y^3 + (1-a2)*Y
Z' = a3*Z^3 + (1-a3)*Z
| ...looking at the graph for f(x)=x^3, in all practicallity the robot motors might not overcome robot weight at all under +/-0.3. |
| I wonder what the effect would be if a<0? That is, more power near zero (to overcome the robot weight) and leveling off at higher speeds. |
| In practice this would have to be adjusted to each individual robot; even similar robots (a prototype and competition robot for example) would have different results. Also adjust to the driver, as different drivers like different reactions. |
*for some reason this thread does not allow me to attach the graph
12-23-2010 05:05 PM
Tom Line
Re: paper: joystick sensitivity (gain) adjustment
We take a somewhat different approach.
We use four linear equations (y=mx+b). First, we test our robot. So far, every robot we have built has been skid-steer. This means that there is an appreciable amount of motor force that it takes to break the robot into a skid to turn. Utilizing a control on the dashboard, we watch the values required to break it free using only one side. This is the B-intercept of our equation, so that the instant you move the joysticks out of the controller's preprogrammed deadband, you have enough power to turn the robot at the slowest possible speed.
So we use one equation from 0 to about 80% power. This portion has a gentle slope. After that, the slope goes from that point up to 1 (maximum joystick), 1 (maximum motor output). The nice part is that we only need to enter two values into our custom VI. The "B" y-intercept value that the drivetrain manages to start turning the robot at, and the intersection point of the two slopes.
For instance, if you were to graph it, the positive domain of the joystick would have these x,y points:
(X,Y)
(0,0.2)
(0.7,0.7)
(1,1)
I'm trying to attach a picture, but it doesn't appear I can do so in this forum.
12-23-2010 05:09 PM
Ether
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by Tom Line
I'm trying to attach a picture, but it doesn't appear I can do so in this forum.
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12-26-2010 11:26 PM
Jogo
Re: paper: joystick sensitivity (gain) adjustment
Really like the idea of that use of throttle.
Out of curiosity, is there anything special about the function x^3+x?
Recently we've used an exponential graph:
Let min = lowest desired value (min>0, usually the highest value at which the robot doesn't move)
Let max = highest desired value (usually, max = 1.0)
Then, output = min(max/min)^joystick value.
This also enables us to vary the max value for the turning axes based on the robot's forward speed.
12-27-2010 10:12 AM
Ether
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by Jogo
Really like the idea of that use of throttle.
Out of curiosity, is there anything special about the function x^3+x? |
As mentioned in the paper, when a=0, it becomes f(x)=x. When a=1, it becomes f(x)=x^3. When 0<a<1, it's something in-between. You can vary the "a" parameter to create a curve between f(x)=x and f(x)=x^3 to obtain the desired gain at low joystick settings.
Also, f(x) maps the domain (-1..1) into the range (-1..1) for any chosen value of "a" between 0 and 1, so there's no extra code required to break the domain up into, say, x<0 and x>0.
|
Recently we've used an exponential graph: Let min = lowest desired value (min>0, usually the highest value at which the robot doesn't move) Let max = highest desired value (usually, max = 1.0) Then, output = min(max/min)^joystick value. |
If you want to add a Y-intercept to the f(x) function, you can do it like this:
g(x) = b + (1-b)*[a*x^3 + (1-a)*x] for x>=0 g(x) = -b + (1-b)*[a*x^3 + (1-a)*x] for x<0
Interestingly, if you set b=0.2 and a=0.5, you get almost exactly the same curve as your exponential curve with min=0.2.
I have a graph prepared to illustrate this but can't attach it to this post for some reason*. I'll upload it when I get a chance.
| This also enables us to vary the max value for the turning axes based on the robot's forward speed. |
*if a moderator happens to be reading, would it be possible to change permissions on this thread to allow attaching graphs?
12-27-2010 10:17 AM
EricVanWyk
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by Jogo
Out of curiosity, is there anything special about the function x^3+x? |
Selecting a joystick mapping function is one of the best teaching opportunities you have in FRC. There are many right answers, it is open to opinion, it is super easy to prototype, you can objectively compare a bunch of them on a whiteboard, and it answers the questions set forth in this article: http://www.fordham.edu/academics/pro...math/index.asp . That is to say, it might be the first time the students go in the "from problem to math" direction, instead of the "from math to problem" direction.
ax^3+(1-a)x does have a few special properties, see if your students come up with these in their lists of "wants" for their formula:
- The function is smooth
- The 1st derivative is smooth
- It is tunable.
- The gain is low near 0.
- ...and high near 1.
