Robot CAMERA dolly - INERTIAL MISMATCH RATIO ??

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Thread Starter

Hugo Eckener

Hello All....

I am looking for opinions on a suitable inertial-mismatch ratio for our system.

I am a vfx supervisor for films and television. We are designing a multipurpose high-speed camera dolly. It’s a semi-autonomous, RF controlled, battery powered dolly that travels back and forth on a single 6" I -beam rail system. The dolly will have four modes of operation:

1. Manual Control (by that I mean being pushed by hand)
2. Motorized Control, via an RF link
3. Repeat Learn mode, wherein the microcontroller remembers and plays back moves
4. Programmable Moves

The first two modes were easy to design for in terms of motors and gear train. Our first design had 48-volt motors with synchronous belt reduction with plenty of torque and speed.

For the 3rd and 4th modes however, a red flag has been thrown up by the 89:1 inertial mismatch ratio of those above motors.

We are selecting new motors/drivers with higher inertia and to reduce the ratio, but I am polling for people’s opinions on a suitable ratio for this system. Obviously weight and size is of primary concern.

Requirements:
1.) The most important aspect of control is smooth starts and stops… there cannot be any jitter or the camera will see it. We will not be jerking the rig around like an industrial robot. Its all about smooth and gentle (but fast) two point moves.

2.) We’d like the drive mechanism to stay absolutely quiet as possible. (thus the synchronous belts)

3.) Need decent controlability down around 1 to 2 RPS of motor shaft, where much of our operation will be.

Specs:
Speed: 25 mph top speed
Range: 50 to 300 feet typical
Number of motors/drive wheels: 4
Weight: 150 pounds total weight of vehicle/motors/batts/camera/payload
Peak Acceleration: 14.66 ft/sec^2
Drive Wheels: 4.5” dia. low d. urethane treadled running on alum beam.
Gearing (current) 2.5:1 via rubber synchronous belt (for quietness)
Peak Torque at motor shaft: 301 in-oz
Peak RPM of motor: 4660 rpm
Feedback: 10/m/s Linear Barcode Reader with .15mm resolution, encoders on motor shafts.
 
Since you don't need high acceleration I would employ a combination of *direct coupled* motor inertia disc and increasing your gear ratio. You are likely going to have a pulley clamped to your motor shaft. Rigidly fasten a large disc of an appropriate inertia to this pulley. Then, make your motor pulley as small as possible and as large as you can get on the wheel.

This does two things:
1) it substantially increases motor inertia because the inertia disc is very rigidly coupled to the motor shaft. I've seen industrial robots use this technique when belt driving things.

2) Your gear ratio will reduce the effective inertia of the wheel pulley and wheel/load by the square of the pulley ratio. The more you can change this the better off you are.

Sorry I can't give you a recommended inertia ratio but it will depend on the rigidity of the system and your tuning. You might be OK with very low proportional gain since you aren't after blazing response but this by itself only goes so far. Try what I said and run it through your calculations it to see if your mismatch is closer to matching.

KEJR
 
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Hugo Eckener

I've been reading the debate over if this works or not...

Now I'm no expert, but from what I can tell, its not black and white whether an inertia in the system should be categorized as "rotor inertia" or "load inertia". But rather maybe its a "continuum" where each inertial component is valued at how rigidly coupled it is... in other words... maybe its ALL load inertia... just how rigid or compliant is it.

Still... I'm still not sure if I need a 5:1 or a 30:1 or a 100:1 ratio.
 
Hi Hugo,

Rigidly coupling to the motor shaft is adding to the motor inertia. I've talked with the motor designer from a major servo motor manufacturer and I was told that they actually are asked to add weights internally to the motor shaft for this express purpose. This is why you often see motor offered with the same electrical specs but different inertias. What I recommended to you is a way to tune in this inertia yourself by bolting it to the pulley.

I've had bad luck assuming other parts of the systems are rigid enough to add to the motor inertia. Bellows couplings, for instance are fairly stiff, but they act like a spring. One of the issues with a motor/ballscrew design is that often most of the inertia is in the ballscrew shaft and it is coupled through a bellows coupling to give the motor some compliance in mounting (i.e. the bearings don't fight each other). Just the lack of stiffness of the bellows in that application can give you enough spring slop so that you need somewhere between a 3:1 or 5:1 ratio (depending on your tuning). Keep in mind that these are relatively stiff bellows couplings too.

In your design, take every inertia attached to the motor shaft (motor inertia, pulley, and extra inertia disk) and sum those. This is your motor inertia. Take everything after the motor as the load. Keep in mind that the tire and tire pulley will act like gearing. Take the combined load and divide it by the square of the pulley ratio.

KEJR
 
B
Hi Hugo,

I'm seeing a bunch of potential land mines to avoid here....

You don't specify the brand or type of motor or control system you've got, but I'm going to assume brushless permanent magnet.

Here's a few things that come to mind...

1) Multi motor coordination. PM brushless motors use rotor position feedback and electronic commutation for torque control. You'll need individual motor controllers, and if you control them with a single velocity command, you're going to get enough differences in response to have problems. I'd use a single motion controller that commands the drives with a single TORQUE command. This gets rid of the individual speed regulators in the drives that are the primary actor in inertia mismatch problems.

