Difference between revisions of "Problems"

Revision as of 17:56, 13 January 2017

Table summarizing some features we want to test. To be refined or extended.

Problem 1 : Tower of Hanoi

Description

Tower of Hanoi with mobile robots^[1].

Challenge

For n discs, 2ⁿ - 1 moves needed ! (in the non-geometric case)
Placing a disk on the central stack may prevent, depending on their relative sizes, to transfer discs from stack 1 to stack 3 (or vice versa). I'm working on converting this problem to a humanoid robot setup.

Problem 2 : Blocks-World 3D

Description

Using top-grasps only, and not using hand-over, stack the blocks in alphabetical order anywhere (on the table, or on one of the trays).

Challenge

Because of the "flying obstacle", the pile cannot be built on the table or the green tray.
Because of the "flying obstacle", no more than 2 blocks can be stacked on the table (then the wrist touches the obstacle).
Whether the red or blue tray is chosen as location for building the pile, both initial piles need to be unstacked somewhere, somewhere reachable by both arms, that is the centre of the table C.
C is limited in size, and no more than 2 blocks can be stacked there, so there is a trade-off between:

• a short symbolic plan with a cluttered C
• a long symbolic plan with manageable C

Here is an example of solution.

Problem 3 : Rearrangement Planning

Description

The goal is to exchange the positions (i.e., the centre of objects) of the red object and the tray.

Challenge

One of the two objects has to be moved first to a temporary location. This may require to move other objects around, carefully choosing places that do not interfere.

The rearrangement planning problem ^{[2] [3]}.

Problem 4 : Sorting Objects

Description

The goal constraints are that all 7 blue blocks must be on the left table and all 7 green blocks must be on the right table. There are also 14 red blocks.

Challenge

The close proximity of the blocks forces the planner to carefully order its operations as well as to move red blocks out of the way.

Problem 5 : Non-Monotonic

Description

The robot must move the green blocks from the left table to a corresponding position on the right table. Both the initial and goal poses are blocked by four blue and cyan blocks respectively.

Challenge

Critically, the blue and cyan blocks have goal conditions to remain in their initial poses. This is the source of the nonmonotonicity as the robot must undo several goals by moving the blue and cyan blocks in order to solve the problem.

References

1. ↑ S. Cambon, R. Alami, and F. Gravot. A hybrid approach to intricate motion, manipulation and task planning. The Int. Journal of Robotics Research, 2009.
2. ↑ G. Havur et al., Geometric rearrangement of multiple movable objects on cluttered surfaces: A hybrid reasoning approach, Proceedings of ICRA 2014.
3. ↑ F. Lagriffoul, B. Andres, Combining Task and Motion Planning: a culprit detection problem, The International Journal of Robotics Research, 2016.