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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., Comment: WAFR 2024 Conference Version

Shortest-path roadmaps, also known as reduced visibility graphs, provides a highly efficient multi-query method for computing optimal paths in two-dimensional environments. Combined with Minkowski sum computations, shortest-path roadmaps can compute optimal paths for a translating robot in 2D. In this study, we explore the intuitive idea of stacking up a set of reduced visibility graphs at different orientations for a polygonal holonomic robot to support the fast computation of near-optimal paths, allowing simultaneous 2D translation and rotation. The resulting algorithm, rotation-stacked visibility graph (RVG), is shown to be resolution-complete and asymptotically optimal. Extensive computational experiments show RVG significantly outperforms state-of-the-art single- and multi-query sampling-based methods on both computation time and solution optimality fronts.

Multi-Agent Path Finding (MAPF) is NP-hard to solve optimally, even on graphs, suggesting no polynomial-time algorithms can compute exact optimal solutions for them. This raises a natural question: How optimal can polynomial-time algorithms reach? Whereas algorithms for computing constant-factor optimal solutions have been developed, the constant factor is generally very large, limiting their application potential. In this work, among other breakthroughs, we propose the first low-polynomial-time MAPF algorithms delivering $1$-$1.5$ (resp., $1$-$1.67$) asymptotic makespan optimality guarantees for 2D (resp., 3D) grids for random instances at a very high $1/3$ agent density, with high probability. Moreover, when regularly distributed obstacles are introduced, our methods experience no performance degradation. These methods generalize to support $100\%$ agent density. Regardless of the dimensionality and density, our high-quality methods are enabled by a unique hierarchical integration of two key building blocks. At the higher level, we apply the labeled Grid Rearrangement Algorithm (RTA), capable of performing efficient reconfiguration on grids through row/column shuffles. At the lower level, we devise novel methods that efficiently simulate row/column shuffles returned by RTA. Our implementations of RTA-based algorithms are highly effective in extensive numerical evaluations, demonstrating excellent scalability compared to other SOTA methods. For example, in 3D settings, \rta-based algorithms readily scale to grids with over $370,000$ vertices and over $120,000$ agents and consistently achieve conservative makespan optimality approaching $1.5$, as predicted by our theoretical analysis., Comment: arXiv admin note: substantial text overlap with arXiv:2201.08976

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., Comment: First three authors made equal contributions to this study

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., Comment: Submitted to IROS

Parking lots and autonomous warehouses for accommodating many vehicles/robots adopt designs in which the underlying graphs are \emph{well-connected} to simplify planning and reduce congestion. In this study, we formulate and delve into the \emph{largest well-connected set} (LWCS) problem and explore its applications in layout design for multi-robot path planning. Roughly speaking, a well-connected set over a connected graph is a set of vertices such that there is a path on the graph connecting any pair of vertices in the set without passing through any additional vertices of the set. Identifying an LWCS has many potential high-utility applications, e.g., for determining parking garage layout and capacity, as prioritized planning can be shown to be complete when start/goal configurations belong to an LWCS. In this work, we establish that computing an LWCS is NP-complete. We further develop optimal and near-optimal LWCS algorithms, with the near-optimal algorithm targeting large maps. A complete prioritized planning method is given for planning paths for multiple robots residing on an LWCS., Comment: ICRA 2024

Path planning for multiple non-holonomic robots in continuous domains constitutes a difficult robotics challenge with many applications. Despite significant recent progress on the topic, computationally efficient and high-quality solutions are lacking, especially in lifelong settings where robots must continuously take on new tasks. In this work, we make it possible to extend key ideas enabling state-of-the-art (SOTA) methods for multi-robot planning in discrete domains to the motion planning of multiple Ackerman (car-like) robots in lifelong settings, yielding high-performance centralized and decentralized planners. Our planners compute trajectories that allow the robots to reach precise $SE(2)$ goal poses. The effectiveness of our methods is thoroughly evaluated and confirmed using both simulation and real-world experiments., Comment: ICRA 2024

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., Comment: To appear in AAAI 2024

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., Comment: Presented on IROS 2023 Corresponding author Siddarth Jain