2)No mention of physical characteristics of the system, wheelbase length/width, center of gravity location and system moment of inertia about the CofG. Under acceleration and deceleration, you're going to get changes in wheel loading that will affect maximum available traction and allowable wheel torque. Also no mention of how dolly is kept following the track. Individual wheel motors will cause problems with this.

3) Skip the cogged belts, pulleys and wheels, etc. Use a flat or multi V/groove urethane belt from a small motor pulley to a larger "wheel" pulley with the back of the belt as the wheel tire. Saves mass and complexity. At 4000+rpm and the tooth counts you're going to need to make the velocity, HDT type belts of 3 or 5mm pitch aren't going to be that quiet.

4) You're talking some significant power for a battery system, nearly 3.5kw just to get the .4G acceleration of a 150# load. What about peak torque fall off at higher rpm on the motors?

5) How critical the inertia ratio is depends on how stiff and responsive you want the system. How small you want the following error to be, velocity gain, etc. If the motion profile and/or repeatability that you need to follow isn't that critical, softening up the gains and using velocity and acceleration feed forward and a low pass commnand filter will make it smooth and responsive at the cost of precision, while making intertia ratio pretty much a non-issue.

Brian.
 
Hi Brian... many thanks to you for a lot of thought and some very intriguing ideas.

Yes... these would be brushless DC motors. We are looking at a few... Kollmorgen AKM32H and AKM42J are the lead contenders
To your points below...

> 1) Multi motor coordination.

Will look into the torque command. For slower motion control moves, we do need very precise positioning.... for high speed repeat moves its not that critical... Perhaps we could have different driver configurations depending on the use as you suggest.

Current plan is to have a single Arduino microcontroller commanding four separate Elmo panther or trombone drivers. Elmo engineers suggest that we go with Velocity control, though I do see your point.

We were going to have a 5000 ppr digital encoder with commutation for feedback.

> 2)No mention of physical characteristics of the system, wheelbase length/width, center of gravity location
> and system moment of inertia about the CofG. Under acceleration and deceleration, you're going to get
> changes in wheel loading that will affect maximum available traction and allowable wheel torque. Also no mention
> of how dolly is kept following the track. Individual wheel motors will cause problems with this.

This is basically a monorail traveling on a six inch I-beam. It has two wheel bogies, fully captured by spring loaded wheels (side guide, load and upstop) not unlike a roller coaster car. The two bogies are separated on a 36 " center. The guide wheels keep the bogie following a curve. The drivewheels are mounted sideways, centered on the bogie, and press against the web of the I-beam. For all intents and purposes, the drivewheels have no differential and the multiple motors always need to travel at the same speed.


> 3) Skip the cogged belts, pulleys and wheels, etc. Use a flat or multi V/groove urethane belt from a small
> motor pulley to a larger "wheel" pulley with the back of the belt as the wheel tire. Saves mass and complexity. At
> 4000+rpm and the tooth counts you're going to need to make the velocity, HDT type belts of 3 or 5mm pitch aren't going to be that quiet.

This is a very unique suggestion and I am giving it a lot of thought. Would almost be like single wheel tank treads. My two biggest concerns with it would be 1.) the extra wear and tear of the belt causing it to break... especially when it is getting physically "sheared" on acceleration and deceleration... and 2.) The traction available on that belt.

We were going to use custom low durometer (i.e. 72 durometer) polyurethane wheels, which I know are very sticky. Current size has those wheels at 6" diameter x 1.25" thick. We are going to sandblast the aluminum beam in the webbing area where they run. Its my hope that these four wheels, when spring loaded with enough force (50lbs pressure each for starters) have enough grip to suspend the vehicle vertically.

For simplicity of quick set up and noise, we don't want to go with anything like a rack and pinion.

Max rpm on that large drivewheel pulley would be 1400 rpm, but for sound would only need to be concerned below about half that speed.

I thought about V-belts, because I know they would be quietest, but for I know that the accuracy probably would not be good enough for repeat pass motion control moves (for camera registration) . Thus the synchronous belts. We have been looking at of course and AT 5 style belt, and also the much quieter Goodyear NRG helical synchronous belt, though these pulleys are quite pricey and don't really come small enough to allow a 5:1 ratio.

I should say that only some of the use of this system would be for motion control work. The bulk of it would be for normal "manual" motor control back and forth kind of stuff.... Typical moco speeds would probably be below 5 feet/sec travel.


> 4) You're talking some significant power for a battery system, nearly 3.5kw just to get the .4G acceleration of a
> 150# load. What about peak torque fall off at higher rpm on the motors?

Our current battery is four 82 volt LiFeP04 lithium packs in series (320vdc). These packs are 2.5 Ah with a max current draw of 70 amps. The max we would see is about 13 amps on level ground and 40 amps if we ever needed to take it vertical.

