Optimally Solving Colored Generalized Sliding-Tile Puzzles: Complexity and Bounds

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.

Asymptotically-Optimal Multi-Query Path Planning for Moving A Convex Polygon in 2D

The classical shortest-path roadmaps, also known as reduced visibility graphs, provide a multi-query method for quickly 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 convex-shaped 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. RVG out-performs SOTA single-query sampling-based methods including BIT* and AIT* on both computation time and solution optimality fronts.

Expected $1.x$-Makespan-Optimal MAPF on Grids in Low-Poly Time

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.

Toward Holistic Planning and Control Optimization for Dual-Arm Rearrangement

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.

Targeted Parallelization of Conflict-Based Search for Multi-Robot Path Planning

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.

Well-Connected Set and Its Application to Multi-Robot Path Planning

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.

Decentralized Lifelong Path Planning for Multiple Ackerman Car-Like Robots

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.

On Computing Makespan-Optimal Solutions for Generalized Sliding-Tile Puzzles

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.

Bin Assignment and Decentralized Path Planning for Multi-Robot Parcel Sorting

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.

EARL: Eye-on-Hand Reinforcement Learner for Dynamic Grasping with Active Pose Estimation

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.