In other words, I'd like like to know how fast you can build a robot that has to start with the cube lying on a table in front of it, and the manipulators (hands, in the human case of course) being away from the cube, with the timer stopping when the cube is back on the table and the manipulators are back in their original position?
In that case, solving a Rubik's cube is a solved problem. It's become boring thing to watch machines do it. These machines are somewhat impressive in their own way, but the task they are doing has no point. I'd even say because "solving" is no longer relevant, the machines should be manipulating the cube in known (non random) patterns since we're down to comparing speeds.
Run one hundred meters, solve a Rubik’s Cube, swim one hundred meters, solve a riddle, cycle five kilometres, then the first two who complete that have to head off in a game of Go.
Why not? There’s people advocating eSports be included in the Olympics, so I’m open to anything at this stage.
In any case, given the fact that the human record for solving a cube is about 4.5 seconds, building a robot that can beat that would certainly be possible, but likely harder to do than the one from the article.
Can you? If you flip all four edge pieces on the bottom face the bottom color shows up at all four side faces, and you wouldn’t be able to determine whether those four edge pieces got permuted, too.
- three edge pieces that share a color, with that color showing on the side.
- two pairs of edge pieces that share a color, with the twice shared colors showing on the side.
The first isn’t uncommon; if you pick three edges at random, the probability that they share a color is 1 * 6/11 * 2/10 = 6/55, and there are four ways to pick three edges from the bottom face, for (I think) a total probability of 24/55 - 4 * 6/55 * 1/9 (the probability that all four share the same color), or a probability of over 1/3 (if that seems high, consider the following: because of the pigeonhole principle, between the edges of any face of the cube there always is at least a pair sharing a color). That means that, even ignoring the second possibility, there’s at least a 1:24 probability of seeing this problem on a random cube.
I think it actually is possible to infer the sixth side of a cube if you can see the other 5, because only only one configuration of the remaining side is actually acheivable.
In retrospect, it was obvious enough that I should have thought of it.
This is awesome. I love that this is what they did to solve this problem, versus something overly technical, like tuning the cameras or post-processing the images.
They also overtightened it
They also explain why they overtightened it.
The blog post for the software side is at http://blog.cactus.zone/2018/03/rubiks-solver-software.html.
It looks like they're using brushed DC motors, which reminds me of what happened with inkjet printers --- they originally used stepper motors for both axes, but then switched to a DC motor + encoder because it was both cheaper and faster while being just as accurate.
But I don’t think they’re overshooting per se. I think they’re landing the centers in the right place, but the outer pieces account for most of the moment of inertia, and they’re flexible, so the overall assembly is deforming. Deriving the optimal control law for that could be a bit messy. I would guess that it involves bringing the center piece nearly to a stop slightly short of 90 degrees and then gently bringing it the rest of the way.
Even in simple linear systems with a PID, a bit of overshoot may improve the response time. It's not always desirable but in this case there is no problem with it. I also liked the other commenters idea that perhaps the parts of the cube are moving further than the centers and then falling back in place.
Though I suspect the thing might fly apart if timed wrong. That’d be worth watching.
I'm aware of human friendly algorithms that aren't always optimal.
Edit: maximum -> GLB
All it means is that you only have to look at them once, at the beginning of the solve.
But since computers have memory, that’s true for all the tiles.
That is, the top center is always the same color, for every solve.
Hmm, so it's not finding the perfect solution but instead one close to perfect. I'm curious as to time tradeoff of trying to find a solution that does one spin better, but takes longer to compute.
It might be possible the longer solutions are mechanically quicker.