Control Schemes for a Simultaneous and Equal Displacement Frame Assembly

Use larger, pneumatic tires.

You have a guy with a controller standing next to it....the controller has a screen on it that gives a read out of a laser pointing from one side to the other, it is aimed at a field of sensors...he uses the grid as a reference to slow one side or the other...the laser tracks up and down automatically....

https://www.anstertrailer.com/spmt-self-propelled-modular-transporter-design-specifications/

https://en.wikipedia.org/wiki/Self-propelled_modular_transporter

Variations of this tracking technique have been used for hundreds of years.

While I obviously enjoy a snarky comment from time to time, there is a point here. You've not identified what this H-frame will be moving on. Will it be a level surface and thus unlikely to add any additional lateral force? More important, how will you or the controller recognize a deviation from the desired path?

I suggest that you abandon this folly and use a hand truck!

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I am offended by some of the useless replies to your question!

There are many possible answers to your question. Which answer is best depends on data you have not yet provided. Most importantly, what precision is required in maintaining the orientation of the unit? In other words, how much can the direction of motion vary from the initial Y direction? If it can vary ±5°, there are many possible methods that will work. If it can only vary by ±0.5°, it will require a much more sophisticated control system. If it can only vary a few arc-seconds, then it will require an extremely sophisticated system.

What you are describing sounds very much like a linear field irrigation system, except that I believe most of those use water motors, while I presume you are referring to electric gearmotors. The main thing those irrigating devices do is to use very large diameter toothed wheels to minimize the effects of irregularities in the terrain and reduce slippage. Some I've seen had wheels between 3 and 4 meters in diameter.

Another major factor you have not yet provided is some idea of the speed and acceleration the device is to use. I have been assuming that the device is to move at crawling speed, with inconsequential accelerations, since you indicate rough terrain. If it needs to move or accelerate quickly, again the control system needs to be more sophisticated.

Finally, how heavy a load does the apparatus need to carry, including its own weight?

Start by investigating those irrigating systems.

This doesn't sound (or look) anything at all like any irrigation systems I've ever seen.

Here's the first one I found:

from http://ww2.valleyirrigation.com/valley-irrigation/us/irrigation-products/linears

I've seen some with MUCH larger wheels (spiked aluminum, instead of pneumatic).

You can't!?

The OP says: "...an H-frame having four wheels with a drive motor and roller/wheel on each side." This indicates two wheels on each end, as shown in his drawing.

The framework with two wheels that are in the foreground of that photo is one side of the "H", and the truss assembly is the cross of the "H". The other side of the "H" is so far away it is hidden by the sprinkler spray. In fact, I believe the unit shown has at least two trusses and three pairs of wheels, but to me, it is exactly the same concept.

Leveling the pathway with a track is certainly a practical answer for some scenarios. Movie camera work is still done with temporary tracks despite the existence of today's gyroscopic cameras and image stabilization software. (Don't be offended by this rebuttal. We all need to vent from time to time.)

As my movie camera and your irrigation system assumption shows, there are lots of plausible scenarios that meet the barely specified conditions. Each assumption makes a different unspecified attribute critical to a tight tolerance and other unspecified attributes so very loosely tolerant that the attribute can be ignored.

Just driving the two, three phase AC synchronous electric motors (?) with the same voltage and frequency source will get this contraption at least part way down a straight dirt road. When mistracking errors occur a tire will just slip a little on the dirt.

Built like an " H frame " , using x to lengthen the framework to go over uneven terrain.

Is this better than z as in independent suspension to get motion control ?

For one side to move respective to the other, there must be some deformation of the angle between the cross bar and the wheel assembly. A method of measuring that deformation and applying it to some corrective algorithm that either stops that wheel set or speeds up the other set should achieve your objective. As long as the controlling program is aware of which direction it is meant to be moving, the controls should keep it all in line in both directions of travel.

It may be that to achieve accurate control you need to provide pivot points at one or both ends to allow the beam to deflect rather than twist.

