Towards time-varying proximal dynamics in Multi-Agent Network Games

Distributed decision making in multi-agent networks has recently attracted significant research attention thanks to its wide applicability, e.g. in the management and optimization of computer networks, power systems, robotic teams, sensor networks and consumer markets. Distributed decision-making problems can be modeled as inter-dependent optimization problems, i.e., multi-agent game-equilibrium seeking problems, where noncooperative agents seek an equilibrium by communicating over a network. To achieve a network equilibrium, the agents may decide to update their decision variables via proximal dynamics, driven by the decision variables of the neighboring agents. In this paper, we provide an operator-theoretic characterization of convergence with a time-invariant communication network. For the time-varying case, we consider adjacency matrices that may switch subject to a dwell time. We illustrate our investigations using a distributed robotic exploration example.Comment: 6 pages, 3 figure

Human-Robot Trust Integrated Task Allocation and Symbolic Motion planning for Heterogeneous Multi-robot Systems

This paper presents a human-robot trust integrated task allocation and motion planning framework for multi-robot systems (MRS) in performing a set of tasks concurrently. A set of task specifications in parallel are conjuncted with MRS to synthesize a task allocation automaton. Each transition of the task allocation automaton is associated with the total trust value of human in corresponding robots. Here, the human-robot trust model is constructed with a dynamic Bayesian network (DBN) by considering individual robot performance, safety coefficient, human cognitive workload and overall evaluation of task allocation. Hence, a task allocation path with maximum encoded human-robot trust can be searched based on the current trust value of each robot in the task allocation automaton. Symbolic motion planning (SMP) is implemented for each robot after they obtain the sequence of actions. The task allocation path can be intermittently updated with this DBN based trust model. The overall strategy is demonstrated by a simulation with 5 robots and 3 parallel subtask automata

Decentralized Control of Partially Observable Markov Decision Processes using Belief Space Macro-actions

The focus of this paper is on solving multi-robot planning problems in continuous spaces with partial observability. Decentralized partially observable Markov decision processes (Dec-POMDPs) are general models for multi-robot coordination problems, but representing and solving Dec-POMDPs is often intractable for large problems. To allow for a high-level representation that is natural for multi-robot problems and scalable to large discrete and continuous problems, this paper extends the Dec-POMDP model to the decentralized partially observable semi-Markov decision process (Dec-POSMDP). The Dec-POSMDP formulation allows asynchronous decision-making by the robots, which is crucial in multi-robot domains. We also present an algorithm for solving this Dec-POSMDP which is much more scalable than previous methods since it can incorporate closed-loop belief space macro-actions in planning. These macro-actions are automatically constructed to produce robust solutions. The proposed method's performance is evaluated on a complex multi-robot package delivery problem under uncertainty, showing that our approach can naturally represent multi-robot problems and provide high-quality solutions for large-scale problems

Planning for Decentralized Control of Multiple Robots Under Uncertainty

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

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019