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., Comment: In review

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 2025

Optimal Multi-Robot Path Planning (MRPP) has garnered significant attention due to its many applications in domains including warehouse automation, transportation, and swarm robotics. Current MRPP solvers can be divided into reduction-based, search-based, and rule-based categories, each with their strengths and limitations. Regardless of the methodology, however, the issue of handling dense MRPP instances remains a significant challenge, where existing approaches generally demonstrate a dichotomy regarding solution optimality and efficiency. This study seeks to bridge the gap in optimal MRPP resolution for dense, highly-entangled scenarios, with potential applications to high-density storage systems and traffic congestion control. Toward that goal, we analyze the behaviors of SOTA MRPP algorithms in dense settings and develop two hybrid algorithms leveraging the strengths of existing SOTA algorithms: DCBS (database-accelerated enhanced conflict-based search) and SCBS (sparsified enhanced conflict-based search). Experimental validations demonstrate that DCBS and SCBS deliver a significant reduction in computational time compared to existing bounded-suboptimal methods and improve solution quality compared to existing rule-based methods, achieving a desirable balance between computational efficiency and solution optimality. As a result, DCBS and SCBS are particularly suitable for quickly computing good-quality solutions for multi-robot routing in dense settings

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/, Comment: Accepted by 2023 IROS - IEEE/RSJ International Conference on Intelligent Robots

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., Comment: Accepted by 2023 IROS - IEEE/RSJ International Conference on Intelligent Robots

For rearranging objects on tabletops with overhand grasps, temporarily relocating objects to some buffer space may be necessary. This raises the natural question of how many simultaneous storage spaces, or "running buffers", are required so that certain classes of tabletop rearrangement problems are feasible. In this work, we examine the problem for both labeled and unlabeled settings. On the structural side, we observe that finding the minimum number of running buffers (MRB) can be carried out on a dependency graph abstracted from a problem instance, and show that computing MRB is NP-hard. We then prove that under both labeled and unlabeled settings, even for uniform cylindrical objects, the number of required running buffers may grow unbounded as the number of objects to be rearranged increases. We further show that the bound for the unlabeled case is tight. On the algorithmic side, we develop effective exact algorithms for finding MRB for both labeled and unlabeled tabletop rearrangement problems, scalable to over a hundred objects under very high object density. More importantly, our algorithms also compute a sequence witnessing the computed MRB that can be used for solving object rearrangement tasks. Employing these algorithms, empirical evaluations reveal that random labeled and unlabeled instances, which more closely mimics real-world setups, generally have fairly small MRBs. Using real robot experiments, we demonstrate that the running buffer abstraction leads to state-of-the-art solutions for in-place rearrangement of many objects in tight, bounded workspace., Comment: Accepted by The International Journal of Robotics Research (IJRR). arXiv admin note: substantial text overlap with arXiv:2105.06357

This paper studies the problem of defending (1D and 2D) boundaries against a large number of continuous attacks with a heterogeneous group of defenders. The defender team has perfect information of the attack events within some time (finite or infinite) horizon, with the goal of intercepting as many attacks as possible. An attack is considered successfully intercepted if a defender is present at the boundary location when and where the attack happens. Through proposing a network-flow and integer programming-based method for computing optimal solutions, and an exhaustive defender pairing heuristic method for computing near-optimal solutions, we are able to significantly reduce the computation burden in solving the problem in comparison to the previous state of the art. Extensive simulation experiments confirm the effectiveness of the algorithms. Leveraging our efficient methods, we also characterize the solution structures, revealing the relationships between the attack interception rate and the various problem parameters, e.g., the heterogeneity of the defenders, attack rate, boundary topology, and the look-ahead horizon.

We study the problem of allocating many mobile robots for the execution of a pre-defined sweep schedule in a known two-dimensional environment, with applications toward search and rescue, coverage, surveillance, monitoring, pursuit-evasion, and so on. The mobile robots (or agents) are assumed to have one-dimensional sensing capability with probabilistic guarantees that deteriorate as the sensing distance increases. In solving such tasks, a time-parameterized distribution of robots along the sweep frontier must be computed, with the objective to minimize the number of robots used to achieve some desired coverage quality guarantee or to maximize the probabilistic guarantee for a given number of robots. We propose a max-flow based algorithm for solving the allocation task, which builds on a decomposition technique of the workspace as a generalization of the well-known boustrophedon decomposition. Our proposed algorithm has a very low polynomial running time and completes in under two seconds for polygonal environments with over $10^5$ vertices. Simulation experiments are carried out on three realistic use cases with randomly generated obstacles of varying shapes, sizes, and spatial distributions, which demonstrate the applicability and scalability our proposed method., Comment: ICRA 2023

