The Generalized Sliding-Tile Puzzle (GSTP), allowing many square tiles on a board to move in parallel while enforcing natural geometric collision constraints on the movement of neighboring tiles, provide a high-fidelity mathematical model for many high-utility existing and future multi-robot applications, e.g., at mobile robot-based warehouses or autonomous garages. Motivated by practical relevance, this work examines a further generalization of GSTP called the Colored Generalized Sliding-Tile Puzzle (CGSP), where tiles can now assume varying degrees of distinguishability, a common occurrence in the aforementioned applications. Our study establishes the computational complexity of CGSP and its key sub-problems under a broad spectrum of possible conditions and characterizes solution makespan lower and upper bounds that differ by at most a logarithmic factor. These results are further extended to higher-dimensional versions of the puzzle game.

Long-horizon task and motion planning (TAMP) is notoriously difficult to solve, let alone optimally, due to the tight coupling between the interleaved (discrete) task and (continuous) motion planning phases, where each phase on its own is frequently an NP-hard or even PSPACE-hard computational challenge. In this study, we tackle the even more challenging goal of jointly optimizing task and motion plans for a real dual-arm system in which the two arms operate in close vicinity to solve highly constrained tabletop multi-object rearrangement problems. Toward that, we construct a tightly integrated planning and control optimization pipeline, Makespan-Optimized Dual-Arm Planner (MODAP) that combines novel sampling techniques for task planning with state-of-the-art trajectory optimization techniques. Compared to previous state-of-the-art, MODAP produces task and motion plans that better coordinate a dual-arm system, delivering significantly improved execution time improvements while simultaneously ensuring that the resulting time-parameterized trajectory conforms to specified acceleration and jerk limits.

Multi-Robot Path Planning (MRPP) on graphs, equivalently known as Multi-Agent Path Finding (MAPF), is a well-established NP-hard problem with critically important applications. As serial computation in (near)-optimally solving MRPP approaches the computation efficiency limit, parallelization offers a promising route to push the limit further, especially in handling hard or large MRPP instances. In this study, we initiated a \emph{targeted} parallelization effort to boost the performance of conflict-based search for MRPP. Specifically, when instances are relatively small but robots are densely packed with strong interactions, we apply a decentralized parallel algorithm that concurrently explores multiple branches that leads to markedly enhanced solution discovery. On the other hand, when instances are large with sparse robot-robot interactions, we prioritize node expansion and conflict resolution. Our innovative multi-threaded approach to parallelizing bounded-suboptimal conflict search-based algorithms demonstrates significant improvements over baseline serial methods in success rate or runtime. Our contribution further pushes the understanding of MRPP and charts a promising path for elevating solution quality and computational efficiency through parallel algorithmic strategies.

In the $15$-puzzle game, $15$ labeled square tiles are reconfigured on a $4\times 4$ board through an escort, wherein each (time) step, a single tile neighboring it may slide into it, leaving the space previously occupied by the tile as the new escort. We study a generalized sliding-tile puzzle (GSTP) in which (1) there are $1+$ escorts and (2) multiple tiles can move synchronously in a single time step. Compared with popular discrete multi-agent/robot motion models, GSTP provides a more accurate model for a broad array of high-utility applications, including warehouse automation and autonomous garage parking, but is less studied due to the more involved tile interactions. In this work, we analyze optimal GSTP solution structures, establishing that computing makespan-optimal solutions for GSTP is NP-complete and developing polynomial time algorithms yielding makespans approximating the minimum with expected/high probability constant factors, assuming randomized start and goal configurations.

At modern warehouses, mobile robots transport packages and drop them into collection bins/chutes based on shipping destinations grouped by, e.g., the ZIP code. System throughput, measured as the number of packages sorted per unit of time, determines the efficiency of the warehouse. This research develops a scalable, high-throughput multi-robot parcel sorting solution, decomposing the task into two related processes, bin assignment and offline/online multi-robot path planning, and optimizing both. Bin assignment matches collection bins with package types to minimize traveling costs. Subsequently, robots are assigned to pick up and drop packages into assigned bins. Multiple highly effective bin assignment algorithms are proposed that can work with an arbitrary planning algorithm. We propose a decentralized path planning routine using only local information to route the robots over a carefully constructed directed road network for multi-robot path planning. Our decentralized planner, provably probabilistically deadlock-free, consistently delivers near-optimal results on par with some top-performing centralized planners while significantly reducing computation times by orders of magnitude. Extensive simulations show that our overall framework delivers promising performances.

