In scenarios like automated warehouses, assigning tasks to robots presents a heterogeneous multi-task and multi-agent task allocation problem. However, existing task allocation study ignores the integration of multi-task and multi-attribute agent task allocation with heterogeneous task allocation. In addition, current algorithms are limited by scenario constraints and can incur significant errors in specific contexts. Therefore, this study proposes a distributed heterogeneous multi-task and multi-agent task allocation algorithm with a time window, called group consensus-based heterogeneous auction (GCBHA). Firstly, this method decomposes tasks that exceed the capability of a single Agent into subtasks that can be completed by multiple independent agents. And then groups similar or adjacent tasks through a heuristic clustering method to reduce the time required to reach a consensus. Subsequently, the task groups are allocated to agents that meet the conditions through an auction process. Furthermore, the method evaluates the task path cost distance based on the scenario, which can calculate the task cost more accurately. The experimental results demonstrate that GCBHA performs well in terms of task allocation time and solution quality, with a significant reduction in the error rate between predicted task costs and actual costs.

In this paper, a novel framework is presented that achieves a combined solution based on Multi-Robot Task Allocation (MRTA) and collision avoidance with respect to homogeneous measurement tasks taking place in industrial environments. The spatial clustering we propose offers to simultaneously solve the task allocation problem and deal with collision risks by cutting the workspace into distinguishable operational zones for each robot. To divide task sites and to schedule robot routes within corresponding clusters, we use K-means clustering and the 2-Opt algorithm. The presented framework shows satisfactory performance, where up to 93\% time reduction (1.24s against 17.62s) with a solution quality improvement of up to 7\% compared to the best performing method is demonstrated. Our method also completely eliminates collision points that persist in comparative methods in a most significant sense. Theoretical analysis agrees with the claim that spatial partitioning unifies the apparently disjoint tasks allocation and collision avoidance problems under conditions of many identical tasks to be distributed over sparse geographical areas. Ultimately, the findings in this work are of substantial importance for real world applications where both computational efficiency and operation free from collisions is of paramount importance.

We consider a probabilistic model for large-scale task allocation problems for multi-agent systems, aiming to determine an optimal deployment strategy that minimizes the overall transport cost. Specifically, we assign transportation agents to delivery tasks with given pick-up and drop-off locations, pairing the spatial distribution of transport resources with the joint distribution of task origins and destinations. This aligns with the optimal mass transport framework where the problem and is in the unequal-dimensional setting. The task allocation problem can be thus seen as a linear programming problem that minimizes a quadratic transport cost functional, optimizing the energy of all transport units. The problem is motivated by time-sensitive medical deliveries using drones, such as emergency equipment and blood transport. In this paper, we establish the existence, uniqueness, and smoothness of the optimal solution, and illustrate its properties through numerical simulations.

In this paper, we explore how to optimize task allocation for robot swarms in dynamic environments, emphasizing the necessity of formulating robust, flexible, and scalable strategies for robot cooperation. We introduce a novel framework using a decentralized partially observable Markov decision process (Dec_POMDP), specifically designed for distributed robot swarm networks. At the core of our methodology is the Local Information Aggregation Multi-Agent Deep Deterministic Policy Gradient (LIA_MADDPG) algorithm, which merges centralized training with distributed execution (CTDE). During the centralized training phase, a local information aggregation (LIA) module is meticulously designed to gather critical data from neighboring robots, enhancing decision-making efficiency. In the distributed execution phase, a strategy improvement method is proposed to dynamically adjust task allocation based on changing and partially observable environmental conditions. Our empirical evaluations show that the LIA module can be seamlessly integrated into various CTDE-based MARL methods, significantly enhancing their performance. Additionally, by comparing LIA_MADDPG with six conventional reinforcement learning algorithms and a heuristic algorithm, we demonstrate its superior scalability, rapid adaptation to environmental changes, and ability to maintain both stability and convergence speed. These results underscore LIA_MADDPG's outstanding performance and its potential to significantly improve dynamic task allocation in robot swarms through enhanced local collaboration and adaptive strategy execution.

We consider a new variant of the multi-robot task allocation problem - Inverse Risk-sensitive Multi-Robot Task Allocation (IR-MRTA). "Forward" MRTA - the process of deciding which robot should perform a task given the reward (cost)-related parameters, is widely studied in the multi-robot literature. In this setting, the reward (cost)-related parameters are assumed to be already known: parameters are first fixed offline by domain experts, followed by coordinating robots online. What if we need these parameters to be adjusted by non-expert human supervisors who oversee the robots during tasks to adapt to new situations? We are interested in the case where the human supervisor's perception of the allocation risk may change and suggest different allocations for robots compared to that from the MRTA algorithm. In such cases, the robots need to change the parameters of the allocation problem based on evolving human preferences. We study such problems through the lens of inverse task allocation, i.e., the process of finding parameters given solutions to the problem. Specifically, we propose a new formulation IR-MRTA, in which we aim to find a new set of parameters of the human behavioral risk model that minimally deviates from the current MRTA parameters and can make a greedy task allocation algorithm allocate robot resources in line with those suggested by humans. We show that even in the simple case such a problem is a non-convex optimization problem. We propose a Branch $\&$ Bound algorithm (BB-IR-MRTA) to solve such problems. In numerical simulations of a case study on multi-robot target capture, we demonstrate how to use BB-IR-MRTA and we show that the proposed algorithm achieves significant advantages in running time and peak memory usage compared to a brute-force baseline.

