In their seminal work, Gauci et al. (2014) studied the fundamental task of aggregation, wherein multiple robots need to gather without an a priori agreed-upon meeting location, using extremely limited hardware. That paper considered differential-drive robots that are memoryless and unable to compute. Moreover, the robots cannot communicate with one another and are only equipped with a simple sensor that determines whether another robot is directly in front of them. Despite those severe limitations, Gauci et al. introduced a controller and proved mathematically that it aggregates a system of two robots for any initial state. Unfortunately, for larger systems, the same controller aggregates empirically in many cases but not all. Thus, the question of whether there exists a controller that aggregates for any number of robots remains open. In this paper, we show that no such controller exists by investigating the geometric structure of controllers. In addition, we disprove the aggregation proof of the aforementioned paper for two robots and present an alternative controller alongside a simple and rigorous aggregation proof.

Motion planning is a central challenge in robotics, with learning-based approaches gaining significant attention in recent years. Our work focuses on a specific aspect of these approaches: using machine-learning techniques, particularly Support Vector Machines (SVM), to evaluate whether robot configurations are collision free, an operation termed “collision detection”. Despite the growing popularity of these methods, there is a lack of theory supporting their efficiency and prediction accuracy. This is in stark contrast to the rich theoretical results of machine-learning methods in general and of SVMs in particular. Our work bridges this gap by analyzing the sample complexity of an SVM classifier for learning-based collision detection in motion planning. We bound the number of samples needed to achieve a specified accuracy at a given confidence level. This result is stated in terms relevant to robot motion-planning such as the system's clearance. Building on these theoretical results, we propose a collision-detection algorithm that can also provide statistical guarantees on the algorithm's error in classifying robot configurations as collision-free or not.

Autonomous inspection tasks require path-planning algorithms to efficiently gather observations frompoints of interest(POIs). However, localization errors in urban environments introduce execution uncertainty, posing challenges to successfully completing such tasks. The existing inspection-planning algorithms do not explicitly address this uncertainty, which can hinder their performance. To overcome this, in this article, we introduceincremental random inspection-roadmap search (IRIS)-under uncertainty(IRIS-U$^{2}$), an inspection-planning algorithm that provides statistical assurances regarding coverage, path length, and collision probability. Our approach builds uponIRIS—our framework fordeterministic, highly efficient, and provably asymptotically optimal framework. This extension adapts IRIS to uncertain settings using a refined search procedure that estimates POI coverage probabilities through Monte Carlo (MC) sampling. We demonstrateIRIS-U$^{2}$through a case study on bridge inspections, achieving improved expected coverage, reduced collision probability, and increasingly precise statistical guarantees as MC samples grow. In addition, we explore bounded suboptimal solutions to reduce computation time while preserving statistical assurances.

In automated warehouses, teams of mobile robots fulfill the packaging process by transferring inventory pods to designated workstations while navigating narrow aisles formed by tightly packed pods. This problem is typically modeled as a Multi-Agent Pickup and Delivery (MAPD) problem, which is then solved by repeatedly planning collision-free paths for agents on a fixed graph, as in the Rolling-Horizon Collision Resolution (RHCR) algorithm. However, existing approaches make the limiting assumption that agents are only allowed to move pods that correspond to their current task, while considering the other pods as stationary obstacles (even though all pods are movable). This behavior can result in unnecessarily long paths which could otherwise be avoided by opening additional corridors via pod manipulation. To this end, we explore the implications of allowing agents the flexibility of dynamically relocating pods. We call this new challenging problem Terraforming MAPD (tMAPD) and develop an RHCR-based approach to tackle it. As the extra flexibility of terraforming comes at a significant computational cost, we utilize this capability judiciously by identifying situations where it could make a significant impact on the solution quality. In particular, we invoke terraforming in response to disruptions that often occur in automated warehouses, e.g., when an item is dropped from a pod or when agents malfunction. Empirically, using our approach for tMAPD, where disruptions are modeled via a stochastic process, we improve throughput by over 10%, reduce the maximum service time (the difference between the drop-off time and the pickup time of a pod) by more than 50%, without drastically increasing the runtime, compared to the MAPD setting.

