[Ether]

The first release of the paper presents the solution to the inverse kinematic problem, i.e., given a desired vehicle translational plus rotational motion, what angle and speed should be commanded for each wheel.

The paper addresses both robot-centric and field-centric commands.

I am working on algorithms for the "do I reverse the wheel speed or do I turn the wheel 180 degrees" problem, and will post those here when they're done.

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Additional explanation of "180 problem":

The algorithms and reference code in the paper properly calculate the correct wheel speed and wheel angle (setpoint variables) for each wheel, for any possible combination of input commands (fwd/rev, strafe, and rotate). Each wheel angle computed will be in the range -pi to +pi. An angle of zero is the straight-ahead direction (relative to the robot). Positive angles are CCW from zero, negative angles are CW from zero. Each wheel speed computed will be in the range 0..+1.

The "180 problem" is how to control each wheel's angle and speed, assuming you have correct setpoint variables (speed and angle) and process variables (speed and angle) for that wheel.

The simplest approach is to control each wheel's speed and angle separately: make each wheel angle go to that wheel's angle setpoint, and each wheel's speed go to that wheel's speed setpoint. For the drivetrain stipulated in the paper in Figure 1 (unlimited steering and continuous wheel angle sensor with no gaps) this may well be perfectly adequate - if the steering motors are powerful enough to provide satisfactory response against the given floor material and wheel tread material.

The initial "180 problem" I hope to address is the case where the steering motors are not sufficiently powerful to provide satisfactory steering response for rapid maneuvers. If, for example, the process variables for a wheel are 10% speed straight forward, and the setpoint variables for that wheel are 10% speed straight backward, perhaps it makes more sense to reverse the wheel's rotational speed rather than turning it 180 degrees. The challenge is to design a tunable (parameterized) algorithm which addresses the shades of gray in between seamlessly.

The second "180 problem" I am looking at is more difficult: if the drivetrain does not have unlimited steering, or if the sensors have have gaps (dead zone). The design goal is to minimize the "bad behavior" around the discontinuity. One approach might be to build some smarts into the control algorithm so that it looks for opportunities to steer the wheels away from the discontinuity whenever doing so would be least disruptive (for example when speeds are very low).

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