Parking in large metropolitan areas is often a time-consuming task with further implications toward traffic patterns that affect urban landscaping. Reducing the premium space needed for parking has led to the development of automated mechanical parking systems. Compared to regular garages having one or two rows of vehicles in each island, automated garages can have multiple rows of vehicles stacked together to support higher parking demands. Although this multi-row layout reduces parking space, it makes the parking and retrieval more complicated. In this work, we propose an automated garage design that supports near 100% parking density. Modeling the problem of parking and retrieving multiple vehicles as a special class of multi-robot path planning problem, we propose associated algorithms for handling all common operations of the automated garage, including (1) optimal algorithm and near-optimal methods that find feasible and efficient solutions for simultaneous parking/retrieval and (2) a novel shuffling mechanism to rearrange vehicles to facilitate scheduled retrieval at rush hours. We conduct thorough simulation studies showing the proposed methods are promising for large and high-density real-world parking applications., Comment: Accepted by ICRA 2023

Performing object retrieval in real-world workspaces must tackle challenges including \emph{uncertainty} and \emph{clutter}. One option is to apply prehensile operations, which can be time consuming in highly-cluttered scenarios. On the other hand, non-prehensile actions, such as pushing simultaneously multiple objects, can help to quickly clear a cluttered workspace and retrieve a target object. Such actions, however, can also lead to increased uncertainty as it is difficult to estimate the outcome of pushing operations. The proposed framework in this work integrates topological tools and Monte-Carlo Tree Search (MCTS) to achieve effective and robust pushing for object retrieval. It employs persistent homology to automatically identify manageable clusters of blocking objects without the need for manually adjusting hyper-parameters. Then, MCTS uses this information to explore feasible actions to push groups of objects, aiming to minimize the number of operations needed to clear the path to the target. Real-world experiments using a Baxter robot, which involves some noise in actuation, show that the proposed framework achieves a higher success rate in solving retrieval tasks in dense clutter than alternatives. Moreover, it produces solutions with few pushing actions improving the overall execution time. More critically, it is robust enough that it allows one to plan the sequence of actions offline and then execute them reliably on a Baxter robot.

We investigate the utility of employing multiple buffers in solving a class of rearrangement problems with pick-n-swap manipulation primitives. In this problem, objects stored randomly in a lattice are to be sorted using a robot arm with k>=1 swap spaces or buffers, capable of holding up to k objects on its end-effector simultaneously. On the structural side, we show that the addition of each new buffer brings diminishing returns in saving the end-effector travel distance while holding the total number of pick-n-swap operations at the minimum. This is due to an interesting recursive cycle structure in random m-permutation, where the largest cycle covers over 60% of objects. On the algorithmic side, we propose fast algorithms for 1D and 2D lattice rearrangement problems that can effectively use multiple buffers to boost solution optimality. Numerical experiments demonstrate the efficiency and scalability of our methods, as well as confirm the diminishing return structure as more buffers are employed., Comment: To present in 2023 IEEE International Conference on Robotics and Automation(ICRA 2023)

Neural network (NN)-based methods have emerged as an attractive approach for robot motion planning due to strong learning capabilities of NN models and their inherently high parallelism. Despite the current development in this direction, the efficient capture and processing of important sequential and spatial information, in a direct and simultaneous way, is still relatively under-explored. To overcome the challenge and unlock the potentials of neural networks for motion planning tasks, in this paper, we propose STP-Net, an end-to-end learning framework that can fully extract and leverage important spatio-temporal information to form an efficient neural motion planner. By interpreting the movement of the robot as a video clip, robot motion planning is transformed to a video prediction task that can be performed by STP-Net in both spatially and temporally efficient ways. Empirical evaluations across different seen and unseen environments show that, with nearly 100% accuracy (aka, success rate), STP-Net demonstrates very promising performance with respect to both planning speed and path cost. Compared with existing NN-based motion planners, STP-Net achieves at least 5x, 2.6x and 1.8x faster speed with lower path cost on 2D Random Forest, 2D Maze and 3D Random Forest environments, respectively. Furthermore, STP-Net can quickly and simultaneously compute multiple near-optimal paths in multi-robot motion planning tasks, Comment: Accepted in IROS 2022

We investigate the problem of coordinating two robot arms to solve non-monotone tabletop multi-object rearrangement tasks. In a non-monotone rearrangement task, complex object-object dependencies exist that require moving some objects multiple times to solve an instance. In working with two arms in a large workspace, some objects must be handed off between the robots, which further complicates the planning process. For the challenging dual-arm tabletop rearrangement problem, we develop effective task planning algorithms for scheduling the pick-n-place sequence that can be properly distributed between the two arms. We show that, even without using a sophisticated motion planner, our method achieves significant time savings in comparison to greedy approaches and naive parallelization of single-robot plans., Comment: Accepted by IROS 2022