An underlying structure in several sampling-based methods for continuous multirobot motion planning (MRMP) is thetensor roadmap, which emerges from combining multiple probabilistic roadmap (PRM) graphs constructed for the individual robots via a tensor product. We study the conditions under which the tensor roadmap encodes a near-optimal solution for MRMP—satisfying these conditions implies near optimality for a variety of popular planners, including dRRT*, and the discrete methods M* and conflict-based search, when applied to the continuous domain. We develop the first finite-sample analysis of this kind, which specifies the number of samples, their deterministic distribution, and magnitude of the connection radii that should be used by each individual PRM graph, to guarantee near-optimality using the tensor roadmap. This significantly improves upon a previous asymptotic analysis, wherein the number of samples tends to infinity. Our new finite sample-size analysis supports guaranteed high-quality solutions in practice within finite time. To achieve our new result, we first develop a sampling scheme, which we call thestaggered grid, for finite-sample motion planning for individual robots, which requires significantly fewer samples than previous work. We then extend it to the much more involved MRMP setting, which requires to account for interactions among multiple robots. Finally, we report on a few experiments that serve as a verification of our theoretical findings and raise interesting questions for further investigation.

Medical steerable needles can follow 3D curvilinear trajectories inside body tissue, enabling them to move around critical anatomical structures and precisely reach clinically significant targets in a minimally invasive way. Automating needle steering, with motion planning as a key component, has the potential to maximize the accuracy, precision, speed, and safety of steerable needle procedures. In this paper, we introduce the first resolution-optimal motion planner for steerable needles that offers excellent practical performance in terms of runtime while simultaneously providing strong theoretical guarantees on completeness and the global optimality of the motion plan in finite time. Compared to state-of-the-art steerable needle motion planners, simulation experiments on realistic scenarios of lung biopsy demonstrate that our proposed planner is faster in generating higher-quality plans while incorporating clinically relevant cost functions. This indicates that the theoretical guarantees of the proposed planner have a practical impact on the motion plan quality, which is valuable for computing motion plans that minimize patient trauma.

We present a centralized algorithm for labeled, disk-shaped Multi-Robot Path Planning (MPP) in a continuous planar workspace with polygonal boundaries. Our method automatically transform the continuous problem into a discrete, graph-based variant termed the pebble motion problem, which can be solved efficiently. To construct the underlying pebble graph, we identify inscribed circles in the workspace via a medial axis transform and organize robots into layers within each inscribed circle. We show that our layered pebble-graph enables collision-free motions, allowing all graph-restricted MPP instances to be feasible. MPP instances with continuous start and goal positions can then be solved via local navigations that route robots from and to graph vertices. We tested our method on several environments with high robot-packing densities (up to 61.6% of the workspace). For environments with narrow passages, such density violates the well-separated assumptions made by state-of-the-art MPP planners, while our method achieves an average success rate of 83%.

In Lifelong Multi-Agent Path Finding (L-MAPF) a team of agents performs a stream of tasks consisting of multiple locations to be visited by the agents on a shared graph while avoiding collisions with one another. L-MAPF is typically tackled by partitioning it into multiple consecutive, and hence similar, "one-shot" MAPF queries, as in the Rolling-Horizon Collision Resolution (RHCR) algorithm. Therefore, a solution to one query informs the next query, which leads to similarity with respect to the agents' start and goal positions, and how collisions need to be resolved from one query to the next. Thus, experience from solving one MAPF query can potentially be used to speedup solving the next one. Despite this intuition, current L-MAPF planners solve consecutive MAPF queries from scratch. In this paper, we introduce a new RHCR-inspired approach called exRHCR, which exploits experience in its constituent MAPF queries. In particular, exRHCR employs an extension of Priority-Based Search (PBS), a state-of-the-art MAPF solver. The extension, which we call exPBS, allows to warm-start the search with the priorities between agents used by PBS in the previous MAPF instances. We demonstrate empirically that exRHCR solves L-MAPF instances up to 39% faster than RHCR, and has the potential to increase system throughput for given task streams by increasing the number of agents a planner can cope with for a given time budget.

