Path Finding Problem Research Articles

Interoperability Between Smart Building and Mobile Robots: Application to the Path Finding Problem

Interoperability Between Smart Building and Mobile Robots: Application to the Path Finding Problem

Interoperability Between Smart Building and Mobile Robots: Application to the Path Finding Problem

Interoperability Between Smart Building and Mobile Robots: Application to the Path Finding Problem

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The Robotic Mobile Fulfillment System (RMFS) is a robotized material handling system where multiple robots transport movable shelves to and from stocking points and workstations in a warehouse. In this paper, we deal with the problem of finding collision-free routes for multiple robots to move from their starting points to destinations in a RMFS, which is defined as a generalization of the multi-agent path finding problem (MAPFP). In RMFSs, collisions among moving robots may occur due to the physical volume of robots and the inexact execution of planned routes by robots in terms of the planned timing of passing through points on the routes, which makes it difficult to directly apply the existing algorithms for MAPFP that assume the exact execution of planned routes by agents with no physical volume. Therefore, we defined the problem as a multi-agent path finding problem with the prespecified time spacing at points to address the possible sources of collisions among robots, and propose an integer optimization model for the problem. Since the proposed integer optimization model has a large number of decision variables and constraints, we propose heuristic and exact algorithms based on the Lagrangian relaxation technique and the conflict based search. Experimental results show that the proposed algorithms are effective in finding good quality solutions within a limited time even when the number of robots or the time spacing are large.

Robust A*-Search Image Segmentation Algorithm for Mine-like Objects Segmentation in SONAR Images

This paper addresses a sonar image segmentation method employing a Robust A*-Search Image Segmentation (RASIS) algorithm. RASIS is applied on Mine-Like Objects (MLO) in sonar images, where an object is defined by highlight and shadow regions, i.e. regions of high and low pixel intensities in a side-scan sonar image. RASIS uses a modified A*-Search method, which is usually used in mobile robotics for finding the shortest path where the environment map is predefined, and the start/goal locations are known. RASIS algorithm represents the image segmentation problem as a path-finding problem. Main modification concerning the original A*-Search is in the cost function that takes pixel intensities and contour curvature in order to navigate the 2D segmentation contour. The proposed method is implemented in Matlab and tested on real MLO images. MLO image dataset consist of 70 MLO images with manta mine present, and 70 MLO images with cylinder mine present. Segmentation success rate is obtained by comparing the ground truth data given by the human technician who is detecting MLOs. Measured overall success rate (highlight and shadow regions) is 91% for manta mines and 81% for cylinder mines.

Complexity of planning for connected agents

We study a variant of the multi-agent path finding (MAPF) problem in which the group of agents are required to stay connected with a supervising base station throughout the execution. In addition, we consider the problem of covering an area with the same connectivity constraint. We show that both problems are PSPACE-complete on directed and undirected topological graphs while checking the existence of a bounded plan is NP-complete when the bound is given in unary (and PSPACE-hard when the encoding is in binary). Moreover, we identify a realistic class of topological graphs on which the decision problem falls in NLOGSPACE although the bounded versions remain NP-complete for unary encoding.

Probabilistic Robust Multi-Agent Path Finding

In a multi-agent path finding (MAPF) problem, the task is to move a set of agents to their goal locations without conflicts. In the real world, unexpected events may delay some of the agents. In this paper, we therefore study the problem of finding a p-robust solution to a given MAPF problem, which is a solution that succeeds with probability at least p, even though unexpected delays may occur. We propose two methods for verifying that given solutions are p-robust. We also introduce an optimal CBS-based algorithm, called pR-CBS, and a fast suboptimal algorithm, called pR-GCBS, for finding such solutions. Our experiments show that a p-robust solution reduces the number of conflicts compared to optimal, non-robust solutions.