We propose a novel Parallel Monte Carlo tree search with Batched Simulations (PMBS) algorithm for accelerating long-horizon, episodic robotic planning tasks. Monte Carlo tree search (MCTS) is an effective heuristic search algorithm for solving episodic decision-making problems whose underlying search spaces are expansive. Leveraging a GPU-based large-scale simulator, PMBS introduces massive parallelism into MCTS for solving planning tasks through the batched execution of a large number of concurrent simulations, which allows for more efficient and accurate evaluations of the expected cost-to-go over large action spaces. When applied to the challenging manipulation tasks of object retrieval from clutter, PMBS achieves a speedup of over $30\times$ with an improved solution quality, in comparison to a serial MCTS implementation. We show that PMBS can be directly applied to real robot hardware with negligible sim-to-real differences. Supplementary material, including video, can be found at https://github.com/arc-l/pmbs., Comment: Accepted for IROS 2022

For enabling efficient, large-scale coordination of unmanned aerial vehicles (UAVs) under the labeled setting, in this work, we develop the first polynomial time algorithm for the reconfiguration of many moving bodies in three-dimensional spaces, with provable $1.x$ asymptotic makespan optimality guarantee under high robot density. More precisely, on an $m_1\times m_2 \times m_3$ grid, $m_1\ge m_2\ge m_3$, our method computes solutions for routing up to $\frac{m_1m_2m_3}{3}$ uniquely labeled robots with uniformly randomly distributed start and goal configurations within a makespan of $m_1 + 2m_2 +2m_3+o(m_1)$, with high probability. Because the makespan lower bound for such instances is $m_1 + m_2+m_3 - o(m_1)$, also with high probability, as $m_1 \to \infty$, $\frac{m_1+2m_2+2m_3}{m_1+m_2+m_3}$ optimality guarantee is achieved. $\frac{m_1+2m_2+2m_3}{m_1+m_2+m_3} \in (1, \frac{5}{3}]$, yielding $1.x$ optimality. In contrast, it is well-known that multi-robot path planning is NP-hard to optimally solve. In numerical evaluations, our method readily scales to support the motion planning of over $100,000$ robots in 3D while simultaneously achieving $1.x$ optimality. We demonstrate the application of our method in coordinating many quadcopters in both simulation and hardware experiments., Comment: Accepted by IROS2022. arXiv admin note: text overlap with arXiv:2201.08976

Object rearrangement is important for many applications but remains challenging, especially in confined spaces, such as shelves, where objects cannot be accessed from above and they block reachability to each other. Such constraints require many motion planning and collision checking calls, which are computationally expensive. In addition, the arrangement space grows exponentially with the number of objects. To address these issues, this work introduces a lazy evaluation framework with a local monotone solver and a global planner. Monotone instances are those that can be solved by moving each object at most once. A key insight is that reachability constraints at the grasps for objects' starts and goals can quickly reveal dependencies between objects without having to execute expensive motion planning queries. Given that, the local solver builds lazily a search tree that respects these reachability constraints without verifying that the arm paths are collision free. It only collision checks when a promising solution is found. If a monotone solution is not found, the non-monotone planner loads the lazy search tree and explores ways to move objects to intermediate locations from where monotone solutions to the goal can be found. Results show that the proposed framework can solve difficult instances in confined spaces with up to 16 objects, which state-of-the-art methods fail to solve. It also solves problems faster than alternatives, when the alternatives find a solution. It also achieves high-quality solutions, i.e., only 1.8 additional actions on average are needed for non-monotone instances., Comment: Accepted to the 32nd International Conference on Automated Planning and Scheduling (ICAPS 2022)

This work explores the use of topological tools for achieving effective non-prehensile manipulation in cluttered, constrained workspaces. In particular, it proposes the use of persistent homology as a guiding principle in identifying the appropriate non-prehensile actions, such as pushing, to clean a cluttered space with a robotic arm so as to allow the retrieval of a target object. Persistent homology enables the automatic identification of connected components of blocking objects in the space without the need for manual input or tuning of parameters. The proposed algorithm uses this information to push groups of cylindrical objects together and aims to minimize the number of pushing actions needed to reach to the target. Simulated experiments in a physics engine using a model of the Baxter robot show that the proposed topology-driven solution is achieving significantly higher success rate in solving such constrained problems relatively to state-of-the-art alternatives from the literature. It manages to keep the number of pushing actions low, is computationally efficient and the resulting decisions and motion appear natural for effectively solving such tasks.