>
> 5) How critical the inertia ratio is depends on how stiff and responsive you want the system. How small you want the
> following error to be, velocity gain, etc. If the motion profile and/or repeatability that you need to follow
> isn't that critical, softening up the gains and using velocity and acceleration feed forward and a low pass
> command filter will make it smooth and responsive at the cost of precision, while making inertia ratio pretty much a non-issue.

This is great advice and leads me to wondering if we can save different drive configs for different running scenarios. What you describe above would be ideal for our "daily running". While precise "Moco" moves could have increased gain and position control.

Since I posted this, I have gleaned two significant pieces of information, though I don't know how accurate they are yet. One states that if you are using position control, your inertia ration should be around 10:1, HOWEVER if you are using torque or velocity control... upwards of 30 or 40:1 is sufficient.

Another source, from a leading drive manufacturer, has been telling us that the inertia ratio is not nearly as important as the "net torque to inertia ratio" . This is defined as the available torque of the motor minus the maximum amount of torque actually used... all divided by the inertia of the entire system. If the value is above 500, then you should have good control.

Ever heard of this?

Again... thanks Brian for you post.
 
Hello,

I didn't pick out the 0.4G acceleration part in the previous post. I agree with Brian in that you will need good belts.

I would consider using Copley Drives attached to a delta Tau Turbo PMAC through torque (current) input (have the Copley drive do the commutation, it's a bit easier). The PMAC has more sophisticated handling of trajectory than you will get with an arduino replaying the position or velocity. The PMAC can be programmed to have what is called PVT moves where you can feed it an array of position and velocity for every point in time that you are concerned with. I'm not a fan of the elmo drives. They use an atypical tuning setup and I could not find any acceleration or feedforward gains to adjust which are useful to gain performance without compromising stability.

Is there any way you can mock up the system, or is this prohibitive?

KEJR
 
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Hugo Eckener

> I agree with Brian in that you will need good belts.

Agreed. We would like to use a large and quiet belt something like the Goodyear Eagle NRG helical synchronous belts. The problem (besides the hefty price tag) is that the smallest pulley is quite large, and we want to get a 5:1 while keeping the large pulley under 6" diameter. Currently looking at Bercoflex (Mulco) AT5 belts with a 17 tooth small pulley and 85tooth large pulley, but would prefer a more quiet tooth profile. Open to suggestions.

25mm belt width meets the basic tensile specs, but considering going wider to reduce compliance. Of course I don't know how much that matters since we've got a much bigger compliance anyway in the urethane treaded drive wheels. At least with 4 of these powered drivewheels, we are basically adding the stiffness of them. (assuming we coordinate their control properly)

>I would consider using Copley Drives

Have you heard about this new "GOLD" line that Elmo has recently released? (with supposedly enhance programming) Perhaps they've addressed your previous concerns. Most of the motors that we've been looking at are 320vdc. Unfortunately, the Copleys mostly seem to max out at 90vdc with a few models at 180vdc. We'd need to pick a lower voltage motor and for which their are fewer options, though it is possible.

> to a delta Tau Turbo PMAC

I'll probably leave this up to our electronics team to decide. They are really big on the Arduino because we have a ton of other stuff programming stuff to do with it besides this one axis of motor control... There are a good number of subroutines and lookup tables that need to be written, a track learn function, and other interfaces that need to be established, such as a barcode reader, a wireless RF control for the entire system, etc... as well as timelapse and other types of functions. The system also has motors for camera pan, tilt roll, zoom, focus, cam start/stop, and possible a boom control.

Perhaps the aruduino could give the PMAC the basic commands and get the best of both worlds.

> Is there any way you can mock up the system, or is this prohibitive?

We are going to build a maximum of maybe 10 of these. The prototype will likely be one of the units. Mock ups will be done to some extent before we start serious machining, but ordering the components is still ordering the components!
 
B
Hugo,

I've never heard of that alternative "measure" for stability planning.

I still think that torque mode is the way to go for multiple motors. Just off the top of my head, I would think that about 0.25mm to 1.0mm positioning accuracy is about as good as you’re going to get out of the mechanical system you describe. But you’re never going to position a multi-segment 6” I beam track with that kind of accuracy to some location site plan. So, what I’m guessing is that what your're more interested in is precision in motion plan duplication rather than accurate implementation of the command plan. Position, velocity and acceleration errors are what drive the system, the high gains that keep them low are the trade off with stability.

I'd do a more rigorous analysis of what precision you REALLY need, and what you can expect from the rest of the system. Track rigidity, etc.

If you're going to go with soft tires, use an auxiliary hard tired idler wheel for position tracking. You'll never keep a fixed and consistent radius on the drive wheels if they deform at the contact point. This is another problem for a distributed velocity command. If you're making 10 units, you have enough quantity for custom made molded urethane wheels on machined aluminum hubs. Make the hubs out of aluminum pulley stock (google aluminum pulley stock), and you've got a simple system. There are TONS of urethane molders out there, and you'll be able to get whatever durometer you want.

Several others have made specific recommendations as far as drives and motors go, including experience with specific parts you've mentioned that are all strangers to me, I'm out of my depth there.

Feel free to contact me at [email protected], your problems sound like neat ones to have (comparatively speaking).

Brian
 
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