paper: 4 wheel independent drive & independent steering ("swerve")

[Ether]

Originally Posted by Ether

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.

Just uploaded a description of how to calculate shortest-path angle error and how to use it with LabVIEW PID.

http://www.chiefdelphi.com/media/papers/download/2858

[Ether]

Sorry, the link got broken when I uploaded a corrected version. Here's the new link:

http://www.chiefdelphi.com/media/papers/download/2858

Also, note that there are two different ways to connect the angle error signal to the LabVIEW PID:

1) Connect the error to the Setpoint input, and connect a constant zero to the ProcessVariable input. This is the way mentioned in the paper.

2) Connect the negative of the error (i.e. -error) to the ProcessVariable input, and connect a constant value of zero to the Setpoint input.

The first way effectively disables the "D" portion of the PID (which you probably don't need for this application anyway).

The second way allows the "D" action of the PID to be used, but in a way perhaps not intended by the designer of the PID, since it causes the PID to use the derivative of both the ProcessVariable and the Setpoint. The PID is designed to take the derivative of the ProcessVariable input only*, so using this second way may result in instability or other unexpected behavior.

* see this thread: http://www.chiefdelphi.com/forums/sh...ad.php?t=88233

[Ether]

I just posted a 2-page summary explanation for those who just want the equations and don't care about the derivation.

[Ether]

Originally Posted by Ether

I just posted a 2-page summary explanation for those who just want the equations and don't care about the derivation.

There was a typo error in the fourth equation at the top of Page 2. It should read D = FWD + RCW*(W/R)

I corrected the typo, and updated the paper to use clockwise angles for the gyro and the wheel steering.

[Ether]

Just added a very simple Excel spreadsheet to demonstrate the swerve wheel speed and steering angle calculations. Might be a useful teaching tool for mentors (or learning tool for students).

User inputs values into cells A1 thru A6. Spreadsheet calculates and displays wheel speed command and wheel steering angle command for each of the 4 wheels.

[Ether]

see updated post

[Ether]

Originally Posted by Ether

Just added a very simple Excel spreadsheet to demonstrate the swerve wheel speed and steering angle calculations. Might be a useful teaching tool for mentors (or learning tool for students).

User inputs values into cells A1 thru A6. Spreadsheet calculates and displays wheel speed command and wheel steering angle command for each of the 4 wheels.

For students who are visual learners, I updated the spreadsheet to add a graphical display of the wheel speeds and steering angles.

Input the vehicle's wheelbase and trackwidth into cells A1 and A2.

Input the forward, strafe_right, and rotate_clockwise commands into cells A4, A5, and A6.


As a point of interest, note that if you enter FWD=1, STR=0.3, and RCW=0.384, you get Ackermann steering.


In fact, for any values of FWD_Ackerman and Turn_Ackermann, if you input

FWD=FWD_Ackermann, 
STR=Turn_Ackermann*sign(FWD)
RCW=STR*sqrt(L^2+W^2)/L

...you will get Ackermann steering. The derivation of this relationship is shown in the PDF attachment "convert Ackermann commands to holonomic".


Or you can get front-wheel Ackermann steering when going forward and rear-wheel Ackermann steering when backing up if you enter:

FWD=FWD_Ackermann
STR=Turn_Ackermann
RCW=STR*sign(FWD)*sqrt(L^2+W^2)/L

Or you can get "snake" steering (both front and rear wheel steering) if you simply set STR=0 and use:

FWD=FWD_snake
RCW=Turn_snake*sign(FWD)

[Ether]

Here's a handy "cheat sheet" for converting Cartesian coodinates to zero to 360 degrees, measured either clockwise or counterclockwise from any of the four quadrantal angles (0, 90, 180, 270):

convert Cartesian coordinates to angle

[Clem1640]

We use a "minimum angle" algorithm to in our swerve code and reverse the drive direction as needed. This works out very well. We code in Labview. 1640 has built 4 wheel independent drive & steering swerve robots for 4 years.

Very clear paper. Thanks.

[MoHottaMoBetta]

Originally Posted by Ether

Sorry, the link got broken when I uploaded a corrected version. Here's the new link:

http://www.chiefdelphi.com/media/papers/download/2858

Unless its just my bad luck, it looks like the links are not working. Can anyone else access the sample LabVIEW file?

Bruce