You are only correct if there is no wheel slip, and on rough terrain, some slip is inevitable. There will also be some twisting of the cross bar as one wheel rises over a protrusion or falls into a dip, unless at least one end is free to rotate around some point on the end of the crossbar.

One or more accelerometers to indicate angular deviation of the cross-beam? A GPS system at each end to indicate relative positioning?

I like the laser idea but the rough terrain rules it out. If the terrain lifts or tilts one side relative to the other the laser will be off target even though both sides could be in the correct orientation. Strain gauges on the ends of the cross bar will keep the motors in synchronisation but in the time needed to take corrective action the whole rig could skew and all subsequent motion will follow the wrong path. Any tilt caused by the terrain will be picked up by the strain gauges and would need to be filtered out to stop the false positive causing an un-needed relative speed correction.

My solution would be to equip one motor with a GPS system. These are now quite common in farm tractors and their prices are dropping. Program the GPS where to start and where to finish. Equip the other motor with a "total station" (TS). This is a sophisticated theodolite with electronic distance and angle measurement. Standard accuracy for a TS is + 20 mm which is much better than any GPS available. You can program the TS to stay perpendicular to the line of travel relative to the GPS motor at a distance of X metres. The X beam will need to be fitted with some type of flexible compensation mechanism (e.g. gas spring) to allow for the 20 mm tracking tolerance. Over a long distance any tilts created by the terrain may be catered for by twisting the beam. If not compensation will be required for this as well..

The laser automatically tracks up and down, so a differing height is compensated for....

Up and down isn't up and down if the front wheel is lower than the rear wheel unless the laser is gimble mounted. The laser theodolite in a TS is gimble mounted but scans both horizontally and vertically to overcome this problem. A laser can measure the distance but that is effectively fixed by the length of the X beam. It is more important to incorporate a gyroscope and thus know the true angle of the X beam so that it can be compared to the direction of travel and pass on a corrective signal to the drive if it varies from 90 deg. to the travel direction. A fixed laser scanning up and down will know when it has lost the target horizontally but how does it know if the target is leading or trailing the correct position? All I was doing was proposing proven technology packaged in a way that gives all the information required to solve the problem. The lower risk and known cost involved in using off the shelf kit should have an advantage over designing from scratch.

Gutmonarch has never returned to give any more information. Another Item I failed to mention previously is the budget.

Since we don't know what this device is supposed to accomplish, nor any of the other details I mentioned, we have no idea what kind of budget (if any) exists to accomplish the desired result, whatever that may be...

My suspicion is that the budget is near zero. If so, all sophisticated solutions are out of the question...

Well the wheel slippage in autonomous tractors is not a new problem, I'm sure there is an off the shelf control box to track and compensate...and probably a number of hacks for linear irrigation systems....

http://www.valleyirrigation.com/technology-control-panels/gps-solutions/gps-position

..."Previous driving systems required manual calibration for hard and soft terrain settings. The new tractor anticipates wheel slippage based on the observed terrain and adjusts its speed and turning rate to compensate. The tractor's driving system "allows for precision down to the centimetre.""...

https://www.popsci.com/technology/article/2011-09/robotractor

Perhaps a GPS guided inertial navigation system at both ends...

https://pdfs.semanticscholar.org/ba6e/3a90bbb7b34b9aa6ce110f66714961d42ef9.pdf

The easiest, crudest method would be to mechanically link the drive wheels on each end and then link them through a small PLC or such with a turns counter. You program in moves for the PLC and each end runs for a specified number of turns and the PLC keeps tabs of keeping them matched. In effect, the PLC applies drive power for 20 turns and stops each end independently when it hits 20 turns. Both ends move in steps and the PLC matches at the end of each step. It would be possible to do this mechanically by running a drive line across, but the PLC would be cheaper and easier.

I used something like this on a bandsaw mill carriage to match movements at both ends of the carriage using a sprocket and magnetic proximity sensor feeding to a pulse counter and to the control PLC.