We describe a probabilistic framework for synthesizing control policies for general multi-robot systems, given environment and sensor models and a cost function. Decentralized, partially observable Markov decision processes (Dec-POMDPs) are a general model of decision processes where a team of agents must cooperate to optimize some objective (specified by a shared reward or cost function) in the presence of uncertainty, but where communication limitations mean that the agents cannot share their state, so execution must proceed in a decentralized fashion. While Dec-POMDPs are typically intractable to solve for real-world problems, recent research on the use of macro-actions in Dec-POMDPs has significantly increased the size of problem that can be practically solved as a Dec-POMDP. We describe this general model, and show how, in contrast to most existing methods that are specialized to a particular problem class, it can synthesize control policies that use whatever opportunities for coordination are present in the problem, while balancing off uncertainty in outcomes, sensor information, and information about other agents. We use three variations on a warehouse task to show that a single planner of this type can generate cooperative behavior using task allocation, direct communication, and signaling, as appropriate.
Emery- @cite_33 introduced a (cooperative) game-theoretic formalization of multi-robot systems which resulted in solving a Dec-POMDP. An approximate forward search algorithm was used to generate solutions, but because a (relatively) low-level Dec-POMDP was used scalability was limited. Also, @cite_24 introduce an MDP-based model where a set of robots with controllers that can execute for varying amount of time must cooperate to solve a problem. However, decision-making in their system is centralized.
@cite_24 @cite_33
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We introduce a principled method for multi-robot coordination based on a general model termed a MacDec-POMDP of multi-robot cooperative planning in the presence of stochasticity, uncertain sensing, and communication limitations. A new MacDec-POMDP planning algorithm is presented that searches over policies represented as finite-state controllers, rather than the previous policy tree representation. Finite-state controllers can be much more concise than trees, are much easier to interpret, and can operate over an infinite horizon. The resulting policy search algorithm requires a substantially simpler simulator that models only the outcomes of executing a given set of motor controllers, not the details of the executions themselves and can solve significantly larger problems than existing MacDec-POMDP planners. We demonstrate significant performance improvements over previous methods and show that our method can be used for actual multi-robot systems through experiments on a cooperative multi-robot bartending domain. Planning under uncertainty faces a scalability problem when considering multi-robot teams, as the information space scales exponentially with the number of robots. To address this issue, this paper proposes to decentralize multi-robot partially observable Markov decision processes (POMDPs) while maintaining cooperation between robots by using POMDP policy auctions. Auctions provide a flexible way of coordinating individual policies modeled by POMDPs and have low communication requirements. In addition, communication models in the multi-agent POMDP literature severely mismatch with real inter-robot communication. We address this issue by exploiting a decentralized data fusion method in order to efficiently maintain a joint belief state among the robots. The paper presents two different applications: environmental monitoring with unmanned aerial vehicles (UAVs); and cooperative tracking, in which several robots have to jointly track a moving target of interest. The first one is used as a proof of concept and illustrates the proposed ideas through different simulations. The second one adds real multi-robot experiments, showcasing the flexibility and robust coordination that our techniques can provide. There has been substantial progress on algorithms for single-agent sequential decision making using partially observable Markov decision processes (POMDPs). A number of efficient algorithms for solving POMDPs share two desirable properties: error-bounds and fast convergence rates. Despite significant efforts, no algorithms for solving decentralized POMDPs benefit from these properties, leading to either poor solution quality or limited scalability. This paper presents the first approach for solving transition independent decentralized Markov decision processes (Dec-MDPs), that inherits these properties. Two related algorithms illustrate this approach. The first recasts the original problem as a deterministic and completely observable Markov decision process. In this form, the original problem is solved by combining heuristic search with constraint optimization to quickly converge into a near-optimal policy. This algorithm also provides the foundation for the first algorithm for solving infinite-horizon transition independent decentralized MDPs. We demonstrate that both methods outperform state-of-the-art algorithms by multiple orders of magnitude, and for infinite-horizon decentralized MDPs, the algorithm is able to construct more concise policies by searching cyclic policy graphs. Decentralized partially observable Markov decision processes (Dec-POMDPs) constitute an expressive framework for multiagent planning under uncertainty, but solving them is provably intractable. We demonstrate how their scalability can be improved by exploiting locality of interaction between agents in a factored representation. Factored Dec-POMDP representations have been proposed before, but only for Dec-POMDPs whose transition and observation models are fully independent. Such strong assumptions simplify the planning problem, but result in models with limited applicability. By contrast, we consider general factored Dec-POMDPs for which we analyze the model dependencies over space (locality of interaction) and time (horizon of the problem). We also present a formulation of decomposable value functions. Together, our results allow us to exploit the problem structure as well as heuristics in a single framework that is based on collaborative graphical Bayesian games (CGBGs). A preliminary experiment shows a speedup of two orders of magnitude.