Wednesday, May 13, 2015

Labyrinth Bot Project

Photo by Cindy Pavlinac

I wrote the following a while back...
Labyrinths have been a part of my spiritual formation. The photo above is of the labyrinth inside Grace Cathedral in San Francisco. It is an eleven circuit labyrinth based on the one at Chartres Cathedral. A labyrinth is a symbolic and physical representation of the spiritual journey. One walks the path toward the center. Reaching the center is, in one sense, the goal – but the point is really the process of walking. At times you get very close to the center and the next moment, find yourself far from the center!

During the process of discernment, prior to ordination as a deacon and then priest, we often had to meet for review at various steps along the way with discernment committees at the Grace Cathedral. A regular part of this process (for me) was arriving early – stilling myself – and walking the labyrinth.

One of the classic robotic problems is that of maze solving (line following or between “walls’). In contests, the robot is programmed to run the maze slowly finding the simplest solution. It is place again at the start point and then runs the maze as quickly as possible. 

A labyrinth has a single path. It does not have a “solution,” but instead is followed – at best – slowly, deliberately, and thoughtfully.

The idea occurred to me to “teach” a robot to follow the labyrinth path or to move through the labyrinth path without an actual labyrinth there. On a large scale this could be done with a larger robot and the robot (perhaps with a candle on it?) could be followed. This could be done in toward the center and the return out into the world could also be done.

Basic circles of each size would be determined by program as well as basic turns. These would be used in the program for the “instructions” to move through the labyrinth and as subroutines in the program.

This is not only an interesting programming problem, but connects two loves. It is also an artistic application for robotics.

My friend Nikos Giannakopoulos has been developing what he calls the Artist Robot. You can see it on this thread over at the Parallax Forums. He then drew a Fibonacci Spiral. You can see that post here. This led to another thread where we created the Nikos Fibonacci Spiral Challenge. The basic tools and ideas all came together! Connecting Nikos ideas and path calculation tools with my dream of the labyrinth bot yield what follows... Below is an image of one of his posts...

Okay - Here is my attempt at drawing the walking or rolling path of a labyrinth. This is not maze solving, but writing a program to "scribble" the path.

I first found the simplified labyrinth posted above, but noticed that it had a "dead spot" - no path actually went there. So, I modified the drawing. Below is what I am calling a Westminster Labyrinth Modified (again, this is a simplified Chartres Labyrinth).
Below, you will find an image of an Excel Calculator that I modified using Nikos FABULOUS version (see above) as a template. I changed up some his colors to make it consistent with the S2 Program Maker GUI and to add a chart for this particular project. You can find working link to the Excel Calculator and the S2 GUI program at this post on our Fibonacci Challenge thread. Give it a try on your S2. 

Here is a photo of multiple runs (not a blurry photo) used to refine the path and arc lengths. Amazing repeatability with the S2 - you can see each slight tweaking of an arc's length - all this was done using the handy Excel calculator. It has two parts per Nikos' Original - It calculates the time to run any distance in cm with wheel speed set at 100, 100 and it calculates the time to run an arc at a fixed radius in cm and an angle of ω, one wheel is set at 100 - and it also calculates the speed of the other wheel (for the same radius).Then you just enter the values in the Motion Control Tile on the S2's Program Maker Software! Amazing and fun!

Here is my best run so far - It is based on v.3.5. Still not perfect but, pretty darn close!

And here is a video of that same run...

So - more work to do, but this ideas is surely within reach!

Nikos - Thanks so much for developing these tools for drawing with the S2 using only the GUI! This is really fun stuff! I learned a lot playing with Excel too and about creating simple tools to help with the work of making the Labyrinth Bot a reality! 

Update: Nikos created this drawing in Geogebra to detail in a very specific way the angles, arc and radii for the path. I am playing with Geogebra now to learn how to use the great resource.

Geogebra is very different from CAD programs, which I have some experience with. (I was an Architect prior to becoming a priest and still have access to very good CAD programs - but I am very rusty using them and I have not kept up with more recent updates).

Just got an old version of AutoCad with the Architectural Desktop from Dad (a retired architect). Will give that whirl to to help generate a drawing for the Labyrinth itself and the path with full dimensions - and in keeping with the spiritual theme of the Labyrinth Project - it will include all the Angles and Arc-angles (sorry it is bad pun - I know!)

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