Rearranging multiple objects is a critical skill for robots so that they can effectively deal with clutter in human spaces. This is a challenging problem as it involves combinatorially large, continuous C-spaces involving multiple movable bodies and complex kinematic constraints. This work initially revisits an existing search-based approach, which solves monotone challenges, i.e., when objects need to be grasped only once so as to be rearranged. The first contribution is the extension of this technique to a method that addresses many non-monotone challenges. The second contribution is the use of either the monotone or of the new non-monotone method as a local planner in the context of a higher-level task planner that searches the space of object placements and which provides stronger guarantees. The paper aims to emphasize the benefit of using more powerful motion primitives in the context of task planning for object rearrangement than an individual pick-andplace. Experiments in simulation using a model of a Baxter robot arm show the capability of solving difficult instances of rearrangement problems and evaluate the methods in terms of success ratio, running time, scalability and path quality.

This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface, where a robot can approach them from above and perform pickand-place operations to rearrange them. The paper considers both the case where the start and goal object poses overlap, and where they do not. For overlapping poses, the primary objective is to minimize the number of pick-and-place actions and then to minimize the distance traveled by the end-effector. For the non-overlapping case, the objective is solely to minimize the travel distance of the end-effector. While such problems do not involve all the complexities of general rearrangement, they remain computationally hard in both cases. This is shown through reductions from well-understood, hard combinatorial challenges to these rearrangement problems. The reductions are also shown to hold in the reverse direction, which enables the convenient application on rearrangement of well studied algorithms. These algorithms can be very efficient in practice despite the hardness results. The paper builds on these reduction results to propose an algorithmic pipeline for dealing with the rearrangement problems. Experimental evaluation, including hardware-based trials, shows that the proposed pipeline computes high-quality paths with regards to the optimization objectives. Furthermore, it exhibits highly desirable scalability as the number of objects increases in both the overlapping and non-overlapping setup.

Manipulating multiple movable obstacles is a hard problem that involves searching high-dimensional C-spaces. A milestone method for this problem was able to compute solutions for monotone instances. These are problems where every object needs to be transferred at most once to achieve a desired arrangement. The method uses backtracking search to find the order with which objects should be moved. This paper first proposes an approximate but significantly faster alternative for monotone rearrangement instances. The method defines a dependency graph between objects given minimum constraint removal paths (MCR) to transfer each object to its target. From this graph, the approach discovers the order of moving objects by performing topological sorting without backtracking search. The approximation arises from the limitation to consider only MCR paths, which minimize, however, the number of conflicts between objects. To solve non-monotone instances, this primitive is incorporated in a higher-level incremental search algorithm for general rearrangement planning, which operates similar to Bi-RRT. Given a start and a goal object arrangement, tree structures of reachable new arrangements are generated by using the primitive as an expansion procedure. The integrated solution achieves probabilistic completeness for the general non-monotone case and based on simulated experiments it achieves very good success ratios, solution times and path quality relative to alternatives.