arXiv subjects

Kiril Solovey

Publications and source records attributed to Kiril Solovey.

At least 37 records · Page 2Linked to original sources

arXiv2022

Leveraging Experience in Lifelong Multi-Agent Pathfinding

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.

cs.MA↗

arXiv2022

Multi-Agent Terraforming: Efficient Multi-Agent Path Finding via Environment Manipulation

Multi-agent pathfinding (MAPF) is concerned with planning collision-free paths for a team of agents from their start to goal locations in an environment cluttered with obstacles. Typical approaches for MAPF consider the locations of obstacles as being fixed, which limits their effectiveness in automated warehouses, where obstacles (representing pods or shelves) can be moved out of the way by agents (representing robots) to relieve bottlenecks and introduce shorter routes. In this work we initiate the study of MAPF with movable obstacles. In particular, we introduce a new extension of MAPF, which we call Terraforming MAPF (tMAPF), where some agents are responsible for moving obstacles to clear the way for other agents. Solving tMAPF is extremely challenging as it requires reasoning not only about collisions between agents, but also where and when obstacles should be moved. We present extensions of two state-of-the-art algorithms, CBS and PBS, in order to tackle tMAPF, and demonstrate that they can consistently outperform the best solution possible under a static-obstacle setting.

cs.AI↗

arXiv2022

Resolution-Optimal Motion Planning for Steerable Needles

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.

cs.RO↗

arXiv2022

Coordinated Multi-Agent Pathfinding for Drones and Trucks over Road Networks

We address the problem of routing a team of drones and trucks over large-scale urban road networks. To conserve their limited flight energy, drones can use trucks as temporary modes of transit en route to their own destinations. Such coordination can yield significant savings in total vehicle distance traveled, i.e., truck travel distance and drone flight distance, compared to operating drones and trucks independently. But it comes at the potentially prohibitive computational cost of deciding which trucks and drones should coordinate and when and where it is most beneficial to do so. We tackle this fundamental trade-off by decoupling our overall intractable problem into tractable sub-problems that we solve stage-wise. The first stage solves only for trucks, by computing paths that make them more likely to be useful transit options for drones. The second stage solves only for drones, by routing them over a composite of the road network and the transit network defined by truck paths from the first stage. We design a comprehensive algorithmic framework that frames each stage as a multi-agent path-finding problem and implement two distinct methods for solving them. We evaluate our approach on extensive simulations with up to $100$ agents on the real-world Manhattan road network containing nearly $4500$ vertices and $10000$ edges. Our framework saves on more than $50\%$ of vehicle distance traveled compared to independently solving for trucks and drones, and computes solutions for all settings within $5$ minutes on commodity hardware.

cs.RO↗

arXiv2022

Balancing Fairness and Efficiency in Traffic Routing via Interpolated Traffic Assignment

System optimum (SO) routing, wherein the total travel time of all users is minimized, is a holy grail for transportation authorities. However, SO routing may discriminate against users who incur much larger travel times than others to achieve high system efficiency, i.e., low total travel times. To address the inherent unfairness of SO routing, we study the $β$-fair SO problem whose goal is to minimize the total travel time while guaranteeing a ${β\geq 1}$ level of unfairness, which specifies the maximum possible ratio between the travel times of different users with shared origins and destinations. To obtain feasible solutions to the $β$-fair SO problem while achieving high system efficiency, we develop a new convex program, the Interpolated Traffic Assignment Problem (I-TAP), which interpolates between a fairness-promoting and an efficiency-promoting traffic-assignment objective. We evaluate the efficacy of I-TAP through theoretical bounds on the total system travel time and level of unfairness in terms of its interpolation parameter, as well as present a numerical comparison between I-TAP and a state-of-the-art algorithm on a range of transportation networks. The numerical results indicate that our approach is faster by several orders of magnitude as compared to the benchmark algorithm, while achieving higher system efficiency for all desirable levels of unfairness. We further leverage the structure of I-TAP to develop two pricing mechanisms to collectively enforce the I-TAP solution in the presence of selfish homogeneous and heterogeneous users, respectively, that independently choose routes to minimize their own travel costs. We mention that this is the first study of pricing in the context of fair routing for general road networks (as opposed to, e.g., parallel road networks).

eess.SY↗

arXiv2021

Fast Near-Optimal Heterogeneous Task Allocation via Flow Decomposition

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 achieving 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.

cs.RO↗

arXiv2021

Efficient Large-Scale Multi-Drone Delivery Using Transit Networks

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 typically within a few seconds on commodity hardware, and that drones travel up to $360 \%$ of their flight range with public transit.