Algorithm Selection for Optimal Multi-Agent Pathfinding

The challenge of finding an optimal solution to a multi-agent path finding (MAPF) problem has attracted significant academic and industrial interest in recent years. While the problem is NP-Hard, modern optimal MAPF algorithms can scale to solve problems with hundreds of agents. Nevertheless, no single optimal MAPF algorithm dominates all benchmarks problems, and there are no clear, provable, guidelines for when each algorithm should be used. To address this, we present the first successful Algorithm Selection (AS) model for optimal MAPF. We propose two approaches for learning an AS model. The first approach uses a standard supervised learning algorithm with a set of handcrafted MAPF-specific features. The second approach, casts a MAPF problem to an image and applies a deep Convolutional Neural Network to classify it. We evaluate both approaches over a large dataset and show that using an AS model to select which algorithm to use for each instance results in solving more problems and in a shorter runtime compared to the state of the art.

Incorporating LSTM Auto-Encoders in Optimizations to Solve Parking Officer Patrolling Problem

The smart parking system is one of the most important problems in smart cities. Recently, an increasing number of sensors installed in parking spaces have provided big spatio-temporal data that be used to analyze parking situations in the city and help parking officers monitor parking violations. The traveling officer problem was customized to formulate a path-finding problem that aims to maximize the probability of catching overstayed cars before they leave. One of the challenges is to extract effective features from the big spatio-temporal data and provide a data-driven solution to replace conventional solutions such as a simple rule-based system or single optimization methods. In this article, we propose a seamless end-to-end learning and optimization framework that combines the long short-term memory auto-encoder neural network, clustering, and path-finding methods to solve the traveling officer problem. Our extensive comparison experiments on a large-scale real-world dataset have shown that our proposed solution outperforms any other single-step or optimization methods.

Idle Time Optimization for Target Assignment and Path Finding in Sortation Centers

In this paper, we study the one-shot and lifelong versions of the Target Assignment and Path Finding problem in automated sortation centers, where each agent needs to constantly assign itself a sorting station, move to its assigned station without colliding with obstacles or other agents, wait in the queue of that station to obtain a parcel for delivery, and then deliver the parcel to a sorting bin. The throughput of such centers is largely determined by the total idle time of all stations since their queues can frequently become empty. To address this problem, we first formalize and study the one-shot version that assigns stations to a set of agents and finds collision-free paths for the agents to their assigned stations. We present efficient algorithms for this task based on a novel min-cost max-flow formulation that minimizes the total idle time of all stations in a fixed time window. We then demonstrate how our algorithms for solving the one-shot problem can be applied to solving the lifelong problem as well. Experimentally, we believe to be the first researchers to consider real-world automated sortation centers using an industrial simulator with realistic data and a kinodynamic model of real robots. On this simulator, we showcase the benefits of our algorithms by demonstrating their efficiency and effectiveness for up to 350 agents.

Implicit Coordination Using FOND Planning

Epistemic planning can be used to achieve implicit coordination in cooperative multi-agent settings where knowledge and capabilities are distributed between the agents. In these scenarios, agents plan and act on their own without having to agree on a common plan or protocol beforehand. However, epistemic planning is undecidable in general. In this paper, we show how implicit coordination can be achieved in a simpler, propositional setting by using nondeterminism as a means to allow the agents to take the other agents' perspectives. We identify a decidable fragment of epistemic planning that allows for arbitrary initial state uncertainty and non-determinism, but where actions can never increase the uncertainty of the agents. We show that in this fragment, planning for implicit coordination can be reduced to a version of fully observable nondeterministic (FOND) planning and that it thus has the same computational complexity as FOND planning. We provide a small case study, modeling the problem of multi-agent path finding with destination uncertainty in FOND, to show that our approach can be successfully applied in practice.