- The gain inflection is always near the middle (.577, per Ether)
12-27-2010 01:36 PM
Jogo
Re: paper: joystick sensitivity (gain) adjustment
@Ether
Cool, will try it with the y-intercept. Really curious if I'll be able to feel a significant difference at different a-values.
When I stated "This also enables us to vary the max value for the turning axes based on the robot's forward speed," I meant that we found at high speeds, a slight tap to the side on the joystick will send the robot flying away. So, for example, when the robot is moving 1.0 (full speed) in the y-direction, then we might only allow the robot to move up to 0.1 in the x-direction. When the robot isn't moving in the y-direction, then we allow the full 1.0 turning speed.
@EricVanWyk
As a student, steering curves was the first time I went from problem->math; it was definitely among my fav. robotics experiences. I will try this with some of the rookie programmers, and maybe my calc teacher 
12-27-2010 02:15 PM
Ether
Re: paper: joystick sensitivity (gain) adjustment
|
Originally Posted by Jogo
When I stated "This also enables us to vary the max value for the turning axes based on the robot's forward speed," I meant that we found at high speeds, a slight tap to the side on the joystick will send the robot flying away. So, for example, when the robot is moving 1.0 (full speed) in the y-direction, then we might only allow the robot to move up to 0.1 in the x-direction. When the robot isn't moving in the y-direction, then we allow the full 1.0 turning speed.
|
To address this problem, you could use the 2-parameter g(x) function, and treat the "b" inverse deadband parameter like a variable instead of a tuning constant. In other words, adjust the value of "b" (for the rotate axis conversion) as a function of speed before running your joystick rotate axis through the g(x) conversion. caveat emptor: I've never tried this.
12-27-2010 03:49 PM
Ether
Re: paper: joystick sensitivity (gain) adjustment
|
Originally Posted by Tom Line
We use four linear equations (y=mx+b). First, we test our robot. So far, every robot we have built has been skid-steer. This means that there is an appreciable amount of motor force that it takes to break the robot into a skid to turn. Utilizing a control on the dashboard, we watch the values required to break it free using only one side. This is the B-intercept of our equation, so that the instant you move the joysticks out of the controller's preprogrammed deadband, you have enough power to turn the robot at the slowest possible speed.
So we use one equation from 0 to about 80% power. This portion has a gentle slope. After that, the slope goes from that point up to 1 (maximum joystick), 1 (maximum motor output). The nice part is that we only need to enter two values into our custom VI. The "B" y-intercept value that the drivetrain manages to start turning the robot at, and the intersection point of the two slopes. For instance, if you were to graph it, the positive domain of the joystick would have these x,y points: (X,Y) (0,0.2) (0.7,0.7) (1,1) |
I took the liberty of parameterizing it, to make it tunable on-the-fly.
Here's an implementation written in Delphi:
if (x>=a) then y := c+(x-a)*((1-c)/(1-a)) else if (x>=0) then y :=b + ((c-b)/a)*x else if (x>=-a) then y := -b + ((c-b)/a)*x else y:= -c + (x+a)*((1-c)/(1-a));
The three parameters are a, b, and c:
- "b" is the y-intercept (inverse deadband), and
- (a,c) are the coordinates of the point at which the slope changes
12-27-2010 06:48 PM
Ether
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by EricVanWyk
|
01-01-2011 10:59 AM
Roger
Re: paper: joystick sensitivity (gain) adjustment
Yesterday I gave this to one of my programmers to put into our LabVIEW code, as a sort of a warm-up exercise. An added bonus was making it a sub-vi to plug into future code.
There is a difference in driving, though perhaps not enough to change a good driver with careful joystick control. We didn't test it fully however.
A suggetion that simplifies changing "a" from rewriting code to letting the driver change it on the fly: use the thumb-thingie on the KOP joystick (it's at the base in the front and is known as axis3). It's range is -1 to +1, but with simple math can be converted to 0 to +1.
01-01-2011 12:44 PM
Ether
Re: paper: joystick sensitivity (gain) adjustment
|
Originally Posted by Roger
Yesterday I gave this to one of my programmers to put into our LabVIEW code, as a sort of a warm-up exercise. An added bonus was making it a sub-vi to plug into future code.
There is a difference in driving, though perhaps not enough to change a good driver with careful joystick control. We didn't test it fully however. |
Which one did you try? The one with just tunable sensitivity, or the one with both sensitivity and inverse deadband tuning parameters?
If you use the one with 2 tunable parameters, you could use three buttons to tune the two parameters: one button to bump parameter "a" up/down; one button to bump parameter "b" up/down; and a third button to select up/down.