In this study, working with the task of object retrieval in clutter, we have developed a robot learning framework in which Monte Carlo Tree Search (MCTS) is first applied to enable a Deep Neural Network (DNN) to learn the intricate interactions between a robot arm and a complex scene containing many objects, allowing the DNN to partially clone the behavior of MCTS. In turn, the trained DNN is integrated into MCTS to help guide its search effort. We call this approach learning-guided Monte Carlo tree search for Object REtrieval (MORE), which delivers significant computational efficiency gains and added solution optimality. MORE is a self-supervised robotics framework/pipeline capable of working in the real world that successfully embodies the System 2 to System 1 learning philosophy proposed by Kahneman, where learned knowledge, used properly, can help greatly speed up a time-consuming decision process over time. Videos and supplementary material can be found at https://github.com/arc-l/more, Comment: Accepted by ICRA 2022

In this study, we explore the application of game theory, in particular Stackelberg games, to address the issue of effective coordination strategy generation for heterogeneous robots with one-way communication. To that end, focusing on the task of multi-object rearrangement, we develop a theoretical and algorithmic framework that provides strategic guidance for a pair of robot arms, a leader and a follower where the leader has a model of the follower's decision-making process, through the computation of a feedback Stackelberg equilibrium. With built-in tolerance of model uncertainty, the strategic guidance generated by our planning algorithm not only improves the overall efficiency in solving the rearrangement tasks, but is also robust to common pitfalls in collaboration, e.g., chattering.

Given a set of terminals in 2D/3D, the network with the shortest total length that connects all terminals is a Steiner tree. On the other hand, with enough budget, every terminal can be connected to every other terminals via a straight edge, yielding a complete graph over all terminals. In this work, we study a generalization of Steiner trees asking what happens in between these two extremes. Focusing on three terminals with equal pairwise path weights, we characterize the full evolutionary pathway between the Steiner tree and the complete graph, which contains intriguing intermediate structures.

Graph-based multi-robot path planning (MRPP) is NP-hard to optimally solve. In this work, we propose the first low polynomial-time algorithm for MRPP achieving 1--1.5 asymptotic optimality guarantees on makespan for random instances under very high robot density, with high probability. The dual guarantee on computational efficiency and solution optimality suggests our proposed general method is promising in significantly scaling up multi-robot applications for logistics, e.g., at large robotic warehouses. Specifically, on an $m_1\times m_2$ gird, $m_1 \ge m_2$, our RTH (Rubik Table with Highways) algorithm computes solutions for routing up to $\frac{m_1m_2}{3}$ robots with uniformly randomly distributed start and goal configurations with a makespan of $m_1 + 2m_2 + o(m_1)$, with high probability. Because the minimum makespan for such instances is $m_1 + m_2 - o(m_1)$, also with high probability, RTH guarantees $\frac{m_1+2m_2}{m_1+m_2}$ optimality as $m_1 \to \infty$ for random instances with up to $\frac{1}{3}$ robot density, with high probability. $\frac{m_1+2m_2}{m_1+m_2} \in (1, 1.5]$. Alongside this key result, we also establish a series of related results supporting even higher robot densities and environments with regularly distributed obstacles, which directly map to real-world parcel sorting scenarios. Building on the baseline methods with provable guarantees, we have developed effective, principled heuristics that further improve the computed optimality of the RTH algorithms. In extensive numerical evaluations, RTH and its variants demonstrate exceptional scalability as compared with methods including ECBS and DDM, scaling to over $450 \times 300$ grids with $45,000$ robots, and consistently achieves makespan around $1.5$ optimal or better, as predicted by our theoretical analysis.