Solving Sum-of-Costs Multi-Agent Pathfinding with Answer-Set Programming

Solving a Multi-Agent Pathfinding (MAPF) problem involves finding non-conflicting paths that lead a number of agents to their goal location. In the sum-of-costs variant of MAPF, one is also required to minimize the total number of moves performed by agents before stopping at the goal. Not surprisingly, since MAPF is combinatorial, a number of compilations to Satisfiability solving (SAT) and Answer Set Programming (ASP) exist. In this paper, we propose the first family of compilations to ASP that solve sum-of-costs MAPF over 4-connected grids. Unlike existing compilations to ASP that we are aware of, our encoding is the first that, after grounding, produces a number of clauses that is linear on the number of agents. In addition, the representation of the optimization objective is also carefully written, such that its size after grounding does not depend on the size of the grid. In our experimental evaluation, we show that our approach outperforms search- and SAT-based sum-of-costs MAPF solvers when grids are congested with agents.

Abstraction and Refinement in Games with Dynamic Weighted Terrain

This abstract looks at one version of the pathfinding problem in games and discusses how it motived our recent work at the AIIDE 2019 conference.

Walk, Stop, Count, and Swap: Decentralized Multi-Agent Path Finding With Theoretical Guarantees

For multi-agent path finding (MAPF) problems, finding the optimal solution has been shown to be NP-Complete. Here we present WSCaS (Walk, Stop, Count, and Swap), a decentralized multi-agent path-finding algorithm that can provide theoretical completeness and optimality guarantees. That is, WSCaS is able to deliver a worst case $\mathbf {\mathcal {O}(1)}$ -approximate distance-optimal solution to MAPF instances on square grids without narrow passages. Moreover, the algorithm‘s cost is independent of the swarm's size with respect to computation complexity, memory complexity, as well as communication complexity, therefore the algorithm can scale well with the number of agents in practice. The algorithm is executed on 1024 simulated agents as well as 100 physical robots, the results show that the WSCaS is robust to real-world non-idealitys.

Integrating safety and mobility for pathfinding using big data generated by connected vehicles

With the emergence of the internet of things, pathfinding problems have recently received a significant amount of attention. Various commercial applications provide automated routing by considering travel time, travel distance, fuel consumption, complexity of the road, etc. However, many of these prospective applications do not consider route safety. Emergence of high-resolution big data generated by connected vehicles (CV) helps us to integrate safety into routing problem. The goal of this study is to address safety aspects in pathfinding problems by developing a methodological framework that simultaneously considers safety and mobility. To reach this goal, the concept of volatility is utilized as a surrogate safety performance measure to quantify route safety and driver behavior. The proposed framework uses CV big data and real-time traffic data to calculate safety indices and travel times. Measured safety indices include 5-year crash history, route speed and acceleration volatility, and driver volatility. Travel time and safety shape a cost function called “route impedance.” The algorithm has the flexibility for the user to predefine the weight for safety consideration. It also uses driver volatility to automatically increase safety weight for volatile drivers. To illustrate the algorithm, a numerical example is provided using an origin-destination pair in Ann Arbor, MI, and more than 42 million CV observations from around 2,500 CVs from the Safety Pilot Model Deployment (SPMD) were analyzed. The sensitivity analysis is performed to discuss the impact of penetration rate of CVs and time of the trip on the results. Finally, this paper shows suggested routes for multiple scenarios to demonstrate the outcome of the study. The results revealed that the algorithm might suggest different routes when considering safety indices and not just travel time.

Programmatic implementation of the Dijkstra algorithm in the Transact-SQL language using relational algebra

The article is devoted to the topical issue of data processing in the database management systems. It presents a solution to the problem of finding paths in a graph using Dijkstra’s algorithm, set as a sequence of relational operations and functions of the Transact-SQL language. The efficiency of the known information system architectures and the impact of various ways of distributing functions between system components are reviewed. The article describes features of the relational algebra and the Transact-SQL operations, and provides a brief description of Dijkstra’s algorithm. For its programmatic implementation, several stages are defined, for each of which a formal description of the relational operations performed on it is given. The outputs of these operations are shown using the example of the database tables, and the algorithm to find the final path is given. The issues of the proposed method’s productivity and security of programmatic implementation of the path search in a graph are discussed separately.