01-01-2011 01:55 PM
Roger
Re: paper: joystick sensitivity (gain) adjustment
Oh dear, I'm way behind, aren't I? We were using the original y = a(x^3) + (1-a)x formula. That "2parm" looks interesting for Monday's programming session.
I think we might be running out of joystick buttons. We've got 2 buttons already for switching gear speed up and down -- yet another parameter in the mix, as "Full cubic" in first gear is really slow.
Another thing I might mention is that we are changing only the "forward/backward" axis of the joystick, and the "left/right" axis is not being changed. (The robot is a standard drive left/right sides.) General thought of the group is that this gives full turning power always.
01-01-2011 05:17 PM
Ether
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by Roger
...the "left/right" axis is not being changed...General thought of the group is that this gives full turning power always.
|
Look carefully at the figures and the associated narrative. This filter does not reduce the maximum available output. It just changes the response curve to reduce the gain for small commands. The maximum output of the filter is +/-1 regardless of the values selected for the tuning parameters.
What kind of drivetrain are you using, and what type of driver interface?
01-01-2011 05:35 PM
AustinSchuh
Re: paper: joystick sensitivity (gain) adjustment
This probably should go in another paper, but it helps handling a lot if you get some speed vs PWM data, and then curve fit it so that you can convert the nonlinear response of the Victors to a nicer linear response. I ended up using a 7th order polynomial last year to do that, and it helped quite a bit.
01-01-2011 05:53 PM
Ether
Re: paper: joystick sensitivity (gain) adjustment
|
Originally Posted by AustinSchuh
This probably should go in another paper, but it helps handling a lot if you get some speed vs PWM data, and then curve fit it so that you can convert the nonlinear response of the Victors to a nicer linear response. I ended up using a 7th order polynomial last year to do that, and it helped quite a bit.
|
01-01-2011 06:05 PM
AustinSchuh
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by Ether
Would you be willing to post your data?
|
# Speed Power Data on blocks. 0.103448 0.020000 -0.103448 -0.020000 0.252874 0.043000 -0.252874 -0.043000 0.333333 0.059000 -0.333333 -0.059000 0.454023 0.082000 -0.454023 -0.082000 0.517241 0.098000 -0.517241 -0.098000 0.614943 0.145000 -0.614943 -0.145000 0.724138 0.184000 -0.724138 -0.184000 0.793103 0.223000 -0.793103 -0.223000 0.885057 0.363000 -0.885057 -0.363000 0.965517 0.559000 -0.965517 -0.559000 1.000000 0.918000 -1.000000 -0.918000
01-01-2011 08:16 PM
Joe Ross
Re: paper: joystick sensitivity (gain) adjustment
By default, RobotDrive squares the inputs before it outputs the PWM, so you should consider the affects of that on any input adjustments.
01-01-2011 09:44 PM
AustinSchuh
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by Joe Ross
By default, RobotDrive squares the inputs before it outputs the PWM, so you should consider the affects of that on any input adjustments.
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01-04-2011 11:22 AM
Roger
Re: paper: joystick sensitivity (gain) adjustment
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Originally Posted by Ether
What kind of drivetrain are you using, and what type of driver interface?
|
Adding the second axis to the formula won't be a problem. It was more of "let's get one working first, then add the second." But now that you wrote it out, it makes sense that full power is always possible. We just ran out of time to do the changes.
This was a perfect project as a warm-up, with just enough learning joystick interfacing, sub-vi creation, and math programming, to get done in an hour then debug and change and test after. Adding the different modes and deciding which is "best" will be fun.
There are also two different drivers that we have to program for, and not for the same time. The first (and obvious) is the high school competition driver, who has practice driving with the robot. The second, more unpredictable, driver is the off-season "carnival" driver, a wanna-drive-the robot seven-year-old that throws the joystick all over the place. The former is easy, the latter we can only slow down the action so the robot doesn't crash too much.
06-20-2014 05:59 PM
jhebbel
Re: paper: joystick sensitivity (gain) adjustment
Sorry to revive a more than dead thread but its really the only relevant thread I could find. Im intrigued by the b + (1-b)*[a*x^3 + (1-a)*x] equation, but also confused, doesnt this need to be formated to solve for x and not y? Has anybody done this yet?
06-21-2014 08:00 AM
jhebbel
Re: paper: joystick sensitivity (gain) adjustment
For anybody else that lands here from Google like I did wondering the similar, The reason I though the equation needed to be formatted to solve for X is I didn't realize this was for inverse deadzone, to calculate for traditional deadzone it is y=G*((x-D)/(1-D))^3+(1-G)*(x-D)/(1-D); Where X is in value, D is Deadzone and G is Gain.
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