Mathematical modelling of manifacture planning in automated engineering

[bvssvni]

Automatic engineering is a requirement for Environmental Mega Robotic Systems. Artificial intelligence needs fast feedback on how viable a design is, in order to optimize it. To make the performance good, one needs a simple model where there is as little data as possible, but accurate enough to predict:

• how long it is going to take assembling it
• which parts are depending on which others in which order
• how much space is required to manufacture the object
• how much space the object will take
• report errors if parts do not fit or space and time constraints can not be satisfied

In addition, this part of the system could have features to search for optimal design or manufacturing process by constraints or similar problems. A huge benefit is if the same language to describe what to produce also can describe temporary constraints. Many kinds of objects require other objects just to put the pieces together, then removed when they are no longer needed. Therefore, the language used must describe both adding and removing objects.

Assumptions

• Objects can be translated across space and time, unless specified otherwise by constraints. This makes it cheaper by planning with relative space and time, such that the same plan can be reused in more places and at different times.
• Assembled parts preserve structure when translated. They do not fall off or bend under transport. Equipment to prevent such cases should be used if this is the case, and constraints for those equipment can be fed into the input to the solver.
• Optimization in general for cost and energy is very complex, but can be simplified to save time and space, since cost and energy is always related to moving matter across time and space. When cost and energy is counter-intuitive to reduced time and space, this should be modeled as constraints.
• At this stage, the design of an object is ready, the problem is how to construct it. Automated planning for manufacturing does not make design modifications other than allowed by the freedom of constraints. Likewise, it is assumed that design of an object is either done independently of how it is manufactured, or using the finished plan for feedback to the design process.
• No liquids or gasses, other than simple fill-in described by constraints. Liquids and gasses are too complicated to reason with. If they are part of the manufacturing process for a closed time period, then other objects should be used to prevent leaks into other systems. Time period required should be encoded into the constraints.
• Objects are assembled from smaller parts that uses a simple constraint type of plugging, gluing, melting, holding or putting them together at known contact surfaces. Parts can be oriented to be aligned normally to contact surface. No non-linear contact surfaces. Error will be reported if parts do no fit.
• If a part has some dynamic property, such as cable length, it can be read back from solution. Dynamic properties might have maximum and minimum constraints.
• All the information you put in also comes out in the finished plan, minus constraints. This makes it easier to keep track of state and reduces chance of errors, since you do not need to combine pre data with post data.

4D vectors makes it easier to visualize, reuse and solve planning problems

One idea I have is to use 4D vectors to describe coordinates in both space and time. Instead of modeling objects as geometric shapes in 3D, they can be translated into 4D where the time dimension contains information about the planning. This could make it possible to use e.g. bounding boxes, packing algorithms and puzzle solvers.

For example, to build a fence using concrete:

||   ||
||   || build support
||   ||

||...||
||...|| fill concrete
||...||

  ...
  ...   remove support
  ...

------------------------------> x

When projected along the x-axis and time, the slice of 4D space looks like this:

time
^
|   ...
|   ...   fence is ready
| ||...|| remove support
| ||...|| concrete is dry
| ||...|| fill concrete
| ||   ||
| ||   || build support
+-----------------------------> x

The benefit of 4D is that all questions you can ask about the plan is possible to answer by examining the data. Spatial information is preserved, but you also get how this changes over time. It is easy to debug by examining slices and see whether constraints of some parts needs to be changed.

The same output format can also be used by different planners/solvers. Instead of outputting the specific answer you might need, it outputs the whole plan such that other useful information can be retrieved from the same data.

[danielbinzhang]

interesting topic. I have worked many years in construction industry and also looking at AI in engineering. Would like to connect and chat. check my linked-in: https://www.linkedin.com/in/daniel-bin-斌-zhang-张-0957501a/

[bvssvni]

I don't use linked-in but you can reach me by email listed here: https://github.com/bvssvni/