Task allocation plays a vital role in multi-robot autonomous cleaning systems, where multiple robots work together to clean a large area. However, most current studies mainly focus on deterministic, single-task allocation for cleaning robots, without considering hybrid tasks in uncertain working environments. Moreover, there is a lack of datasets and benchmarks for relevant research. In this paper, to address these problems, we formulate multi-robot hybrid-task allocation under the uncertain cleaning environment as a robust optimization problem. Firstly, we propose a novel robust mixed-integer linear programming model with practical constraints including the task order constraint for different tasks and the ability constraints of hybrid robots. Secondly, we establish a dataset of \emph{100} instances made from floor plans, each of which has 2D manually-labeled images and a 3D model. Thirdly, we provide comprehensive results on the collected dataset using three traditional optimization approaches and a deep reinforcement learning-based solver. The evaluation results show that our solution meets the needs of multi-robot cleaning task allocation and the robust solver can protect the system from worst-case scenarios with little additional cost. The benchmark will be available at {https://github.com/iamwangyabin/Multi-robot-Cleaning-Task-Allocation}.

We consider the general problem of geometric task allocation, wherein a large, decentralised swarm of simple mobile agents must detect the locations of tasks in the plane and position themselves nearby. The tasks are represented by an a priori unknown demand profile $\Phi(x,y)$ that determines how many agents are needed in each location. The agents are autonomous, oblivious and indistinguishable, and have finite sensing range. They must configure themselves according to $\Phi$ using only local information about $\Phi$ and about the positions of nearby agents. All agents act according to the same local sensing-based rule of motion, and cannot explicitly communicate nor share information. We propose an optimization-based approach to the problem which results in attraction-repulsion dynamics. Repulsion encourages agents to spread out and explore the region so as to find the tasks, and attraction causes them to accumulate at task locations. We derive this approach via gradient descent over an appropriate ``error'' functional, and test it extensively through numerical simulations. The figures in this work are snapshots of simulations that can be viewed online at https://youtu.be/kyUiGYSaaoQ.

Much research has been done to apply auctions, markets, and negotiation mechanisms to solve the multiagent task allocation problem. However, there has been very little work on human-agent group task allocation. We believe that the notion of bounty hunting has good properties for human-agent group interaction in dynamic task allocation problems. We use previous experimental results comparing bounty hunting with auction-like methods to argue why it would be particularly adept at handling scenarios with unreliable collaborators and unexpectedly hard tasks: scenarios we believe highlight difficulties involved in working with humans collaborators.

Task allocation has been a well studied problem. In most prior problem formulations, it is assumed that each task is associated with a unique set of resource requirements. In the scope of multi-robot task allocation problem, these requirements can be satisfied by a coalition of robots. In this paper, we introduce a more general formulation of multi-robot task allocation problem that allows more than one option for specifying the set of task requirements--satisfying any one of the options will satisfy the task. We referred to this new problem as the multi-robot task allocation problem with task variants. First, we theoretically show that this extension fortunately does not impact the complexity class, which is still NP-complete. For solution methods, we adapt two previous greedy methods for the task allocation problem without task variants to solve this new problem and analyze their effectiveness. In particular, we "flatten" the new problem to the problem without task variants, modify the previous methods to solve the flattened problem, and prove that the bounds still hold. Finally, we thoroughly evaluate these two methods along with a random baseline to demonstrate their efficacy for the new problem.

Social sensing has emerged as a new sensing paradigm where humans (or devices on their behalf) collectively report measurements about the physical world. This paper focuses on a quality-cost-aware task allocation problem in multi-attribute social sensing applications. The goal is to identify a task allocation strategy (i.e., decide when and where to collect sensing data) to achieve an optimized tradeoff between the data quality and the sensing cost. While recent progress has been made to tackle similar problems, three important challenges have not been well addressed: (i) "online task allocation": the task allocation schemes need to respond quickly to the potentially large dynamics of the measured variables in social sensing; (ii) "multi-attribute constrained optimization": minimizing the overall sensing error given the dependencies and constraints of multiple attributes of the measured variables is a nontrivial problem to solve; (iii) "nonuniform task allocation cost": the task allocation cost in social sensing often has a nonuniform distribution which adds additional complexity to the optimized task allocation problem. We evaluate the QCO-TA scheme through a real-world social sensing application and the results show that our scheme significantly outperforms the state-of-the-art baselines in terms of both sensing accuracy and cost. Introduction This paper presents an online reinforcement learning framework to solve the quality-cost-aware task allocation problem in multi-attribute social sensing applications. Social sensing has emerged as a new sensing paradigm in pervasive and mobile computing applications where humans (or devices on their behalf) collectively report measurements about the physical world [1, 2]. Examples of social sensing applications include air quality and environment monitoring in smart cities using mobile devices [3], malfunctioning urban infrastructures reporting using geotagging [4], and damage assessment in disaster response using online social media [5]. In social sensing applications, participants perform sensing tasks at assigned locations to collect different attributes of the measured variables that are of interests to the application [6]. For example, in an urban air quality sensing application, participants are tasked to measure various air quality attributes (e.g., PM 2.5, PM 10, CO 2) at different locations of the city to estimate the overall air quality and identity potential health risks. We refer to this category of applications as multi-attribute social sensing applications . In multi-attribute social sensing applications, there exists a fundamental tradeoff between data quality and sensing (task allocation) cost [3, 7]. 2 In particular, it is essential to obtain comprehensive and accurate measurements to ensure the desired data quality of the social sensing applications.