Modelling and simulating forces of a robot

[decimad]

Hey guys!
I'm lately bending my mind into getting fit with delta robots (which admittedly might not be your focus judging from overall topics found here).
For constructing a real one, I'd like to get a hang of the moments and forces I'll have to expect during movement. Over at youtube I saw a video of a talented guy, who programmed a dynamic simulation model of a delta robot. No matter how much I thought about it, I imagine that a terribly complex task. From my understanding, the system sports coupled nonlinear differential equations (3 input, MANY constrained inner forces/momentums, 3 output).
Can you guys think of ways to break a real simulation into a manageable approximation? I was thinking on using normal forward kinematics of a given path and then somehow calculate the forces "backwards". But I always end up with coupled equations I cannot get broken up and the amount of forces and angles is discouraging when I don't have the feeling I'm on the right path.
Do you guys know an answer or can you point me to resources which could help me with this? I fully expect I'll have to spend some quality time on this!

Thanks in advance,
Michael

[Gertlex]

We've got a tutorial for that

http://forums.trossenrobotics.com/tu...nematics-3276/

I've not taken the time to make heads/tails of it, though... (But it has pictures!)

From my experience with modeling kinematics (4DoF leg, 4 legged quad), I found visualization with Mathematica to be a helpful start/debugging tool.

[decimad]

Hi Gertlex,
thank you for your quick and kind reply!
I must have been unclear. I can calculate the forward and inverse kinematics already. But given them and a path over time I have enormous difficulties thinking of a way to calculate the momentums and forces involved in the movement. For example, when I apply moment M on one Motor, I'd like to calculate the the resulting momentums on the other two motors. Or if I have a path from A to B I'd like to calculate the momentums involved under time-constraints (move there in .2s, what does that mean for the motor momentums and the stress on the legs).

Thank you,
Michael

[jwatte]

If you have characterized the system, typically as a set of bodies (centers of mass/rotation) and joints (constraints such as axis of rotation,) then the moment/force needed is a simple algebraic expression of the various involved bodies. Practice is a lot different from theroy, though, because of losses, play, and deflection -- how much of a problem it is, depends on the relative magnitudes of the different variables.

Personally, I come at this from a modeling-and-simulation point of view, where systems such as building constraints as linear constraint problems, and solving them step-wise for some delta-t, reign supreme. (Check for example the classic Baraff physical modeling paper.) These systems are good for figuring out "what would happen if..." and you can easily measure forces involved (simply back-integrate the delta-v of a particular body for a particular time-step,) but they are not as good for analytic determination ahead of time.

If you want to try this out, check out some open source physics engines, like Bullet Game Physics, or ODE (Open Dynamics Engine -- not the differential equation :-)

[decimad]

Hello jwatte,

thanks a bunch, especially for the pointer to that great article.

I attempted the classical (newtonian?) modelling approach already. I've had troubles coming up with modeling equations for the rotational parts of the lower arms (which I'm certain I could sort out with some efforts and your paper). Those equations already get "huge" if I simply omit the rotational momentum of the lower arms. But my biggest problem is modelling the constraints, as I couldn't come up with a different idea than introducing realistic "elastic" joints to keep the bodies aligned during a practical simulation. Could I possibly just run a simulation and "fix" the positions and orientations inbetween the simulation iterations with the normal forward transformation? I suppose the simulation as a whole would wander off the real situation but otoh it would stay stable and I wouldnt need those inner elastics.

Then I also came across some articles about lagrangian representation of dynamics which supposedly help working with kinematic contraints much more easily without having to introduce tons of "inner spring" forces. However I'd need a serious read up for that stuff, so I try to avoid going that road for now.

Today I somewhat thought about cheating alltogether by "backwards" calculating the forces by "assuming" some given ("smooth") effector path over time, calculating the body movements by inverse kinematics and deriving two times by discrete differences. If I then omit forces introduced by angular acceleration of the lower arms I'd have a really simple way to calculate the momentums necessary to make the assumed movement (in most problems after all you already have a desired movement path). I wonder if that might yield reasonable values to be expected despite its oversimplification.

That's the roundup of my mental situation

Thank you,
Michael