cs.RO↗

arXiv2020

Revisiting the Asymptotic Optimality of RRT$^*$

RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. This algorithm 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 in 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 $γ\left(\frac{\log n}{n}\right)^{1/d}$ to $γ' \left(\frac{\log n}{n}\right)^{1/(d+1)}$ in order to account 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.

cs.RO↗

arXiv2020

Complexity of Planning

This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct solution (a motion path or trajectory in our setting), or to report that none exists otherwise (in case that for instance, no feasible path exists). Complexity theory is a fundamental tool in computer science for analyzing the performance of algorithms, in terms of the amount of resources they require. (While complexity can express different quantities such as space and communication effort, our focus in this chapter is on time complexity.) Moreover, complexity theory helps to identify ``hard'' problems which require excessive amount of computation time to solve. In the context of motion planning, complexity theory can come in handy in various ways, some of which are illustrated here.

cs.RO↗

arXiv2020

Refined Analysis of Asymptotically-Optimal Kinodynamic Planning in the State-Cost Space

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 AO-RRT. We also discuss practical aspects of AO-RRT and present experimental comparisons of variants of the algorithm.

cs.RO↗

arXiv2020

On Local Computation for Optimization in Multi-Agent Systems

A number of prototypical optimization problems in multi-agent systems (e.g., task allocation and network load-sharing) exhibit a highly local structure: that is, each agent's decision variables are only directly coupled to few other agent's variables through the objective function or the constraints. Nevertheless, existing algorithms for distributed optimization generally do not exploit the locality structure of the problem, requiring all agents to compute or exchange the full set of decision variables. In this paper, we develop a rigorous notion of "locality" that quantifies the degree to which agents can compute their portion of the global solution based solely on information in their local neighborhood. This notion provides a theoretical basis for a rather simple algorithm in which agents individually solve a truncated sub-problem of the global problem, where the size of the sub-problem used depends on the locality of the problem, and the desired accuracy. Numerical results show that the proposed theoretical bounds are remarkably tight for well-conditioned problems.

cs.MA↗

arXiv2019

Sample Complexity of Probabilistic Roadmaps via $ε$-nets

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 ${\mathcal{X}}$ and connection radius ${r>0}$. We develop the notion of ${(δ,ε)}$-completeness of the parameters ${\mathcal{X}, r}$, which indicates that for every motion-planning problem of clearance at least ${δ>0}$, PRM using ${\mathcal{X}, r}$ returns a solution no longer than ${1+ε}$ times the shortest $δ$-clear path. Leveraging the concept of $ε$-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 $ε$-nets that achieves nearly the same coverage as grids while using significantly fewer samples.

cs.DS↗

arXiv2019

Scalable and Congestion-aware Routing for Autonomous Mobility-on-Demand via Frank-Wolfe Optimization

We consider the problem of vehicle routing for Autonomous Mobility-on-Demand (AMoD) systems, wherein a fleet of self-driving vehicles provides on-demand mobility in a given environment. Specifically, the task it to compute routes for the vehicles (both customer-carrying and empty travelling) so that travel demand is fulfilled and operational cost is minimized. The routing process must account for congestion effects affecting travel times, as modeled via a volume-delay function (VDF). Route planning with VDF constraints is notoriously challenging, as such constraints compound the combinatorial complexity of the routing optimization process. Thus, current solutions for AMoD routing resort to relaxations of the congestion constraints, thereby trading optimality with computational efficiency. In this paper, we present the first computationally-efficient approach for AMoD routing where VDF constraints are explicitly accounted for. We demonstrate that our approach is faster by at least one order of magnitude with respect to the state of the art, while providing higher quality solutions. From a methodological standpoint, the key technical insight is to establish a mathematical reduction of the AMoD routing problem to the classical traffic assignment problem (a related vehicle-routing problem where empty traveling vehicles are not present). Such a reduction allows us to extend powerful algorithmic tools for traffic assignment, which combine the classic Frank-Wolfe algorithm with modern techniques for pathfinding, to the AMoD routing problem. We provide strong theoretical guarantees for our approach in terms of near-optimality of the returned solution.

