Solving Rearrangement Puzzles Using Path Defragmentation in Factored State Spaces

Abstract

Rearrangement puzzles are variations of rearrangement problems in which the elements of a problem are potentially logically linked together. To efficiently solve such puzzles, we develop a motion planning approach based on a new state space that is logically <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">factored</i> , integrating the capabilities of the robot through factors of simultaneously manipulatable joints of an object. Based on this factored state space, we propose less-actions RRT (LA-RRT), a planner which optimizes for a low number of actions to solve a puzzle. At the core of our approach lies a new path defragmentation method, which rearranges and optimizes consecutive edges to minimize action cost. We solve six rearrangement scenarios with a Fetch robot, involving planar table puzzles and an escape room scenario. LA-RRT significantly outperforms the next best asymptotically-optimal planner by 4.01 to 6.58 times improvement in final action cost.