In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The problem models the optimal placement of line sensors (e.g., infrared laser beams) for isolating many types of regions in a pair-wise manner for practical purposes (e.g., guarding against intrusions). The problem is NP-hard even if we want to find the minimum number of lines to separate two sets of points in the plane. Under the umbrella problem of barrier forming with minimum number of line segments, three settings are examined: barrier forming for point sets, point sets with polygonal obstacles, polygonal sets with polygonal obstacles. We describe methods for computing the optimal solution for the first two settings with the assistance of mathematical programming, and provide a 2-OPT solution for the third. We demonstrate the effectiveness of our methods through extensive simulations., Comment: Accepted to ICRA 2022

In this paper, we examine the problem of rearranging many objects on a tabletop in a cluttered setting using overhand grasps. Efficient solutions for the problem, which capture a common task that we solve on a daily basis, are essential in enabling truly intelligent robotic manipulation. In a given instance, objects may need to be placed at temporary positions ("buffers") to complete the rearrangement, but allocating these buffer locations can be highly challenging in a cluttered environment. To tackle the challenge, a two-step baseline planner is first developed, which generates a primitive plan based on inherent combinatorial constraints induced by start and goal poses of the objects and then selects buffer locations assisted by the primitive plan. We then employ the "lazy" planner in a tree search framework which is further sped up by adapting a novel preprocessing routine. Simulation experiments show our methods can quickly generate high-quality solutions and are more robust in solving large-scale instances than existing state-of-the-art approaches. source:github.com/arc-l/TRLB, Comment: Summitted to 2022 IEEE International Conference on Robotics and Automation(ICRA 2022)

We perform a systematic exploration of the principle of Space Utilization Optimization (SUO) as a heuristic for planning better individual paths in a decoupled multi-robot path planner, with applications to both one-shot and life-long multi-robot path planning problems. We show that the decentralized heuristic set, SU-I, preserves single path optimality and significantly reduces congestion that naturally happens when many paths are planned without coordination. Integration of SU-I into complete planners brings dramatic reductions in computation time due to the significantly reduced number of conflicts and leads to sizable solution optimality gains in diverse evaluation scenarios with medium and large maps, for both one-shot and life-long problem settings., Comment: Submitting to ICRA 2022

We investigate the capacitated vehicle routing problem (CVRP) under a robotics context, where a vehicle with limited payload must complete delivery (or pickup) tasks to serve a set of geographically distributed customers with varying demands. In classical CVRP, a customer location is modeled as a point. In many robotics applications, however, it is more appropriate to model such "customer locations" as 2D regions. For example, in aerial delivery, a drone may drop a package anywhere in a customer's lot. This yields the problem of CVRG (Capacitated Vehicle Routing with Target Geometric Constraints). Computationally, CVRP is already strongly NP-hard; CVRG is therefore more challenging. Nevertheless, we develop fast algorithms for CVRG, capable of computing high quality solutions for hundreds of regions. Our algorithmic solution is guaranteed to be optimal when customer regions are convex. Numerical evaluations show that our proposed methods significantly outperform greedy best-first approaches. Comprehensive simulation studies confirm the effectiveness of our methods., Comment: To appear in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2021)

For tabletop rearrangement problems with overhand grasps, storage space outside the tabletop workspace, or buffers, can temporarily hold objects which greatly facilitates the resolution of a given rearrangement task. This brings forth the natural question of how many running buffers are required so that certain classes of tabletop rearrangement problems are feasible. In this work, we examine the problem for both the labeled (where each object has a specific goal pose) and the unlabeled (where goal poses of objects are interchangeable) settings. On the structural side, we observe that finding the minimum number of running buffers (MRB) can be carried out on a dependency graph abstracted from a problem instance, and show that computing MRB on dependency graphs is NP-hard. We then prove that under both labeled and unlabeled settings, even for uniform cylindrical objects, the number of required running buffers may grow unbounded as the number of objects to be rearranged increases; we further show that the bound for the unlabeled case is tight. On the algorithmic side, we develop highly effective algorithms for finding MRB for both labeled and unlabeled tabletop rearrangement problems, scalable to over a hundred objects under very high object density. Employing these algorithms, empirical evaluations show that random labeled and unlabeled instances, which more closely mimics real-world setups, have much smaller MRBs., Comment: 1. Add a complete version of proof for the upper bound; 2. Add a complete version of MIP model

We 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 become computationally intractable to optimally solve. Despite their NP-hardness, we prove that efficient cycle-following-based algorithms remain optimal in the asymptotic sense 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. The implementation of the algorithms from the paper can be found at github.com/arc-l/lattice-rearrangement., Comment: Pre-print of the extended and accepted IJRR manuscript

