Re: Swerve with a twist
 

If you want holonomic omnidirectionality (swerve is by definition non holonomic, the system discussed here is likewise non holonomic), here is a link to a fact sheet on a system we developed that uses powered casters which provided holonomic omnidirectionality using conventional tires.

http://web.ornl.gov/sci/ees/eesrd/res/OCILOW.pdf

Its a slight twist on the swerve (e.g. in-line orientable wheels) and the conventional car steering topology discussed here. It's the third option for a powered steering/rolling system. OCILOW - Off-Center In-Line Orientable wheels (e.g. a fancy way of saying powered caster). By having the steering axis offset from the rolling axis and behind the wheel rather than next to it, the steering axis causes a velocity vector that is orthogonal to the rolling axis. Coordinated control of the steering and rolling enable instantaneous velocity vectors in any direction (e.g. holonomic) using conventional tires. You get very cool catenary type coordinated motions of the wheels, no skid while transitioning instantaneously from forward to sideway motion. The system is very robust and is highly redundant. You can still have full holonomic control with only two wheel pods active, the one or two being passive casters. It had a very cool double enveloping worm gear to drive the rolling axis. The challenge is the controls. If you have 4 active pods, you have 8 motors to control 3 degrees of freedom (x, y, theta). However, there is a closed for solution for the inverse kinematics, solving for the instantaneous velocities for all rolling and steering motors giving a desired Cartesian velocity vector (x_dot, y_dot, theta_dot). The cool part is that, no matter what the wheel pod configuration (if you look at the picture, we intentionally got the steering axes all different), it can still instantaneously move in any direction.

My group actually developed the split hub spherical wheel in the mid 1990s which was similar to the mecanum. We built a weapon loading system for the Air Force but the tires would wear out fast. It had a 7 DOF force reflecting arm on a holonomic omnidirectional platform. One person could load a 2000 lb weapon on the wing of an aircraft feeling the wedging and jamming when loading the weapon on the wing pylon. The holonomic motion was necessary for navigating under the wing. Unfortunately, like the mecanum, you have point, rather than surface, contact with the ground so your traction is low and tire stresses are high (not good when handling a bomb). If you really want/need holonomic omnidirectionality and you want to use conventional tires, it's the only way.

Re: Swerve with a twist
 

Please post a link to the definition referred to above.


Please provide a link to your paper, or post it here.

Re: Swerve with a twist
 

The best paper I've seen was by Wada and Morit, "Holonomic and Omnidirectional Vehicle with Conventional Tires" in 1996 IEEE Int. Conf on Robotics and Automation. Unfortunately, they didn't provide the closed for solution for the inverse kinemtatics . However, figure 1 in the paper says it all. Just take a minute and look at it and it will explain why you will never, by definition, get holonomic omnidirectionality with a swerve.

http://ftp.imp.fu-berlin.de/pub/Roja...l/00509272.pdf

I'll dig up our work on OCILOW.

Re: Swerve with a twist
 

The word "swerve" appears nowhere in that paper. Please define what you mean by swerve in the context of your previous post ("swerve is by definition non holonomic").

Re: Swerve with a twist
 

Swerve is what everyone is FIRST is calling the in-line orientable wheel, figure 1 a) in the paper.

Re: Swerve with a twist
 

"Swerve module" is the phrase most CD folks use to refer to an in-line orientable wheel like figure 1 a) in the paper.

"Swerve" usually refers to a vehicle using swerve modules in a particular way.


This is from page 3671 of the paper you linked:
Is the above-quoted description your intended meaning of swerve in your earlier statement "swerve is by definition non holonomic"?

Or are you claiming that a swerve vehicle with four swerve modules -- each of which can be steered and driven independently of the others -- is "non holonomic" ?

Or did you mean something else entirely ?

Re: Swerve with a twist
 

My son Bryce, has dreamed of trying to implement what he refers to as "caster drive" for FRC for a couple of years now. It took me a bit of pondering to understand the differences.