Reinforcement Learning Method with Generalization Ability Developed by Using Deep Learning for Solving a Path Finding Problem

Reinforcement Learning Method with Generalization Ability Developed by Using Deep Learning for Solving a Path Finding Problem

Cooperative Pathfinding Based on Memory-Efficient Multi-Agent RRT*

In cooperative pathfinding problems, non-conflict paths that bring several agents from their start location to their destination need to be planned. This problem can be efficiently solved by Multi-agent RRT*(MA-RRT*) algorithm, which is still state-of-the-art in the field of coupled methods. However, the implementation of this algorithm is hindered in systems with limited memory because the number of nodes in the tree of RRT* grows indefinitely as the paths get optimized. This paper proposes an improved version of MA-RRT*, called Multi-agent RRT* Fixed Node(MA-RRT*FN), which limits the number of nodes stored in the tree of RRT* by removing the weak nodes on the path which are not likely to reach the goal. The results show that MA-RRT*FN performs close to MA-RRT* in terms of scalability and solution quality while the memory required is much lower and fixed.

Coordinated Charging Scheduling of Electric Vehicles: A Mixed-Variable Differential Evolution Approach

The increasing popularity of battery-limited electric vehicles puts forward an important issue of how to charge the vehicles effectively. This problem, commonly referred to as Electric Vehicle Charging Scheduling (EVCS), has been proven to be NP-hard. Most of the existing works formulate the EVCS problem simply as a constrained shortest path finding problem and treat it by discrete optimization. However, other variables such as the charging amount of energy and the charging option at a station need to be considered in practical use. This paper hence formulates the EVCS problem as a hierarchical mixed-variable optimization problem, considering the dependency among the station selection, the charging option at each station and the charging amount settings. To adapt to the new problem model, we specifically design a Mixed-Variable Differentiate Evolution (MVDE) as the scheduling algorithm for our proposed EVCS system. The MVDE contains several specific operators, including a charging station route construction, a hierarchical mixed-variable mutation operator and a constraint-aware evaluation operator. Experimental results validate the effectiveness of our proposed MVDE-based system on both synthetic and real-world transportation networks.

Multiobjective model-free learning for robot pathfinding with environmental disturbances

This article addresses the robot pathfinding problem with environmental disturbances, where a solution to this problem must consider potential risks inherent in an uncertain and stochastic environment. For example, the movements of an underwater robot can be seriously disturbed by ocean currents, and thus any applied control actions to the robot cannot exactly lead to the desired locations. Reinforcement learning is a formal methodology that has been extensively studied in many sequential decision-making domains with uncertainty, but most reinforcement learning algorithms consider only a single objective encoded by a scalar reward. However, the robot pathfinding problem with environmental disturbances naturally promotes multiple conflicting objectives. Specifically, in this work, the robot has to minimise its moving distance so as to save energy, and, moreover, it has to keep away from unsafe regions as far as possible. To this end, we first propose a multiobjective model-free learning framework, and then proceed to investigate an appropriate action selection strategy by improving a baseline with respect to two dimensions. To demonstrate the effectiveness of the proposed learning framework and evaluate the performance of three action selection strategies, we also carry out an empirical study in a simulated environment.

Pathfinding and Abstraction with Dynamic Terrain Costs

Abstraction and refinement is a common approach used in games to improve the speed of pathfinding by planning in an abstract space and then refining abstract paths to traversable paths. While there are many variants of this approach that have been developed and studied, research on this problem has largely ignored the problem of pathfinding with terrain types, terrain costs, and dynamic terrain. This paper studies the problem of pathfinding in domains with terrain costs and proposes an abstraction approach that is built around handling terrain costs and dynamic terrain. The resulting approach is able to handle costs in a way that existing approaches do not, and provides a good balance between memory usage, path quality, and pathfinding speed.