swerve FORWARD kinematics

[James Critchley]

good stuff.

Originally Posted by Ether

In general, there is no unique solution for the Forward Kinematic problem for arbitrarily chosen values for the 4 wheel steering angles and tangential velocities.

However, your solution should be limited to debugging activities only... You mention this as an application but the front matter can be misleading. This is because solving for the motions is a DYNAMICS (Kinematics AND Kinetics) problem. And with the exception of rare stick-slip frictional paradoxes (not present in tire models) motions are both solvable and UNIQUE. Allowing the tires to slip means that the wheel/ground interface is compliant and requires representation as forces not exact kinematic constraints (pure rolling). Kinematics is then the wrong tool for general motion prediction.

From a kinematics perspective, the system becomes LOCKED (grinds to a halt) as soon as one of the wheels does not track with the motion of the other three. Because you also specify the wheel speeds (instead of torques), inconsistent kinematic variables would instead be visualized as tearing the chassis apart (into 2, 3, or even 4 pieces). The kinematics problem is very much over constrained and as a least squares solve of the same, it is really only valid in the immediate neighborhood of kinematically consistent states (a measure of "scrubbing" as you say). In this case, the slight compliance in the tires and chassis flexure will make-up for "nearly" perfect outputs.

Actual wheel tracking will have much more to do with the normal force under each wheel AND bias will be present for those wheels that are currently in a pure rolling (not skidding) configuration. It is entirely possible that this least squares solve will result in nice smooth, fluid, and straight motions if you miss your target angles and speeds, where the actual system will instead rock, hop, and hunt for a direction of travel (not to mention being torque limited).

Given all of the off season interest here in Swerve Drive, I've been thinking about putting out a configurable 3D Swerve Drive simulator. If there really is is interest in physics based virtual system test, programming before you build it, or just having fun with something you've no intention of building, then PM me or post a reply in the VIRSYS thread with your request. I can support LabVIEW, C/C++, Java, Python...