This paper considers the problem of retrieving an object from many tightly packed objects using a combination of robotic pushing and grasping actions. Object retrieval in dense clutter is an important skill for robots to operate in households and everyday environments effectively. The proposed solution, Visual Foresight Trees (VFT), intelligently rearranges the clutter surrounding a target object so that it can be grasped easily. Rearrangement with nested nonprehensile actions is challenging as it requires predicting complex object interactions in a combinatorially large configuration space of multiple objects. We first show that a deep neural network can be trained to accurately predict the poses of the packed objects when the robot pushes one of them. The predictive network provides visual foresight and is used in a tree search as a state transition function in the space of scene images. The tree search returns a sequence of consecutive push actions yielding the best arrangement of the clutter for grasping the target object. Experiments in simulation and using a real robot and objects show that the proposed approach outperforms model-free techniques as well as model-based myopic methods both in terms of success rates and the number of executed actions, on several challenging tasks. A video introducing VFT, with robot experiments, is accessible at https://youtu.be/7cL-hmgvyec. The full source code is available at https://github.com/arc-l/vft., Comment: Accepted by RA-L

In this work, we systematically examine the application of spatio-temporal splitting heuristics to the Multi-Robot Motion Planning (MRMP) problem in a graph-theoretic setting: a problem known to be NP-hard to optimally solve. Following the divide-and-conquer principle, we design multiple spatial and temporal splitting schemes that can be applied to any existing MRMP algorithm, including integer programming solvers and Enhanced Conflict Based Search, in an orthogonal manner. The combination of a good baseline MRMP algorithm with a proper splitting heuristic proves highly effective, allowing the resolution of problems 10+ times than what is possible previously, as corroborated by extensive numerical evaluations. Notably, spatial partition of problem fusing with the temporal splitting heuristic and the enhanced conflict based search (ECBS) algorithm increases the scalability of ECBS on large and challenging DAO maps by 5--15 folds with negligible impact on solution optimality., Comment: Accepted by ICRA 2021

We carry out a structural and algorithmic study of a mobile sensor coverage optimization problem targeting 2D surfaces embedded in a 3D workspace. The investigated settings model multiple important applications including camera network deployment for surveillance, geological monitoring/survey of 3D terrains, and UVC-based surface disinfection for the prevention of the spread of disease agents (e.g., SARS-CoV-2). Under a unified general "sensor coverage" problem, three concrete formulations are examined, focusing on optimizing visibility, single-best coverage quality, and cumulative quality, respectively. After demonstrating the computational intractability of all these formulations, we describe approximation schemes and mathematical programming models for near-optimally solving them. The effectiveness of our methods is thoroughly evaluated under realistic and practical scenarios.

Object rearrangement is a widely-applicable and challenging task for robots. Geometric constraints must be carefully examined to avoid collisions and combinatorial issues arise as the number of objects increases. This work studies the algorithmic structure of rearranging uniform objects, where robot-object collisions do not occur but object-object collisions have to be avoided. The objective is minimizing the number of object transfers under the assumption that the robot can manipulate one object at a time. An efficiently computable decomposition of the configuration space is used to create a "region graph", which classifies all continuous paths of equivalent collision possibilities. Based on this compact but rich representation, a complete dynamic programming primitive DFSDP performs a recursive depth first search to solve monotone problems quickly, i.e., those instances that do not require objects to be moved first to an intermediate buffer. DFSDP is extended to solve single-buffer, non-monotone instances, given a choice of an object and a buffer. This work utilizes these primitives as local planners in an informed search framework for more general, non-monotone instances. The search utilizes partial solutions from the primitives to identify the most promising choice of objects and buffers. Experiments demonstrate that the proposed solution returns near-optimal paths with higher success rate, even for challenging non-monotone instances, than other leading alternatives., Comment: Accepted to IEEE International Conference on Robotics and Automation (ICRA 2021)

We propose a Deep Interaction Prediction Network (DIPN) for learning to predict complex interactions that ensue as a robot end-effector pushes multiple objects, whose physical properties, including size, shape, mass, and friction coefficients may be unknown a priori. DIPN "imagines" the effect of a push action and generates an accurate synthetic image of the predicted outcome. DIPN is shown to be sample efficient when trained in simulation or with a real robotic system. The high accuracy of DIPN allows direct integration with a grasp network, yielding a robotic manipulation system capable of executing challenging clutter removal tasks while being trained in a fully self-supervised manner. The overall network demonstrates intelligent behavior in selecting proper actions between push and grasp for completing clutter removal tasks and significantly outperforms the previous state-of-the-art. Remarkably, DIPN achieves even better performance on the real robotic hardware system than in simulation. Videos, code, and experiments log are available at https://github.com/rutgers-arc-lab/dipn., Comment: ICRA 2021

We investigate the task and motion planning problem of clearing clutter from a workspace with limited ingress/egress access for multiple robots. We call the problem multi-robot clutter removal (MRCR). Targeting practical applications where motion planning is non-trivial but is not a bottleneck, we focus on finding high-quality solutions for feasible MRCR instances, which depends on the ability to efficiently compute high-quality object removal sequences. Despite the challenging multi-robot setting, our proposed search algorithms based on A*, dynamic programming, and best-first heuristics all produce solutions for tens of objects that significantly outperform single robot solutions. Realistic simulations with multiple Kuka youBots further confirms the effectiveness of our algorithmic solutions. In contrast, we also show that deciding the optimal object removal sequence for MRCR is computationally intractable.

