Steering characteristics of a 4-wheeled platform

This is the "skid steer" approach popular with skip loaders, like the
Bobcat. The point of steering is actually between the wheels, so the
vehicle makes turns by wheel slippage over the ground, similar to a
tank. Similart design principles apply.

I've designed several of these, and you can see basic pics and read the
dimensions on my site:

http://www.budgetrobotics.com/shop/?shop=1&cat 4&
http://www.budgetrobotics.com/shop/?shop=1&cat 6&

Like tank designs, it's best to keep the vehicle width narrow. This
affords better steering control. It doesn't matter to change the speed
or direction of the motors that are on the same side. For practical
purposes, the two wheels on each side act as one. I happen to use
separate motors because it's actually cheaper to do it this way, rather
than to buy or revise a gear train. However for larger vehicles you may
find a single motor per side, driving a chain or gear, is the more
affordable solution.

Wheel surface is critical. On the first link above (trhe 4WD unit), the
nubs in the tires pretty much prevent the vehicle from running over
carpet. You need to clip the nubs off and run on smooth rubber. I leave
the nubs on the wheels for those who will always run it over dirt or
concrete.

The Rigel wheels are harder plastic, which can be a benefit for
application over different surfaces without modifying the tire. The
wheels slide a bit more readily, which obviously has its pros and cons.

Tracked and 4WD vehicles require more horsepower to turn than the
traditionally-steered vehicle, so be sure the motors are well suited for
the job. Both of the vehicles above use four 57 oz-in servos, which for
the size and weight of the vehicles gives good oopmph.

-- Gordon

Can you explain your reasoning for that?  I would expect the opposite
to be true, that the shorter and wider the vehicle, the better the
steering control.  If you have a long narrow wheelbase the wheels have
to travel almost sideways when turning and produce little turning
torque; if you have a wide, short wheelbase they travel almost
forward/backward and produce high turning torque.

-chris

There are several 4WD skid-steered platforms around, in addition to
Gordon's Rigel ...

http://www.robotcombat.com/marketplace_machinelab.html
http://www.totalrobots.com/program_files/x4e_rover.htm
http://www.lynxmotion.com/Category.aspx?CategoryID0

Despite what Gordon said, the wheelbase on the Rigel is a lot shorter
than the distance between wheels side to side [roughly 3" versus 6"],
and I think this does aid turning. I found the Rigel to turn well on
most surfaces, including deep-pile carpets. OTOH, on my Radio Shack A1
tank, the grounded tread length is 7" front-to-back, and the
side-to-side distance between tracks is 4.5", so I'm not sure what the
final conclusion is. The tank treads are hard plastic, and tread "bars"
do run sideways which will aid sideways slippage on turns.


- dan michaels
www.oricomtech.com
=====================

Sorry...I think I used some poor terminology. See my other message which
hopefully clears up what I meant.

I don't have a made-up Rigel on hand at the moment, but I recall the
centerline width between wheels should be more like 5" wide, by about 3"
in length. That equates to more or less 1.6:1 ratio. (I had remembed it
more like 1.15:1, but I think 5x3 is correct) The Bobcat, my real-life
model, is 1.3:1, as is the "Rigel XL," the new 4WD drive unit I did.

Both of the Rigel chassis, though, are "narrow." Sigh. <g>

-- Gordon

Neither do I, so I guesstimated off of your own picture ;-) ... bottom
view.

http://www.budgetrobotics.com/shop/?shop=1&cart25447&cat 6&

Note how Gordon mounted the rear wheels further apart using a spacer to
give the base a rakish look.



but I recall the

Never was able to determine if the Rakish Look had any bearing on
steerability, but it looks cool! Seriously, I got the idea it from (I
think) an iRobot design, though I note there are just as many 4WD
vehicles without it. In any case it can be assembled without the spacer.

I remember now why I thought the ratio was 1.1:1 or so: In the original
I had larger wheels, so the servos were turned outward. That increases
the front-to-back wheelbase distance (as the servo shafts are
off-center). When I found the current wheels, which I liked better, I
discovered I could keep the design and just turn the servos inward. That
had the effect of increasing the width-to-length ratio. Some things just
work out! <g>

-- Gordon

Correct that a short, wide wheelbase sees less drag in a turn, but
that's indirectly related to what I was referring to. Of course "narrow"
is a relative term; in the two example robots I provided the width to
length of the wheelbase represents a square-ish box. In both robots the
width between the wheels is wider than pitch between the two wheels on
each side. The vehicle chassis itself is narrow, but the contact area of
the wheels is a box that is wider than it is long. To get these wheel
dimensions, which seem to be a good compromise for at least these
particular designs, the chassis of the vehicle has to be "narrow."

