Can Mass Distribution and Spring Constants Keep a Hovering Platform Stable?

[Nemos]

Hi there.
I have got very good help from this forum in the past and I have yet another question.

Take a square platform with a thruster at each corner. Put a weight in the centre of it. Now, with the weight in the centre the platform is stable but as you move the weight to one side the platform tilts as the centre of gravity changes.
I am trying to create an intelligent system that will increase power to the appropriate thruster to keep the platform stable. I started with a basic spring/damper formula something like this:
SpringForce = SpringConstant * CompressedSpringLength
DamperForce = DamperConstant * RelativeVelocityOfConnectedBodies
OverallThrustForce = SpringForce - DamperForce

This works when the centre of gravity is also the centre of the platform but if I move the centre of gravity back the platform will tilt back. I had thought that the compressed length of the springs at the back would provide the necessary input to produce the correct thrust amount to keep the platform stable but I was wrong.
My current theory is that I need to take the mass over each thruster into consideration when calculating the spring constant for each one but I am not really sure. I can make it work by incrementing the spring constant for each of the back thrusters and running the program and eventually getting a stable hover through trial and error but this is no good as the positions of various masses on the platform need to be variable (Like as the fuel is used the mass of the tank will decrease).

I am a little bit stumped now so any input on this would be much appreciated chaps.

 

[russ_watters]

You didn't say what/where these springs are. Are they accelerometers at the corners of the structure? Are you building the accelerometers from scratch?

You could vary the thrust force to the corners simply based on the difference in force between the accelerometers. Ie, if the platform is rolling right, the accelerometers on the right will show less weight and the accelerometers on the left will show more.

Problem: while this will stop the rotation, it won't be able to tell you what the attitude of the platform is. That's a lot tougher...

 

[DaveC426913]

Consider some passive design before resorting to active design.

Light airplanes have a canted wing like this: \/ to provide stability in cross winds. As the plane is tilted to one side, the uptilted wing wing provides less lift while the downtilted wing provides more, thus helping the plane to return to level flight without any active correction.

On your platfrom, if you canted your thrusters to direct their thrust outward from the platform by a certain amount, then they would automatically act to stabilize it. The thruster on the corner that's dropped will point directly downwards, whereas the thruster on the lifted corner is directed more obliquely, and will provide less lifting power.

At least, I *think* that would work.


Another method of stabilization would be to place the centre of gravity hanging well below the thrusters (like a helicopter).

 

[Nemos]

OK I was a bit to absorbed in my own little world there. Will try to explain further.

The reason I used a spring/damper formula is that I am trying to build a realistic hover racing sim. The hover cars are actually rectangular and have a thruster at each corner. Each thruster projects a line to detect the ground height.
I defined a spring start position which is 50 units above the ground.
The detected ground height minus the spring start position gives me the spring length. I also defined a rest length for the spring which is 100 units above the spring start position. So, the spring length minus the rest length gives me the current compressed length of the spring at any given point in time.
The compressed length * the spring constant then gives me the force exerted by the spring. Once I have subtracted the damper force I then feed the value for each thruster into my physics engine (All forces applied to body in body fixed coordinates and then converted to world coordinates). The engine uses the spring force values and each thrusters position from the centre of gravity to calculate the moments about the centre of gravity and the overall force on the body.

That’s about it, I hope that's what you meant. I think talking about it in terms of springs and dampers was a little bit misleading so apologies for that.

Also, I am not a physics expert by any stretch, I’m just a web developer with delusions of grandeur so I’m afraid I don't understand the word accelerometers. If you could explain I would be most grateful.

 

[Nemos]

Thanks for that suggestion Dave. I didn't see it yesterday when i replied to russ so hopefully i will get a chance to try it out tonight when i get home from work. Sounds good in theory.

 

[Nemos]

Hi there.
I tried your plan Dave but it still settles at an angle if the centre of gravity is not in the centre of the car. I have been trying to make a system work that adjusts the thrusters just based on their height from the ground but it is quite dodgy so far. I think the answer might have something to do with using the distance from the centre of gravity for each thruster and maybe the total mass of the car to create some proportional method of scaling the thrust values but I can't quite work out how.

Thanks for your input chaps and of course any further suggestions would be much appreciated.