We investigate the problem of using mobile robots equipped with 2D range sensors to optimally guard perimeters or regions, i.e., 1D or 2D sets. Given such a set of arbitrary shape to be guarded, and $k$ mobile sensors where the $i$-th sensor can guard a circular region with a variable radius $r_i$, we seek the optimal strategy to deploy the $k$ sensors to fully cover the set such that $\max r_i$ is minimized. On the side of computational complexity, we show that computing a $1.152$-optimal solution for guarding a perimeter or a region is NP-hard, i.e., the problem is hard to approximate. The hardness result on perimeter guarding holds when each sensor may guard at most two disjoint perimeter segments. On the side of computational methods, for the guarding perimeters, we develop a fully polynomial time approximation scheme (FPTAS) for the special setting where each sensor may only guard a single continuous perimeter segment, suggesting that the aforementioned hard-to-approximate result on the two-disjoint-segment sensing model is tight. For the general problem, we first describe a polynomial-time (2+$\epsilon)$-approximation algorithm as an upper bound, applicable to both perimeter guarding and region guarding. This is followed by a high-performance integer linear programming (ILP) based method that computes near-optimal solutions. Thorough computational benchmarks as well as evaluation on potential application scenarios demonstrate the effectiveness of these algorithmic solutions.

A great number of robotics applications demand the rearrangement of many mobile objects, e.g., organizing products on shelves, shuffling containers at shipping ports, reconfiguring fleets of mobile robots, and so on. To boost the throughput in systems designed for solving these rearrangement problems, it is essential to minimize the number of atomic operations, e.g., the pick-n-places of individual objects. However, this optimization task poses a rather difficult challenge due to complex inter-dependency between objects, especially in high-density settings. In tackling the aforementioned challenges, we develop a novel algorithmic tool, Rubik Tables, that provides a clean abstraction of object rearrangement problems as the proxy problem of shuffling items stored in a table or lattice. In its basic form, a Rubik Table is an $n\times n$ table containing $n^2$ items. We show that the reconfiguration of items in such a Rubik Table can be achieved using at most $2n$ column/row shuffles in the partially labeled setting, where each column (resp., row) shuffle may arbitrarily permute the items stored in a column (resp., row) of the table. When items are fully distinguishable, additional $n$ shuffles are needed. Rubik Tables allow many generalizations, e.g., to higher dimensions. Using Rubik Table, we have designed a first constant-factor optimal algorithm for stack rearrangement problems. We show that, for $nd$ items stored in $n$ stacks of depth $d$ each, using one empty stack as the swap space, $O(nd)$ stack pop-push operations are sufficient for an arbitrary reconfiguration of the stacks where $d \le n^{\frac{m}{2}}$ for arbitrary fixed $m >0$. Rubik Table results also allow the development of constant-factor optimal solutions for solving multi-robot motion planning problems under extreme robot density. These algorithms based on Rubik Table results run in low-polynomial time., Comment: Pre-print of extended manuscript accepted by IJRR in 2022

Robotic pick-and-place (PnP) operations on moving conveyors find a wide range of industrial applications. In practice, simple greedy heuristics (e.g., prioritization based on the time to process a single object) are applied that achieve reasonable efficiency. We show analytically that, under a simplified telescoping robot model, these greedy approaches do not ensure time optimality of PnP operations. To address the shortcomings of classical solutions, we develop algorithms that compute optimal object picking sequences for a predetermined finite horizon. Employing dynamic programming techniques and additional heuristics, our methods scale to up to tens to hundreds of objects. In particular, the fast algorithms we develop come with running time guarantees, making them suitable for real-time PnP applications demanding high throughput. Extensive evaluation of our algorithmic solution over dominant industrial PnP robots used in real-world applications, i.e., Delta robots and Selective Compliance Assembly Robot Arm (SCARA) robots, shows that a typical efficiency gain of around 10-40% over greedy approaches can be realized.