Items on top of cloth, and dragging the cloth to move those items [blend files attached] Using Blender 2.82a, I'm simulating items on top of cloth (which itself is on top of a larger plane) and then using the cloth to drag the items. I have a method that works reasonably well, but I'm wondering if anyone has advice on improving it or extending it to rigid objects. Here's the setup at a high level:


Create a flat plane at the bottom, with collision modifier enabled.
Create a new plane, sub-divide it, add the cloth and collision modifiers. Increase the number of quality steps.
Create three cubes so that they fall on top of the cloth. The cubes also have the cloth and collision modifiers. Increase the number of quality steps.
Following this tutorial, attach two armatures (and join them), and make them the parents of the cloth. Have the armatures move, so that two pinned points of the cloth move with the armatures.


Right now, the main hyperparameter that I have tuned which shows successful results is the Collision -> Softbody And Cloth -> Friction value:



This is for the cloth, not the cubes. 

By default, the value is 5.0. Above, I changed it to 50.0. You can see the progression from the three GIFs with friction of 5.0, 15.0, and 50.0, respectively:







Here is the .blend for the above gif that uses friction = 50.0. 



This setup seems to be working reasonably well. Now, I am wondering if it's possible to have rigid objects on the cloth. (The cubes have the cloth modifier.) If I make the following changes:


Make the middle block an active rigid body of type box, and remove the cloth and collision modifiers. Note: I also tried keeping cloth only, keeping collision only, and keeping both cloth and collision modifiers, none of which produced better physics.
Make the plane a passive rigid body modifier of type mesh, in addition to its collision modifier.


I get this:



Ah, but unfortunately now that the middle block is rigid, it no longer interacts with the cloth.  This is definitely hard to simulate with physics. Does Blender have a solution for this? Here is the .blend for the above gif. 



A second question I have would be hyperparameter tuning. While I think tuning just this single friction hyperparameter work reasonably well, are there any others I should be aware of for testing purposes to produce realistic movements? The cubes, for example, are cloth and have their own friction hyperparameters, which might also need tuning, etc.

So, to summarize: (a) rigid objects on top of fabric, and (b) which hyperparameters to further tune? Thanks everyone.
Much like rigid body physics, the cloth modifier in vers,2.77a at least, won't allow the cloth to be animated or shapekeyed whilst the physics cache is active.
The cache's frame range can be set however (physics properties) so we turn that off at frame 140 when the cloth has settled down.
Whilst the cloth physics is still active, two 'cloth shapers' are underneath the table that physically 'lift' the cloth ends.  The cylinder moves to the right between frames 91 &amp; 98, the other end's triangular cube, from frame 98 to 105.
Both lifters are given Collision Physics.  They don't interfere with other collision objects such as the table and are invisible when rendered.  (eye &amp; camera icons in the Outliner)
In order to animate the cloth, we'd need to  &quot;Apply&quot; the cloth modifier at frame 140 when it's settled down and therefore 'freeze' it in it's current shape, allowing keyframed animation.
In this example we don't need to animate the cloth at all.  Instead we duplicate the table and get rid of the copy's inherited physics so it's just scenery.
The original table is made invisible in the Outliner and remains stationary to support the cloth.
At the frames where the cloth is supposed to be pulled to the right, we instead move the duplicate table to the left with the camera parented to it so the cloth appears to be pulled to the right.

As the falling cubes physics are baked we can add keyframes to simulate their inertia.  All three are parented to an empty so they can be moved as one.
Should there be other objects and scenery behind, simply render the tables, cloth etc. out with a transparent background and render that as one clip.  Render the background objects as another and mix them in the VSE.