  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 factored, 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.