It's not that swerves can't move in the same directions, but if you don't want wiggling or squirming in unintentional directions at first, you really need to wait until the steering motors find their correct directions before powering the drive motors. In real use, the steering motors can get oriented up to the maximum required 90 degrees in less than 0.25 seconds, so we don't actually wait. For an FRC weight robot running on carpet, it's just not necessary.

The magic of the caster, is that by gradually mixing the steering rotation and the driving rotation into a cross blended function, you can achieve any motion direction instantly and with zero slip other than that due to the width of the tire. The tire will scrub only slightly due to differing path lengths for the inside and outside of the tire. Think of pushing a cart with 4 casters, not 2 like a shopping cart, you can make it move in precisely any direction with no wheel slippage, regardless of wheel direction. A powered robot is the same mechanically, except that the forces come from the wheels to move the cart, instead of the cart moving the wheels. The key is that any desired vector of motion can be expressed as the weighted sum of the two perpendicular directions created by the steering and drive wheel motors. The downside is that it takes a lot of simultaneous accurate control of both steering and driving motors. Is it worth it for FRC? I kind of doubt it, but I hope someone tries it in the off season some year, and decides to unveil it during build season anyway.

The 1996 paper referred to above has some nice drawings and graphs of the kinematic problem, which I've never seen before. Thanks for sharing.

Re: Swerve with a twist
 

"gradually mixing" and "instantly" seem like odd bedfellows in the same sentence.

Suppose I am driving your caster vehicle directly forward and I want to "instantly" go sideways? How is your caster vehicle superior to a properly designed and coded swerve?

Re: Swerve with a twist
 

Good summary Bob and you're son is extremely bright. The controls actually are fairly easy. Tracking errors are stabilizing instead of destabilizing. e.g. if one of the casters is off, the reaction forces due to the other casters push it in the right direction. We implemented this on a large system for the Navy. It had a 10,000 lb payload capacity and could position loads with sub mm accuracy. When we first powered it up, we didn't have the gains right on two of the drives. We drove it around for days and didn't notice.

One of the items I loved about our drive train was the double enveloping worm gear. We do a lot of printing and I've debated about trying to print the OCILOW drive with a complex worm drive. We had some kids design and print an OCILOW out last year but they used chains for the drive.

Re: Swerve with a twist
 

The motion in the desired direction can begin instantly. However, after the steering has rotated a bit, the lateral motion of rotation changes and "gradual mixing" of driving motion with the steering motion is required.

Apparently less than 1/4 second. A swerve drive with no trail must first be steered to the proper direction before applying drive to achieve motion only in the desired direction. With trail (offset between the two axes), the steering motion itself begins the motion in the desired direction (along the drive wheel axis).

This is not a meaning of holonomic I have seen before - I suppose it would have to be "having the ability to immediately move in an arbitrary direction while in any arbitrary state"

Re: Swerve with a twist
 

I guess I should have had my wife edit my sentences.

Correct. If you are going to stop and change direction, swerve is fine. But if you want truly holonomic omnidirectionality, being able to move and rotate in any direction without the swerving action, casters are a better solution. I was just trying to show a different solution. Whether anyone wants to try it makes no difference to me.

Re: Swerve with a twist
 

If you want to make a really tight right angle turn, you're going to have to come to an effective stop anyway because you can only get so much traction. I don't think that the fraction of a second where your steering motor happens to be pushing you in the right direction is going to be worth it in any FRC application.

On the other hand, it may be worth an experiment or two to see if the self-correcting nature of having the wheel trail the steering axis improves drive handling and stability.

Re: Swerve with a twist
 

6/2 2:38am
6/2 12:40pm
6/2 1:00pm
Waiting patiently for this paper. Are you still digging?

Re: Swerve with a twist
 

I checked and it's not online. I've got the pdf, emailed it to another person that requested it. You're settings don't permit me to email you. If you'd like it, send me a request at lovelj@ornl.gov.

Lonnie

Re: Swerve with a twist
 

Would you be willing to post it here so others reading this thread can see it as well.