This page starts with this solution's refusals, because an example that shows
only the easy case teaches the wrong lesson. Then it follows the solution
through three of the examiner's 50 test tables. Each number for a table comes
from the run recorded in
results-tables.json.
Contents#
1. When a glass cannot be pushed safely#
A planner must know when not to push. This section shows how this solution refuses a glass.
Pushing without toppling gives the shared rule for when a glass would tip instead of slide. This solution does not apply that rule yet. The main idea explains this gap.
Instead, the planner has its own refusals, based on the model. It can refuse a glass in two ways, and it records which one.
- Every candidate was dropped. All 1,500 candidate pushes for that glass failed one of the three filters. So no push got past all five copies of the model on all five readings of the table. The reason names the filter that dropped the most: the topple veto or the map.
- No push was worth making. Some pushes passed the filters. But the best push on the whole table would clear less than 2 mm of the missing room.
On the 50 test tables, only the second kind ever happened. The run left 85
glasses behind, and
results.json
gives each one's reason:
- 53 were on a table where a glass had fallen over. Nothing more is touched on such a table.
- 14 had no push that the model expected to make room.
- 10 were on a table whose 16 pushes were spent.
- 8 had been pushed four times, the most any glass is allowed, and still had no room.
No glass was refused because every push was dropped. So the first kind of refusal exists in the code but did not fire here.
The model has one serious weakness here. It can be sure and wrong, because all five copies can agree on a wrong answer. Where it is strong and where it breaks explains this.
The next section follows the planner through single tables, step by step.
2. A worked example#
The section above showed the refusals. This section follows the planner through three single tables.
The first way can trace any test table step by step. Its folder writes a picture for each step. It also writes a file with three things for each push: the 34 numbers the model was given, the 14 numbers each of the five copies gave back, and the 14 numbers that really happened.
Table 10004 is the ordinary case. The first look reports six glasses of one kind. Several pairs are closer than the 76 mm of clear room the gripper needs. So no glass can be taken yet, and the planner works on every crowded glass in turn.
For the first glass, the search draws 600 candidate pushes. They cover every direction, every point across the glass, and every travel from one to ten centimetres. All of them go to the five copies, and most fail on the predicted table:
- the glass would land outside the glass zone, or
- the jaw's path would leave the arm's reach, or
- the predicted movement is much longer than the push.
The topple veto drops more. Some of these really look like they would tip the glass, such as a short push high on a wide part. For others the five copies simply disagree. Both count the same. The rest are scored by how much clear room is still missing afterwards.
Three more rounds narrow the candidates onto the region that scored best. The same search runs for each of the other crowded glasses. The single best push over all of them is the one made.
The jaw comes down behind the glass, moves forward until it touches, pushes, and backs off. Then the arm looks again. This step is what makes the method work. The glass did not land exactly where the model said. The planner does not need to know, because it plans again from the new look, not from the prediction. Three pushes on three different glasses finish this table, and all six glasses are racked.
Table 10006 ends badly. It holds five stemmed glasses. The planner makes two pushes, and one glass falls over. Nothing more is touched on a table with a glass lying on it. So the other glasses are refused, and the table counts as wrong.
Table 10012 ends well. It holds five straight glasses. The planner makes three pushes, and all five glasses are racked.
Some pushes go wrong without breaking anything. A push can be blocked on the way down, when the jaw touches something before it reaches the table. The jaw then goes straight back up. The loop simply looks again and plans again, so a blocked push costs one push and nothing else. A table can also end with glasses refused and nothing broken. The examiner counts that as correct but incomplete, as the problem explains.
This page followed single tables. Where it sits among the other five gives the score over all 50 tables.
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