An underlying structure in several sampling-based methods for continuous multi-robot motion planning (MRMP) is the tensor roadmap (PR), which emerges from combining multiple PRM graphs constructed for the individual robots via a tensor product. We study the conditions under which the TR encodes a near-optimal solution for MRMP—satisfying these conditions implies near optimality for a variety of popular planners, including dRRT*, and the discrete methods M* and CBS when applied to the continuous domain. We develop the first finite-sample analysis of this kind, which specifies the number of samples, their deterministic distribution, and magnitude of the connection radii that should be used by each individual PRM graph, to guarantee near-optimality using the TR. This significantly improves upon a previous asymptotic analysis, wherein the number of samples tends to infinity. Our new finite sample-size analysis supports guaranteed high- quality solutions in practice within finite time. To achieve our new result, we first develop a sampling scheme, which we call the staggered grid, for finite-sample motion planning for individual robots, which requires significantly less samples than previous work. We then extend it to the much more involved MRMP setting which requires to account for interactions among multiple robots. Finally, we report on a few experiments that serve as a verification of our theoretical findings and raise interesting questions for further investigation.

Multi-robot systems are uniquely well-suited to performing complex tasks such as patrolling and tracking, information gathering, and pick-up and delivery problems, offering significantly higher performance than single-robot systems. A fundamental building block in most multi-robot systems is task allocation: assigning robots to tasks (e.g., patrolling an area, or servicing a transportation request) as they appear based on the robots’ states to maximize reward. In many practical situations, the allocation must account for heterogeneous capabilities (e.g., availability of appropriate sensors or actuators) to ensure the feasibility of execution, and to promote a higher reward, over a long time horizon. To this end, we present the FlowDec algorithm for efficient heterogeneous task-allocation, and show that it achieves an approximation factor of at least 1/2 of the optimal reward. Our approach decomposes the heterogeneous problem into several homogeneous subproblems that can be solved efficiently using min-cost flow. Through simulation experiments, we show that our algorithm is faster by several orders of magnitude than a MILP approach.

Rearranging objects on a planar surface arises in a variety of robotic applications, such as product packaging. Using two arms can improve efficiency but introduces new computational challenges. This article studies the problem structure of object rearrangement using two arms in synchronous, monotone tabletop setups and develops an optimal mixed-integer model. It then describes an efficient and scalable algorithm, which first minimizes the cost of object transfers and then moves between objects. This is motivated by the fact that, asymptotically, object transfers dominate the cost of solutions. Moreover, a lazy strategy minimizes the number of motion planning calls and results in significant speedups. Theoretical arguments support the benefits of using two arms and indicate that synchronous execution, in which the two arms perform together either transfers or moves, introduces only a small overhead. Experiments support these claims and show that the scalable method can quickly compute solutions close to the optimal for the considered setup.Note to Practitioners—Monotone tabletop rearrangement challenges arise in a variety of automation scenarios, including product sorting or packing. Performing this task with two robotic manipulators introduces the overhead of coordinating them in the shared workspace, as well as an increase in the size of the underling search space. The objective of this work is to study the feasibility of such dual-arm solutions, providing both theoretical bounds, as well as a fast, and approximate solution. The approach leverages an effective algorithmic decomposition of the problem so as to take advantage of efficient motion planners and mixed-integer linear programming solvers. The proposed solution has been evaluated in settings that include delta robots as well as seven-degree-of-freedom (DOF) manipulators. Interesting extensions of this work correspond to studying the case of additional arms, nonmonotone, and general manipulation scenarios.

We consider the problem of controlling a large fleet of drones to deliver packages simultaneously across broad urban areas. To conserve energy, drones hop between public transit vehicles (e.g., buses and trams). We design a comprehensive algorithmic framework that strives to minimize the maximum time to complete any delivery. We address the multifaceted complexity of the problem through a two-layer approach. First, the upper layer assigns drones to package delivery sequences with a near-optimal polynomial-time task allocation algorithm. Then, the lower layer executes the allocation by periodically routing the fleet over the transit network while employing efficient bounded-suboptimal multi-agent pathfinding techniques tailored to our setting. Experiments demonstrate the efficiency of our approach on settings with up to 200 drones, 5000 packages, and transit networks with up to 8000 stops in San Francisco and Washington DC. Our results show that the framework computes solutions within a few seconds (up to 2 minutes at most) on commodity hardware, and that drones travel up to 450% of their flight range with public transit.