What I've found is that the control of steering is more difficult when
the width greatly exceeds the length (I'm talking wheelbases here, not
chassis dimensions). I imagine this is precisely because of drag that
the vehicle tends to go straight even with slight variations in the
motor speeds on each side. Maybe steering control isn't a good phrase.
More like heading control, or something. If you're just R/Cing it, I
guess it doesn't really matter. You can manually adjust the heading as
you steer the thing around. Odometers on the motors to keep their speeds
constant would help in computer control, but not everyone uses these.
And odometers for calculating bearing are fairly inaccurate on any
skid-steer vehicle (in my experience).

FWIW, I tried to design the overall dimensions of the wheelbase after
the Bobcat, in reduced scale, of course. I figured it's a tried and true
design. For those interested, the wheel width to length is a ratio of
about 1.3:1. On the larger (newer) 4WD I recenrly did, the ratio is
exactly the same. On the Rigel it's about 1.1:1. It's probably not as
critical with that robot because of the plastic (rather than rubber)
wheels.

-- Gordon

Ok.  What I mean by control is the predictability of (relatively
difficult to measure) robot motion as a function of (relatively easy to
measure) actuator motion.  My interest in this is that I am presently
building a tank-tread robot; I am using servos (i.e. pm dc brushmotors
with optical encoders, not rc servos) to drive the treads, however, so
I do not expect driving straight to be a problem.  That is admittedly
not an option for "budget" robots.  (then again, you can get a nice
pittman servo on ebay for about the same price of an rc servo in a
store...)

As width goes from much less than to much greater than length, mobility
can be classified in roughly three categories:

1. platform cannot steer at all, at least on high-friction terrain
2. platform can steer effectively, but not predictably
3. platform can steer predictably

Going for #3 is probably not worthwhile; for dead reckoning to be more
accurate than magnetic or inertial reference sensors the geometry would
be awful for other reasons.  On the other hand, #1 can be a very real
problem.  I had trouble with that on an old robot
(http://jormungand.net/projects/tiggerbot/ ) while driving on certain
carpets, though that platform was admittedly underpowered and
overloaded.

In any case, it's also important to remember that the ideal shape for a
robot that operates in an enclosed area is exactly round, as that shape
optimizes the ratio of footprint to area swept while turning in place.
As such, and since there was no compelling reason to alter the tread
geometry one way or the other, I ended up making my new robot exactly
square.

-chris.

Excellent points all. I just wanted to note that I agree the surplus/RFE
Pittmans, especially the ones with an encoder, are absolutely fantastic.
But the price starts accumulating when you add on A) some form of hub to
attach the motor shaft to the drive sprocket and B) a suitable H-bridge.
Of course, if one has to buy the Pittman motors new, the price
skyrockets. I was quoted over $100 each, in quantities I don't even want
to think about!


-- Gordon

On Thu, 17 Aug 2006 08:34:34 -0700, Gordon McComb


I hadn't seen your site before. The discussion further down this
thread gives me some ideas. I was likely to end up with a fairly
square-ish robot, since I've used the case of a CD ROM drive as the
starting point. I think I'll leave it as a 3-wheeler for now but knock
up some hardware for later.

BTW the PIC and MOSFETS stepper motor driver works well. I'm running
the motors off a 12V SLA battery and they're unstoppable.


____________________________________________________
"I like to be organised. A place for everything. And everything all over the
place."

I have been experimenting with 4 wheel drive differential / skid steering
using Vex parts. I found that as the distance between the front and rear
wheels increases, the steering becomes less effective. I have tried web
searching for any guidelines that describe the optimal dimensions for this
style platform, but the closest I found is this thesis paper:

http://etd.lib.fsu.edu/theses/available/etd-04102006-171127/unrestricted/Thesis.pdf

While it discusses the forces involved for differential steering, it does
not identify any optimal conditions.

Anyone know if there are some established guidelines as to what the
front-to-rear and left-to-right dimensions should be for skid steering?

Experimentally I have found that I get better operation if the separation
between the left / right wheels is greater than the separation between the
front / rear wheels. Can anyone else confirm this finding?

Mike



--
Posted via a free Usenet account from http://www.teranews.com

For wheeled skid-steer I think the best teachers are the skip loaders
and other vehicles on the commercial market, most of which are provided
with wheel-base specifications. Just go to the company Web sites. I
centered on the Bobcat and its 1.3:1 ratio, because it's iconic. Though
I'm sure there are others, with variations in design. These would be
good starting points.