math.OC↗

arXiv2019

dRRT*: Scalable and Informed Asymptotically-Optimal Multi-Robot Motion Planning

Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle, by exploring the composite space of all robots. Sampling-based planners do so by building a roadmap or a tree data structure in the corresponding configuration space and can achieve asymptotic optimality. The hardness of motion planning, however, renders the explicit construction of such structures in the composite space of multiple robots impractical. This work proposes a scalable solution for such coupled multi-robot problems, which provides desirable path-quality guarantees and is also computationally efficient. In particular, the proposed \drrtstar\ is an informed, asymptotically-optimal extension of a prior sampling-based multi-robot motion planner, \drrt. The prior approach introduced the idea of building roadmaps for each robot and implicitly searching the tensor product of these structures in the composite space. This work identifies the conditions for convergence to optimal paths in multi-robot problems, which the prior method was not achieving. Building on this analysis, \drrt\ is first properly adapted so as to achieve the theoretical guarantees and then further extended so as to make use of effective heuristics when searching the composite space of all robots. The case where the various robots share some degrees of freedom is also studied. Evaluation in simulation indicates that the new algorithm, \drrtstar\, converges to high-quality paths quickly and scales to a higher number of robots where various alternatives fail. This work also demonstrates the planner's capability to solve problems involving multiple real-world robotic arms.

cs.RO↗

arXiv2018

The Critical Radius in Sampling-based Motion Planning

We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli (2011) and subsequent work. Particularly, we prove the existence of a critical connection radius proportional to ${Θ(n^{-1/d})}$ for $n$ samples and ${d}$ dimensions: Below this value the planner is guaranteed to fail (similarly shown by the aforementioned work, ibid.). More importantly, for larger radius values the planner is asymptotically (near-)optimal. Furthermore, our analysis yields an explicit lower bound of ${1-O( n^{-1})}$ on the probability of success. A practical implication of our work is that asymptotic (near-)optimality is achieved when each sample is connected to only ${Θ(1)}$ neighbors. This is in stark contrast to previous work which requires ${Θ(\log n)}$ connections, that are induced by a radius of order ${\left(\frac{\log n}{n}\right)^{1/d}}$. Our analysis is not restricted to PRM and applies to a variety of PRM-based planners, including RRG, FMT* and BTT. Continuum percolation plays an important role in our proofs. Lastly, we develop similar theory for all the aforementioned planners when constructed with deterministic samples, which are then sparsified in a randomized fashion. We believe that this new model, and its analysis, is interesting in its own right.

cs.RO↗

arXiv2018

Fast, High-Quality Dual-Arm Rearrangement in Synchronous, Monotone Tabletop Setups

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 paper studies the structure of dual-arm rearrangement for 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 of 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 points and show that the scalable method can quickly compute solutions close to the optimal for the considered setup.

cs.RO↗

arXiv2017

Effective Metrics for Multi-Robot Motion-Planning

We study the effectiveness of metrics for Multi-Robot Motion-Planning (MRMP) when using RRT-style sampling-based planners. These metrics play the crucial role of determining the nearest neighbors of configurations and in that they regulate the connectivity of the underlying roadmaps produced by the planners and other properties like the quality of solution paths. After screening over a dozen different metrics we focus on the five most promising ones- two more traditional metrics, and three novel ones which we propose here, adapted from the domain of shape-matching. In addition to the novel multi-robot metrics, a central contribution of this work are tools to analyze and predict the effectiveness of metrics in the MRMP context. We identify a suite of possible substructures in the configuration space, for which it is fairly easy (i) to define a so-called natural distance which allows us to predict the performance of a metric. This is done by comparing the distribution of its values for sampled pairs of configurations to the distribution induced by the natural distance; (ii) to define equivalence classes of configurations and test how well a metric covers the different classes. We provide experiments that attest to the ability of our tools to predict the effectiveness of metrics: those metrics that qualify in the analysis yield higher success rate of the planner with fewer vertices in the roadmap. We also show how combining several metrics together leads to better results (success rate and size of roadmap) than using a single metric.

cs.RO↗

arXiv2017

Scalable Asymptotically-Optimal Multi-Robot Motion Planning

Finding asymptotically-optimal paths in multi-robot motion planning problems could be achieved, in principle, using sampling-based planners in the composite configuration space of all of the robots in the space. The dimensionality of this space increases with the number of robots, rendering this approach impractical. This work focuses on a scalable sampling-based planner for coupled multi-robot problems that provides asymptotic optimality. It extends the dRRT approach, which proposed building roadmaps for each robot and searching an implicit roadmap in the composite configuration space. This work presents a new method, dRRT* , and develops theory for scalable convergence to optimal paths in multi-robot problems. Simulated experiments indicate dRRT* converges to high-quality paths while scaling to higher numbers of robots where the naive approach fails. Furthermore, dRRT* is applicable to high-dimensional problems, such as planning for robot manipulators

cs.MA↗