ORLA*: Mobile Manipulator-Based Object Rearrangement with Lazy A*

Effectively performing object rearrangement is an essential skill for mobile manipulators, e.g., setting up a dinner table or organizing a desk. A key challenge in such problems is deciding an appropriate manipulation order for objects to effectively untangle dependencies between objects while considering the necessary motions for realizing the manipulations (e.g., pick and place). To our knowledge, computing time-optimal multi-object rearrangement solutions for mobile manipulators remains a largely untapped research direction. In this research, we propose ORLA*, which leverages delayed (lazy) evaluation in searching for a high-quality object pick and place sequence that considers both end-effector and mobile robot base travel. ORLA* also supports multi-layered rearrangement tasks considering pile stability using machine learning. Employing an optimal solver for finding temporary locations for displacing objects, ORLA* can achieve global optimality. Through extensive simulation and ablation study, we confirm the effectiveness of ORLA* delivering quality solutions for challenging rearrangement instances. Supplementary materials are available at: https://gaokai15.github.io/ORLA-Star/Comment: Submitted to ICRA 202

Rearrangement on Lattices with Pick-n-Swaps: Optimality Structures and Efficient Algorithms

We propose and study a class of rearrangement problems under a novel pick-n-swap prehensile manipulation model, in which a robotic manipulator, capable of carrying an item and making item swaps, is tasked to sort items stored in lattices of variable dimensions in a time-optimal manner. We systematically analyze the intrinsic optimality structure, which is fairly rich and intriguing, under different levels of item distinguishability (fully labeled, where each item has a unique label, or partially labeled, where multiple items may be of the same type) and different lattice dimensions. Focusing on the most practical setting of one and two dimensions, we develop low polynomial time cycle-following based algorithms that optimally perform rearrangements on 1D lattices under both fully- and partially-labeled settings. On the other hand, we show that rearrangement on 2D and higher dimensional lattices becomes computationally intractable to optimally solve. Despite their NP-hardness, we prove that efficient cycle-following based algorithms remain asymptotically optimal for 2D fully- and partially-labeled settings, in expectation, using the interesting fact that random permutations induce only a small number of cycles. We further improve these algorithms to provide 1.x-optimality when the number of items is small. Simulation studies corroborate the effectiveness of our algorithms.Comment: To appear in R:SS 202

On Rearrangement of Items Stored in Stacks

There are $n \ge 2$ stacks, each filled with $d$ items, and one empty stack. Every stack has capacity $d > 0$. 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 $nd$ items are distinguishable and are initially randomly scattered in the $n$ stacks. The items must be rearranged using pop-and-pushs so that in the end, the $k^{\rm th}$ stack holds items $(k-1)d +1, \ldots, kd$, in that order, from the top to the bottom for all $1 \le k \le n$. In an {\em unlabeled} problem, the $nd$ items are of $n$ types of $d$ each. The goal is to rearrange items so that items of type $k$ are located in the $k^{\rm th}$ stack for all $1 \le k \le n$. 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 $n^2$ items stored in an $n \times n$ table using only $2n$ column and row permutations, and its generalization, and (2) an algorithm with a guaranteed upper bound of $O(nd)$ steps for solving both versions of the stack rearrangement problem when $d \le \lceil cn \rceil$ for arbitrary fixed positive number $c$. In terms of the required number of steps, the labeled and unlabeled version have lower bounds $\Omega(nd + nd{\frac{\log d}{\log n}})$ and $\Omega(nd)$, respectively