I'm afraid I did confuse things a bit in my other messsage to Tim, but
indeed, a >1:1 width-to-length ratio provides better results. This
doesn't mean something like a 3:1 width-to-length would have superior
performance; in my tests I found those harder to steer, as in keep
straight. I'm sure someone better at math could explain why. (Or maybe
it's just me! <g>)

For tracked skid-steer, I have never found anything, and have instead
relied on dimensional specifications of military tanks, and also treaded
skip loaders and construction vehicles. Specs for these are similarly
available.

-- Gordon

..........

He, he. I do have your servo tank bot, which I just bought a week or so
ago, and the front-to rear length of tread on the floor is just under
3", while the side-side width between tread centers is 4.25", so the
ratio is 1 : 1.5 :: length : width.

OTOH, the Radio Shack tank I mentioned is just the opposite at 1 : 0.68
[7" tread base to 4.75" width between centers]. We're certainly all
over the place.

Offhand, do you know the ratio on the original Tamiya treaded base that
uses the same treads?

The servo tank bot is pretty cool, although I made a few mechanical
mods so far :).

For the regular Tankbot (the DC motor one), I pretty much kept things
exactly the way Tamiya has them in their kits that use the same track.
This is by necessity, as it uses the Twin Motor, and the supplied steel
axles. I kept the overall standard track lengths as used on the Tamiya
bulldozer, etc. As you know you can mix-and-match the links to make a
couple of different lengths.

For the Tankbot Servo, the stance is about an inch wider, because of the
depth of the motors. The track is the same length, with about the same
amount of track on the ground. That makes the width slightly wider on
this version.

On the new tank I have
(http://www.budgetrobotics.com/shop/?shop=1&cat 5), I provide framing
so that you can build it any of four ways. The first is the traditional
"long track" method. The track patch is fairly long, without "lifting"
any of the idlers. Probably similar to the Radio Shack tank you
measured.

On the other, you can use it in any of three ways: with 2 or 4 idlers on
the ground, or 6 idlers. In this version, and using the 6 idlers, the
two outer idlers on are stepped up 1/16". This prevents the whole length
of the track from sitting flat on the ground, exposing a considerable
surface area that has to be slid over. This is what some tank designs do
to minimize the track patch, when that is a critical factor (to be
honest, it isn't often for dirt or sand).

Because I believe in people deciding for themselves what works best,
I'll note that these new designs are constructed in a way where you can
widen the stance how ever you want. Each use independent "side rails"
where the motors attach to, and a center piece that holds things
together. You can use your own center piece of any width. Right now, the
width is about the minimum it can be, due to the dimensions of the
motors. So one can experiment by making the stance wider, just by
attaching their own piece of plastic, metal, or wood as the center.
Maybe someday I'll provide pre-cut/pre-drilled pieces with different
widths, but that'll need to wait until I can add some more of the bases
I'm working on.

-- Gordon

Hi Gordon. Your new tank bots look pretty cool, since they're longer
and lower than the original servo tankbot. Do they still use the same
Tamiya treads, or a different tread? It's not quite clear from the
photos on your site.

The downside to having a longer treadbase is the ability to turn, as
you note on your site. I would imagine the base with 6 idler rollers
will have a lot of trouble turning on nasty carpets, given my
experience with your original servo tank with 3 idlers and 3"
treadbase.

The first thing I did was set the servo tank to the fastest turn speed
[with both treads moving opposite directions, of course], and put it
down onto several different surfaces. I have one throw rug with a very
tough woven underside, which proved the worst case, and the treads
would derail, until I played a few games with the iders.

The derailing would occur on the rearmost idler with the long throw
back to the drive gear, and I found that changing that idler to a
toothed idler helped a lot. It could partially derail and still
recover.

I imagine there might be a similar derailing problem on your Tankbot XL
with flip base, since it also has long throws on the endmost idlers. Of
course, besides my "mods", the other way to deal with derailing is to
turn slower :).


- dan
===========

Not the Tamiya treads, but brand new and exclusive to us. I'll add an
explicit note about these new treads this weekend. (Though I would have
thought just by appearances in the photos people familiar with the
Tamiya treads would know these aren't Tamiya.)


Carpet is the bane of any rubber tread, but it depends on the carpet.


