Complexity Results and Fast Methods for Optimal Tabletop Rearrangement with Overhand Grasps

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 pick-and-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.

Similar Part Rearrangement With Pebble Graphs

This work proposes a method for effectively computing manipulation paths to rearrange similar objects in a cluttered space. The solution can be used to place similar products in a factory floor in a desirable arrangement or for retrieving a particular object from a shelf blocked by similarly sized objects. These are challenging problems as they involve combinatorially large, continuous configuration spaces due to the presence of multiple moving bodies and kinematically complex manipulators. This work leverages ideas from algorithmic theory, multi-robot motion planning and manipulation planning to propose appropriate graphical representations for this challenge. These representations allow to quickly reason whether manipulation paths allow the transition between entire sets of objects arrangements without having to explicitly enumerate the path for each pair of arrangements. The proposed method also allows to take advantage of precomputation given a manipulation roadmap for transferring a single object in the same cluttered space. The resulting approach is evaluated in simulation for a realistic model of a Baxter robot and executed in open-loop on the real system, showing that the approach solves complex instances and is promising in terms of scalability and success ratio.