Efficient task allocation for large-scale Heterogeneous Multi-Robot Systems (HMRS) is critical, yet dealing with complex temporal logic tasks in partially known environment (PKE) remains a computational bottleneck. Existing approaches often struggle to balance exploring uncertain regions and exploiting known resources, while also suffering from exponential computational complexity. To address these issues, this paper presents a robust planning framework that simultaneously handles high-level logical constraints and environmental uncertainty without sacrificing scalability. We formulate the problem as a min-max regret optimization, proposing a Region-Binding Atomic Proposition (RbAP) to capture resource uncertainty within the automaton structure. To solve this, we propose the Extended Planning Decision Tree (E-PDT) equipped with a novel Regret-based Branch-and-Bound (BnB) strategy. Unlike traditional methods that rely on prior probabilities or worst-case analysis, our approach dynamically prunes suboptimal policies, effectively balancing the need for information gathering (exploration) and task completion (exploitation). Theoretical analysis confirms the feasibility and completeness of our approach. Extensive numerical and physical experiments demonstrate that the proposed framework achieves near-linear scalability with respect to the number of robots and types, significantly outperforming MILP-based baselines in both solution quality and computational efficiency.
Robots operate under significant uncertainty, from quantifiable noise to unquantifiable unknowns, and must account for strict operational constraints, such as limited resources. In this paper, we consider the problem of synthesizing robust strategies to guide a robot's actions in fulfilling a given task, while ensuring the system never exhausts its resources. To solve this problem, we first model the robotic system as a Consumption Markov Decision Process with Set-valued Transitions(CMDPST), a unified framework modelling nondeterministic actions, quantifiable and unquantifiable uncertainty, and resource consumption. Then, we combine the CMDPST with the task specification, expressed as a Linear Temporal Logic over finite traces (LTLf ) formula. Lastly, we address the resource constrained optimal robust strategy synthesis problem, which aims to synthesize a strategy that maximizes the probability of satisfying the LTLf objective without resource exhaustion. Our solution involves two techniques: a direct unrolling-based method and a more efficient, optimized approach that leverages state-space pruning for better performance. Experiments on a warehouse transportation network show the effectiveness of the proposed solutions.
Multi-Robot Task Allocation (MRTA) is a central challenge in decentralized multi-agent systems, where teams of robots must cooperatively assign and execute tasks under limited communication while optimizing global performance objectives. Auction-consensus algorithms, such as the Consensus-Based Bundle Algorithm (CBBA), provide scalable decentralized coordination with provable convergence, but rely on hand-crafted greedy scoring functions that often lead to suboptimal task allocations. This paper proposes a learning-enhanced auction-consensus framework in which CBBA's deterministic bidding mechanism is replaced by a neural bidding policy trained using reinforcement learning. Under a centralized training and decentralized execution paradigm, agents learn to compute task bids from partial local observations while retaining the standard auction and consensus phases for decentralized coordination. The learned bidding policy is trained using Proximal Policy Optimization with rewards shaped by proximity to globally optimal solutions obtained via mixed-integer linear programming. Multiple neural architectures are evaluated, including a Neural Additive Model, the Long Short-Term Memory (LSTM) model, and the Set Transformer Model. Experimental results across varying swarm sizes demonstrate that learned bidding policies can improve solution quality over classical CBBA while preserving decentralized execution. The proposed approach highlights the effectiveness of integrating reinforcement learning with classical distributed coordination algorithms, offering a scalable pathway toward higher-quality decentralized multi-robot task allocation.
Jose Rodriguez, Constantine Tarawneh, Sven Koenig +2
This paper presents a scalable framework for multi-robot task allocation in complex environments where estimating task execution costs is computationally expensive. While combinatorial auction-based approaches offer reliable solutions, the exponential complexity of bundle generation typically renders them intractable for real-time reactive applications, particularly when accurate path planning is required for cost validation. We address this through a distributed, two-stage multi-fidelity bundle generation approach. Agents utilize a local search tree guided by a low-fidelity heuristic (such as euclidean distance) to rapidly explore the bundle space, applying high-fidelity path planning only to the most promising candidates in a best-first manner. These refined bids are then submitted to a central coordinator that solves a set packing problem to ensure global feasibility and maximize the overall utility. Simulation results in multiple environments demonstrate that the framework is able to improve the performance of reactive auction-based task allocation. Overall, the presented framework is shown to enable reactive task allocation with dynamic bundle sizes in multiple settings without exposing the agents' state and internal cost estimation models.
Niklas Dahlquist, Shridhar Velhal, George Nikolakopoulos