22 research outputs found
PushPush and Push-1 are NP-hard in 2D
We prove that two pushing-blocks puzzles are intractable in 2D. One of our
constructions improves an earlier result that established intractability in 3D
[OS99] for a puzzle inspired by the game PushPush. The second construction
answers a question we raised in [DDO00] for a variant we call Push-1. Both
puzzles consist of unit square blocks on an integer lattice; all blocks are
movable. An agent may push blocks (but never pull them) in attempting to move
between given start and goal positions. In the PushPush version, the agent can
only push one block at a time, and moreover when a block is pushed it slides
the maximal extent of its free range. In the Push-1 version, the agent can only
push one block one square at a time, the minimal extent---one square. Both
NP-hardness proofs are by reduction from SAT, and rely on a common
construction.Comment: 10 pages, 11 figures. Corrects an error in the conference version:
Proc. of the 12th Canadian Conference on Computational Geometry, August 2000,
pp. 211-21
On Rearrangement of Items Stored in Stacks
There are stacks, each filled with items, and one empty stack.
Every stack has capacity . A robot arm, in one stack operation (step),
may pop one item from the top of a non-empty stack and subsequently push it
onto a stack not at capacity. In a {\em labeled} problem, all items are
distinguishable and are initially randomly scattered in the stacks. The
items must be rearranged using pop-and-pushs so that in the end, the stack holds items , in that order, from the top to
the bottom for all . In an {\em unlabeled} problem, the
items are of types of each. The goal is to rearrange items so that
items of type are located in the stack for all . In carrying out the rearrangement, a natural question is to find the least
number of required pop-and-pushes.
Our main contributions are: (1) an algorithm for restoring the order of
items stored in an table using only column and row
permutations, and its generalization, and (2) an algorithm with a guaranteed
upper bound of steps for solving both versions of the stack
rearrangement problem when for arbitrary fixed
positive number . In terms of the required number of steps, the labeled and
unlabeled version have lower bounds
and , respectively
Push-Pull Block Puzzles are Hard
This paper proves that push-pull block puzzles in 3D are PSPACE-complete to
solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve,
settling an open question by Zubaran and Ritt. Push-pull block puzzles are a
type of recreational motion planning problem, similar to Sokoban, that involve
moving a `robot' on a square grid with obstacles. The obstacles
cannot be traversed by the robot, but some can be pushed and pulled by the
robot into adjacent squares. Thin walls prevent movement between two adjacent
squares. This work follows in a long line of algorithms and complexity work on
similar problems. The 2D push-pull block puzzle shows up in the video games
Pukoban as well as The Legend of Zelda: A Link to the Past, giving another
proof of hardness for the latter. This variant of block-pushing puzzles is of
particular interest because of its connections to reversibility, since any
action (e.g., push or pull) can be inverted by another valid action (e.g., pull
or push).Comment: Full version of CIAC 2017 paper. 17 page
Local Navigation Among Movable Obstacles with Deep Reinforcement Learning
Autonomous robots would benefit a lot by gaining the ability to manipulate
their environment to solve path planning tasks, known as the Navigation Among
Movable Obstacle (NAMO) problem. In this paper, we present a deep reinforcement
learning approach for solving NAMO locally, near narrow passages. We train
parallel agents in physics simulation using an Advantage Actor-Critic based
algorithm with a multi-modal neural network. We present an online policy that
is able to push obstacles in a non-axial-aligned fashion, react to unexpected
obstacle dynamics in real-time, and solve the local NAMO problem. Experimental
validation in simulation shows that the presented approach generalises to
unseen NAMO problems in unknown environments. We further demonstrate the
implementation of the policy on a real quadrupedal robot, showing that the
policy can deal with real-world sensor noises and uncertainties in unseen NAMO
tasks.Comment: 7 pages, 7 figures, 4 table