Autonomous: Mixing Drive Distance PID's with Turn Angle PID's.

[Joe Ross]

Originally Posted by Ether

What is the point of creating two separate polynomials and then adding them together?

Here's some data you can play with. http://forums.usfirst.org/showthread...ghlight=jaguar.

When I looked at it years ago, I wasn't happy with a 5th order polynomial approximation. We used the following lookup table below with the IFI system (input range 0-254, output range 0-254). It wasn't perfect, but greatly improved over nothing.

0	10	10	10	10	10	10	10	10	10	10	10	10	10	10	11	11	11	11	11	11	11	11	11	12	12	12	12	12	13	13	13	13	13	13	13	13	13	14	14	14	14	14	14	14	14	14	14	15	15	15	15	15	15	15	16	16	17	17	17	17	17	18	18	18	18	18	18	19	19	19	19	19	19	20	20	20	20	20	20	20	21	21	22	22	23	23	23	23	24	24	24	25	26	26	27	27	28	29	29	30	30	31	32	33	33	34	35	36	37	38	39	41	43	45	47	48	51	52	55	59	66	68	73	79	84	92	127	127	143	144	144	144	144	144	145	145	145	145	145	145	145	145	145	145	146	146	146	146	146	146	146	146	146	146	146	146	147	147	147	147	147	147	147	148	148	148	148	149	149	149	149	149	149	149	149	150	150	150	150	150	150	150	150	151	151	151	151	151	151	151	151	152	152	152	152	154	154	154	154	155	155	155	156	156	155	157	157	157	157	157	157	157	159	159	159	159	160	160	160	161	162	163	163	164	164	164	165	166	167	168	169	169	170	171	172	173	174	175	176	177	178	179	182	183	188	191	192	193	196	203	207	211	220	229	254

[Tom Line]

Thanks guys.

In the end, I kind of expected some derivation-based way of doing this as opposed to brute force best-fit-line equations, but this makes it easier for me.

By removing the 'tail' of the victor response down at the intermediate pulse widths that generally fall within the deadband of robot motion due to friction, I was able to get a very nice fit on a couple of 6th order polynomials. I'll poke through the rest of it tonight.

I WISH I trusted the jaguars enough to use them on our drivetrain. Perhaps I'm being paranoid, but I still worry about them burning out on fast full-reverse to full-forward transitions. The voltage mode and their linearity looks wonderful!

[Jared Russell]

Originally Posted by Tom Line

I WISH I trusted the jaguars enough to use them on our drivetrain. Perhaps I'm being paranoid, but I still worry about them burning out on fast full-reverse to full-forward transitions. The voltage mode and their linearity looks wonderful!

You and me both. The 2011 hardware beta test teams have been experimenting with a new version of the Jaguar firmware that implements an "output ramp" function in both PWM and CAN modes to help deal with this case, so hopefully that will help.

[Tom Line]

Originally Posted by Jared341

You and me both. The 2011 hardware beta test teams have been experimenting with a new version of the Jaguar firmware that implements an "output ramp" function in both PWM and CAN modes to help deal with this case, so hopefully that will help.

Yeah, we've been playing with it, but the practical side of me screams that I don't want that tiny delay between full back and full forward. The delay is infintesimal and practically we wouldn't ever see it..... it's just the engineer in me crying out to fix the problem and not the symptom.

[Ether]

Originally Posted by Joe Ross

Here's some data you can play with. http://forums.usfirst.org/showthread...ghlight=jaguar.

When I looked at it years ago, I wasn't happy with a 5th order polynomial approximation.

I got a pretty nice fit using just 2 cubics by splitting the curve into 2 sections.

See attached screenshot.

Cells A2-A21 and C2-C21 are pulse and volts data from the link you provided. I normalized that data to the range +/-1 for command and output in cells B2-B21 and D2-D21.

I copied the positive half of the curve to cells A27-B38, reversing the cmd & out to get the inverse function, and divided it into 2 sections: cells E27-F33 and E35-F41.

Then I fit a cubic to each section. The equations are in the two graphs at the bottom.

I spliced the 2 cubics together and you can see the net result at the top. It's a pretty nice fit, and for not much math.

To use it, test your desired (positive) command. If it's less than 0.842 use the first cubic, otherwise use the second. If it's zero, use zero.

You could use the same cubics for the negative half of the curve, or create new curves for that half.

[Tom Line]

Thanks guys. It's been a long time since I've had one of those AH HA! moments.....

I guess I never realized how far from linear the Victors can be. We've used joystick input modification VI's in the past to make the bots easier to drive, but I never put 2 and 2 together and realized a huge portion of that issue is caused by the Victor's response.

We noticed last year that the logitech dual action game pad (at least one of them) had a hokey joystick that wasn't even close to linear. We threw that one away, but after modeling the cim response like this, I'm almost tempted to do the same to the game pad joysticks so I can linearize them too.