We present a novel analysis of AO-RRT: a tree-based planner for motion planning with kinodynamic constraints, originally described by Hauser and Zhou (AO-X, 2016). AO-RRT explores the state-cost space and has been shown to efficiently obtain high-quality solutions in practice without relying on the availability of a computationally-intensive two-point boundary-value solver. Our main contribution is an optimality proof for the single-tree version of the algorithm-a variant that was not analyzed before. Our proof only requires a mild and easily-verifiable set of assumptions on the problem and system: Lipschitz-continuity of the cost function and the dynamics. In particular, we prove that for any system satisfying these assumptions, any trajectory having a piecewise-constant control function and positive clearance from the obstacles can be approximated arbitrarily well by a trajectory found by AORRT. We also discuss practical aspects of AORRT and present experimental comparisons of variants of the algorithm.

RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. RRT* laid the foundations for optimality in motion planning as a whole, and inspired the development of numerous new algorithms in the field, many of which build upon RRT* itself. In this paper, we first identify a logical gap in the optimality proof of RRT*, which was developed by Karaman and Frazzoli (2011). Then, we present an alternative and mathematically-rigorous proof for asymptotic optimality. Our proof suggests that the connection radius used by RRT* should be increased from γ (log n/n)1/dto γ' (log n/n)1/(d+1)in order to account n n for the additional dimension of time that dictates the samples' ordering. Here γ, γ' are constants, and n, d are the number of samples and the dimension of the problem, respectively.

We study fundamental theoretical aspects of probabilistic roadmaps (PRM) in the finite time (non-asymptotic) regime. In particular, we investigate how completeness and optimality guarantees of the approach are influenced by the underlying deterministic sampling distribution X and connection radius r > 0. We develop the notion of (δ, ε)-completeness of the parameters X, r, which indicates that for every motion-planning problem of clearance at least δ > 0, PRM using X, r returns a solution no longer than 1+ε times the shortest δ-clear path. Leveraging the concept of e-nets, we characterize in terms of lower and upper bounds the number of samples needed to guarantee (δ, ε)-completeness. This is in contrast with previous work which mostly considered the asymptotic regime in which the number of samples tends to infinity. In practice, we propose a sampling distribution inspired by e-nets that achieves nearly the same coverage as grids while using fewer samples.

We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map M : RdÅ R, which assigns to every point in space a real value, we wish to find a path connecting two given points, which minimizes the maximal value with respect to M. We demonstrate the capabilities of our algorithm, which we call bottleneck tree (BTT), on several challenging instances of the problem involving multiple agents, where it outperforms the state-of-the-art cost-map planning technique T-RRT. In addition to its efficiency, BTT requires the tuning of only a single parameter: the number of samples. On the theoretical side, we study the asymptotic properties of our method and consider the special setting where the computed trajectories must be monotone in all coordinates. This constraint arises in cases where the problem involves the coordination of multiple agents that are restricted to forward motions along predefined paths.

We describe a general probabilistic framework to address a variety of Fréchet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in d-dimensional Euclidean space between given start and goal points, namely paths that minimize the maximal value over a continuous cost map. We present an efficient and simple sampling-based framework for this problem, which is inspired by, and draws ideas from, techniques for robot motion planning. We extend the framework to handle not only standard bottleneck pathfinding, but also the more demanding case, where the path needs to be monotone in all dimensions. Finally, we provide experimental results of the framework on several types of problems.

We consider the following motion-planning problem: we are given \mbim unit discs in a simple polygon with \mbin vertices, each at their own start position, and we want to move the discs to a given set of \mbim target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in \mbiO(m2+mn) time, assuming that the start and target positions are at least some minimal distance from each other. This is in sharp contrast to the standard (labeled) and more general multi-robot motion planning problem for discs moving in a simple polygon, which is known to be strongly NP-hard.