swerve FORWARD kinematics

[James Critchley]

Originally Posted by Ether

Lots of luck modeling rocking, hopping, and hunting accurately!

Have some faith. We all know how to do something, this and leading others in the same would be my thing. Writing clear forum replies apparently is not. I will stick to answering questions specifically about the VIRSYS capability from now on. *CHEERS!*

In our first season of dynamic simulation, Team 302 is doing a great job with 6 wheel skid steer and used very few actual measurements. We reproduced jumping and sluggishness in our speed based controls and went back to open loop power for less precise but smoother and faster performance. The model showed all of this (but it was late in the game when we finished development).

In the case of swerve drive, the onset of any instability is all we really want to know about. That should not be difficult to capture. Exactly how it goes from there... we don't really care to capture with lots of accuracy. We just know to avoid it.

Like I said, I volunteer to code it for anybody that wants to play with it and document their findings. No takers yet.

Answers to your questions are below:

Originally Posted by Ether

2) the non-uniqueness statement in the paper was entirely in the context of FK, and in that context is true as it stands. The FK problem (for swerve) involves an overdetermined system of nonlinear equations. There is no unique solution, in general, for this kind of problem; but a least-squares solution can be found and is useful subject to the caveats discussed here.

In forward kinematics it is NOT that there is no UNIQUE solution to this problem. It is that is NO solution in general. The kinematic constraints are violated in your "solution", so by definition it is NOT a solution. The mechanism locking or exploding is just as valid and a much more spectacular solution!!! I can't remember which, but one software solver used to do this for you.

Originally Posted by Ether

1) It's not clear what you meant by "paradoxes" in this context, or why stick-slip should be "rare" (more about this below).

Stick-slip is not rare. A paradox generated by stick-slip behavior is, for example: http://en.wikipedia.org/wiki/Painlevé_paradox. Furthermore, dynamic models of tires don't usually apply a stick-slip intermittent "constraint". It is done with applied forces. Sorry no link, you'll have to do a bit of research for that one.

Originally Posted by Ether

There was no suggestion to use forward kinematics (FK) in the code that goes on the robot. The FK solution was presented for its mathematical interest and for possible use to check the correctness of inverse kinematic (IK) calculations. For those purposes it is entirely suitable.

The inverse kinematics determines ideal control set points. Your forward kinematics is suggested to verify performance of actual output subject to hardware limitations such as truncations (you specifically say truncations). Agreed, it should be limited to verification of the ideal set points. It can also be useful as a measure of badness but you don't need least squares for that.

A dynamic model is required for verification of system performance approximating real conditions. The intention is not to put it on the robot for FRC applications. It is used instead of a robot for virtual verification and software integration. You know... best practice systems engineering.