Here's my final result using a single 6th order polynomial.

Darn do I love learning.

(Note: The numbers between .08 and -.08 are not representative in this graph - those are our dead band and will be modified to zero output).

[Jared Russell]

Pertinent response RE: 5th and 7th order polynomials here: http://www.chiefdelphi.com/forums/sh...t=98267&page=2

[Ether]

The Victor data from the link Joe provided:

pulse		volts
1.04		-12
1.07		-11.99
1.12		-11.7
1.27		-11.27
1.36		-10.12
1.41		-8.52
1.46		-3.8
1.48		-0.8
1.49		0
1.55		0
1.56		0.8
1.58		2.8
1.6		5.4
1.65		8.9
1.7		10.1
1.75		10.87
1.8		11.25
1.85		11.55
1.9		11.8
2		12

...normalized to +/-1:

cmd		out
-1		-1
-0.9375		-0.999166667
-0.833333333	-0.975
-0.520833333	-0.939166667
-0.333333333	-0.843333333
-0.229166667	-0.71
-0.125		-0.316666667
-0.083333333	-0.066666667
-0.0625		0
0.0625		0
0.083333333	0.066666667
0.125		0.233333333
0.166666667	0.45
0.270833333	0.741666667
0.375		0.841666667
0.479166667	0.905833333
0.583333333	0.9375
0.6875		0.9625
0.791666667	0.983333333
1		1

Swap the command and the output
(to get inverse function for linearization)
and select only the positive commands:

out		cmd
0		0.0625
0.066666667	0.083333333
0.233333333	0.125
0.45		0.166666667
0.741666667	0.270833333
0.841666667	0.375
0.905833333	0.479166667
0.9375		0.583333333
0.9625		0.6875
0.983333333	0.791666667
1		1

Fit a rational function model to the data:

(p1*x^4+p2*x^3+p3*x^2+p4*x+p5) / (x^2+p6*x+p7)

Here are the p1..p7 model parameters:

-0.43231217703332, 1.136975493080563, -1.043577770662604, 0.26894582879701, 0.069994693624, -2.151432791900253,  1.151458861241842

Attached graph shows the actual data (blue), the model (red), and the error (green). The error is multiplied by 10 to make it visible. The maximum error is 0.01 (1% of full scale).

[Jared Russell]

Here is an interesting post from the old IFI Robotics forum that describes what is going on "under the hood" of a Victor.

http://www.ifirobotics.com/forum/viewtopic.php?t=317

Note that there are only 94 discrete output states in each direction. This would make a look-up table a pretty attractive solution. Also, "Be aware that it may take 3 or 4 input steps before the Victor changes its Output."

EDIT: Although this post seems to contradict the last bit about latency: http://www.ifirobotics.com/forum/viewtopic.php?t=375

[Tom Line]

Originally Posted by Ether

The Victor data from the link Joe provided:

pulse		volts
1.04		-12
1.07		-11.99
1.12		-11.7
1.27		-11.27
1.36		-10.12
1.41		-8.52
1.46		-3.8
1.48		-0.8
1.49		0
1.55		0
1.56		0.8
1.58		2.8
1.6		5.4
1.65		8.9
1.7		10.1
1.75		10.87
1.8		11.25
1.85		11.55
1.9		11.8
2		12

...normalized to +/-1:

cmd		out
-1		-1
-0.9375		-0.999166667
-0.833333333	-0.975
-0.520833333	-0.939166667
-0.333333333	-0.843333333
-0.229166667	-0.71
-0.125		-0.316666667
-0.083333333	-0.066666667
-0.0625		0
0.0625		0
0.083333333	0.066666667
0.125		0.233333333
0.166666667	0.45
0.270833333	0.741666667
0.375		0.841666667
0.479166667	0.905833333
0.583333333	0.9375
0.6875		0.9625
0.791666667	0.983333333
1		1

Swap the command and the output
(to get inverse function for linearization)
and select only the positive commands:

out		cmd
0		0.0625
0.066666667	0.083333333
0.233333333	0.125
0.45		0.166666667
0.741666667	0.270833333
0.841666667	0.375
0.905833333	0.479166667
0.9375		0.583333333
0.9625		0.6875
0.983333333	0.791666667
1		1

Fit a rational function model to the data:

(p1*x^4+p2*x^3+p3*x^2+p4*x+p5) / (x^2+p6*x+p7)

Here are the p1..p7 model parameters:

-0.43231217703332, 1.136975493080563, -1.043577770662604, 0.26894582879701, 0.069994693624, -2.151432791900253,  1.151458861241842

Attached graph shows the actual data (blue), the model (red), and the error (green). The error is multiplied by 10 to make it visible. The maximum error is 0.01 (1% of full scale).

That's almost exactly what we did ether. Nice to know I was on the right track.