The really cute part of it is using electrical conduit as rails, which are shockingly inexpensive. Like a couple bucks for 4 feet! Holy shnikes!
We’ve been printing up a storm for the last couple weeks. A ton of parts!
We already had a lot of motors and stuff lying around. Declan bought a lot of stuff too just for this. Assorted bearings and bolts. The plans have a bill of materials.
Repetier host seemed to work pretty well for controlling the board
Used the RAMPS branch of the mpcnc marlin repo
Edited the header files as described in this post so that we could use both extruders as extra x and y motor drivers. It did not seem like driving two motors from the same driver board was acceptable. Our bearings are gripping the rails a little too tight. It is tough to move.
This is an interesting web based g-code maker. Ultimately a little to janky though. It works good enough to get started http://jscut.org/jscut.html . Not entirely clear what pocket vs interior vs whatever is. engrave sort of seemed like what I wanted. Went into inkscape with a reasonable png and traced bitmapped it, then object to path. It’s also nice to just find an svg on the internet
The following code was needed to zero repetier and the RAMPS at the touch off point. We added it as a macro. It is doing some confusing behavior though.
G92 X0 Y0 Z0
pycam is the best I can find for 3d machining. Haven’t actually tried it yet
Casadi is something I’ve been aware of and not really explored much. It is a C++ / python / matlab library for modelling optimization problems for optimal control with bindings to IPOpt and other solvers. It can produce C code and has differentiation stuff. See below for some examples after I ramble.
I’ve enjoyed cvxpy, but cvxpy is designed specifically for convex problems, of which many control problems are not.
Casadi gives you a nonlinear modelling language and easy access to IPOpt, an interior point solver that works pretty good (along with some other solvers, many of which are proprietary however).
While the documentation visually looks very slick I actually found it rather confusing in contents at first. I’m not sure why. Something is off.
It also has a bunch of helper classes for DAE building and other things. They honestly really put me off. The documentation is confusing enough that I am not convinced they give you much.
The integrator classes give you access to external smart ode solvers from the Sundials suite. They give you good methods for difficult odes and dae (differential algebraic equations, which are ODEs with weird constraints like x^1 + y^1 == 1) Not clear to me if you can plug those in to an optimization, other than by a shooting method.
Casadi can also output C which is pretty cool.
I kind of wondered about Casadi vs Sympy. Sympy has lot’s of general purpose symbolic abilities. Symbolic solving, polynomial smarts, even some differential equation understanding. There might be big dividends to using it. But it is a little harder to get going. I feel like there is an empty space for a mathemtical modelling language that uses sympy as it’s underlying representation. I guess monkey patching sympy expressions into casadi expression might not be so hard. Sympy can also output fast C code. Sympy doesn’t really have any support for sparseness that I know of.
As a side note, It can be useful to put these other languages into numpy if you need extended reshaping abilities. The other languages often stop at matrices, which is odd to me.
Hmm. Casadi actually does have access to mixed integer programs via bonmin (and commercial solvers). That’s interesting. Check out lotka volterra minlp example
The optim interface makes some of this look better. optim.minimize and subject_to. Yeah, this is more similar to the interfaces I’m used to. It avoids the manual unpacking of the solution and the funky feel of making everything into implicit == 0 expressions.
Here is a simple harmonic oscillator example using the more raw casadi interface. x is positive, v is velocity, u is a control force. I’m using a very basic leap frog integration. You tend to have to stack things into a single vector with vertcat when building the final problem.
from casadi import *
import matplotlib.pyplot asplt
#theta = SX('theta', N)
#thdot = SX('thetadot', N)
constraints=[x-1,v]# expressions that must be zero
Very fast. Very impressive. Relatively readable code. I busted this out in like 15 minutes. IPopt solves the thing in the blink of an eye (about 0.05s self reported). Might be even faster if I warm start it with a good solution, as I would in online control (which may be feasible at this speed). Can add the initial condition as a parameter to the problem
There is a reasonable piecewise linear approximation for the pendulum replacing the the sinusoidal potential with two quadratic potentials (one around the top and one around the bottom). This translates to a triangle wave torque.
Cvxpy curiously has support for Mixed Integer Programming.
Cbc is probably better than GLPK MI. However, GLPK is way easier to get installed. Just brew install glpk and pip install cvxopt.
Getting cbc working was a bit of a journey. I had to actually BUILD Cylp (god forbid) and fix some problems.
Special Ordered Set constraints are useful for piecewise linear approximations. The SOS2 constraints take a set of variables and make it so that only two consecutive ones can be nonzero at a time. Solvers often have built in support for them, which can be much faster than just blasting them with general constraints. I did it by adding a binary variable for every consecutive pair. Then these binary variables suppress the continuous ones. Setting the sum of the binary variables to 1 makes only one able to be nonzero.
One downside is that every evaluation of these non linear functions requires a new set of integer and binary variables, which is possibly quite expensive.
For some values of total time steps and step length, the solver can go off the rails and never return.
At the moment, the solve is not fast enough for real time control with CBC (~ 2s). I wonder how much some kind of warm start might or more fiddling with heuristics, or if I had access to the built in SOS2 constraints rather than hacking it in. Also commercial solvers are usually faster. Still it is interesting.