The new treads have an inner cog that positively engages into the idlers
-- all of the idlers are sprocketed, and rear idler has keepers inside
and out that prevent the track from jumping there. You can see the cog
in the bottom picture of the catalog page:

http://www.budgetrobotics.com/shop/?shop=1&cat 5

It sounds like you may be over-weighting your robot, and/or should play
with the tension of the treads. Rubber treads will elongate enough to
detrack in turns if you put too much weight on the vehicle. This is
especially true of the Tamiya tracks. Change the tensioning to keep them
from stretching too much that they'll detrack. If they've been assembled
properly they won't easily come apart, but if you're worried about that,
you can dab on silicone caulking at the joints. Mine have not come apart
in 2-3 years of play. Be sure to smooth out the caulking so that there
isn't a rough spot there that will interfere with the drive sprocket.

Since it's impossible to know what surfaces people will be using, it's
not possible to know for sure if the tracks will jump, which is why the
XL can be built in different configurations. But I rather doubt it'll
happen much especially with the flip base.

The biggest problem is that people want to use tracked bases when they
shouldn't. Tracked bases with rubber treads are best on non-compliant
surfaces (i.e. concrete, low nap commercial carpeting, closed loop
Berber carpets, etc.). Problems arise when the tread is compliant and so
is the surface it's going over. Friction is very high in turns, so even
if the treads don't detrack, it takes a lot of torque to negotiate the
turn, and often the turn results in skiddering and other conditions not
helpful in an autonomous vehicle. You want to avoid this condition on
many levels.

For some time I've offered a track base with hard plastic (ABS) treads,
the Tracked Drive, that navigates over the toughest of carpets, for
those people who want a rugbot. The treads absolutely cannot stretch and
detrack. However, the hard plastic is very slippery on hard surfaces, so
traction in those cases isn't very good. I provide a length of rubbery
non-slip tape you can put on the treads, for these situations.

-- Gordon

Excellent. I thought the treads on the new tanks look different, but
the web pictures are a little too dark to tell, which is why I asked.

However, I just took the sprocket pic and jiggered it using
Photostyler, and can easily see the new treads have keeper/extensions
in the center of the treads, which will fit into cutouts on the
sprockets. This is how my Radio Shack tank treads are designed. Much
better for reducing chance of derailing, I think.

Are you going to be selling the treads alone? Are these ABS?

...........

I've not put any more weight than just batteries and a small contorller
board on the tank so far. After I adjusted the tread tension better,
the advent of derailing when way down. Also, changing the rearmost
idler from smooth to toothed helped a lot.

The tread tension adjustment is really quite moderate, as I've only
moved the servos back 2mm in the slots. The one thing I do dislike a
bit with the tankbot servo is that, even at moderately low tread
tension, this pulls the large front idler back at any angle [not too
large]. I imagine this doesn't happen on the original Tamiya base,
since it uses a rod that extends all the way acorss to hold the idlers,
rather than screws. Just some constructive feedback.

Once the tread tension was increased, I super-glued [CA] the links to
make them permanent. Seems to be ok.


...............

Are the new treads for the XL tanks also hard ABS, or a softer variety?

Only with the other base parts. As you can imagine, the tread set is the
most expensive part (other than the motors), and besides, it is not easy
to work up the alignments for a treaded drive system. For people that
want some cheap rubber treads there are those 1/24-scale tank toys
available.


ABS is usually a hard plastic. The treads on the Tracked Drive units are
hard ABS, and the XL treads are rubber. I'm not sure what the rubber
composition is on the Tankbot XL treads, but it's probably butyl-based,
so it's all in the family.


A little bit of looseness is fine, but maybe tighten the screw against
the lock nut a little more. Tighten it so that it "locks," then back off
just slightly. There should be only a very modest amount of play there.
Once you get it set it will stay there permanently. The lock nuts are
very agressive. I just measured the play in my picture prototype and if
it's 1/2mm I'd be surprised!

Some new designs coming down the pike allow for using the axles (cut
down) with the supplied retainer caps and some Dura collars. Of course,
eight Dura collars adds a couple more bucks to the price, and you
remember the name of my business... The play seems about the same,
though, because the hole in the idler is a bit oversizedThis is why I
use those small washers in the idlers.
 

That should work for at least a while, though super glue doesn't like
mechanical stress this way. A compliant adhesive like silicone sealant
might be better if these joints give out. But they probably never will
anyway.


They are soft rubber, but maybe not quite as soft as the Tamiya treads.

-- Gordon

    It's straightforward to build a skid-steer machine, and it will work, but
don't try to estimate heading from odometry.  You'll need an IMU/compass
combo.

    It's a reasonable approach for operation on dirt.  For floors or
pavement, probably not.

                John Nagle
                Animats