In this paper, we explore the dynamic grasping of moving objects through active pose tracking and reinforcement learning for hand-eye coordination systems. Most existing vision-based robotic grasping methods implicitly assume target objects are stationary or moving predictably. Performing grasping of unpredictably moving objects presents a unique set of challenges. For example, a pre-computed robust grasp can become unreachable or unstable as the target object moves, and motion planning must also be adaptive. In this work, we present a new approach, Eye-on-hAnd Reinforcement Learner (EARL), for enabling coupled Eye-on-Hand (EoH) robotic manipulation systems to perform real-time active pose tracking and dynamic grasping of novel objects without explicit motion prediction. EARL readily addresses many thorny issues in automated hand-eye coordination, including fast-tracking of 6D object pose from vision, learning control policy for a robotic arm to track a moving object while keeping the object in the camera's field of view, and performing dynamic grasping. We demonstrate the effectiveness of our approach in extensive experiments validated on multiple commercial robotic arms in both simulations and complex real-world tasks.

In practice, many types of manipulation actions (e.g., pick-n-place and push) are needed to accomplish real-world manipulation tasks. Yet, limited research exists that explores the synergistic integration of different manipulation actions for optimally solving long-horizon task-and-motion planning problems. In this study, we propose and investigate planning high-quality action sequences for solving long-horizon tabletop rearrangement tasks in which multiple manipulation primitives are required. Denoting the problem rearrangement with multiple manipulation primitives (REMP), we develop two algorithms, hierarchical best-first search (HBFS) and parallel Monte Carlo tree search for multi-primitive rearrangement (PMMR) toward optimally resolving the challenge. Extensive simulation and real robot experiments demonstrate that both methods effectively tackle REMP, with HBFS excelling in planning speed and PMMR producing human-like, high-quality solutions with a nearly 100% success rate.

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/

Object rearrangement is a fundamental sub-task in accomplishing a great many physical tasks. As such, effectively executing rearrangement is an important skill for intelligent robots to master. In this study, we conduct the first algorithmic study on optimally solving the problem of Multi-layer Object Rearrangement on a Tabletop (MORT), in which one object may be relocated at a time, and an object can only be moved if other objects do not block its top surface. In addition, any intermediate structure during the reconfiguration process must be physically stable, i.e., it should stand without external support. To tackle the dual challenges of untangling the dependencies between objects and ensuring structural stability, we develop an algorithm that interleaves the computation of the optimal rearrangement plan and structural stability checking. Using a carefully constructed integer linear programming (ILP) model, our algorithm, Stability-aware Integer Programming-based Planner (SIPP), readily scales to optimally solve complex rearrangement problems of 3D structures with over 60 building blocks, with solution quality significantly outperforming natural greedy best-first approaches. Upon the publication of the manuscript, source code and data will be available at https://github.com/arc-l/mort/

Effectively rearranging heterogeneous objects constitutes a high-utility skill that an intelligent robot should master. Whereas significant work has been devoted to the grasp synthesis of heterogeneous objects, little attention has been given to the planning for sequentially manipulating such objects. In this work, we examine the long-horizon sequential rearrangement of heterogeneous objects in a tabletop setting, addressing not just generating feasible plans but near-optimal ones. Toward that end, and building on previous methods, including combinatorial algorithms and Monte Carlo tree search-based solutions, we develop state-of-the-art solvers for optimizing two practical objective functions considering key object properties such as size and weight. Thorough simulation studies show that our methods provide significant advantages in handling challenging heterogeneous object rearrangement problems, especially in cluttered settings. Real robot experiments further demonstrate and confirm these advantages. Source code and evaluation data associated with this research will be available at https://github.com/arc-l/TRLB upon the publication of this manuscript.