Swarms of autonomous agents are useful in many applications due to their ability to accomplish tasks in a decentralized manner, making them more robust to failures. Due to the difficulty in running experiments with large numbers of... more
Swarms of autonomous agents are useful in many applications due to their ability to accomplish tasks in a decentralized manner, making them more robust to failures. Due to the difficulty in running experiments with large numbers of hardware agents, researchers often make simplifying assumptions and remove constraints that might be present in a real swarm deployment. While simplifying away some constraints is tolerable, we feel that two in particular have been overlooked: one, that agents in a swarm take up physical space, and two, that agents might be damaged in collisions. Many existing works assume agents have negligible size or pass through each other with no added penalty. It seems possible to ignore these constraints using collision avoidance, but we show using an illustrative example that this is easier said than done. In particular, we show that collision avoidance can interfere with the intended swarming behavior and significant parameter tuning is necessary to ensure the be...
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Abstract—This paper considers a class of scenarios where targets emerge from some known location and move towards some unknown destinations in a weighted acyclic digraph. A decision maker with knowledge of the target positions must decide... more
Abstract—This paper considers a class of scenarios where targets emerge from some known location and move towards some unknown destinations in a weighted acyclic digraph. A decision maker with knowledge of the target positions must decide when preparations should be made at any given destination for their arrival. The decision maker faces a timing trade-off: early decisions mean more time for preparation at the cost of higher uncertainty in the target’s true destination while later decisions mean less uncertainty at the cost of having less time to prepare. We show how this problem can be formulated as an optimal stopping problem on a Markov chain. This sets the basis for the introduction of the BEST INVESTMENT ALGORITHM which prescribes when investments must be made conditioned on the target’s motion along the digraph. We establish the optimality of this prescription and examine its robustness against changes in the problem parameters, identifying sufficient conditions to determine ...
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This paper considers a planar multi-agent coordination problem. Unlike other related works, we explicitly consider a globally shared wireless communication channel where individual agents must choose both a frequency and power to transmit... more
This paper considers a planar multi-agent coordination problem. Unlike other related works, we explicitly consider a globally shared wireless communication channel where individual agents must choose both a frequency and power to transmit their messages at. This problem is motivated by the pressing need for algorithms that are able to efficiently and reliably operate on overcrowded wireless networks or otherwise poor-performing RF environments. We develop a self-triggered coordination algorithm that guarantees convergence to the desired set of states with probability 1. The algorithm is developed by using ideas from event/self-triggered coordination and allows agents to autonomously decide for themselves when to broadcast information, at which frequency and power, and how to move based on information received from other agents in the network. Simulations illustrate our results.
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In this paper, we study the problem of certifying the stability of a closed loop system which receives feedback from an energy harvesting sensor. This is important, as energy harvesting sensors are recharged stochastically, and may only... more
In this paper, we study the problem of certifying the stability of a closed loop system which receives feedback from an energy harvesting sensor. This is important, as energy harvesting sensors are recharged stochastically, and may only be able to provide feedback intermittently. Thus, stabilizing plants with feedback provided by energy harvesting sensors is challenging in that the feedback signal is only available stochastically, complicating the analysis of the closed-loop system. As the main contribution of the paper, we show that for a broad class of energy harvesting processes and transmission policies, the system can be modeled as a Markov jump linear system (MJLS), which thereby enables a rigorous stability analysis. We discuss the types of transmission policies and energy harvesting processes which can be accommodated in detail, demonstrating the generality of the results.
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In this paper, we study the problem of computing the minimum battery capacity required to stabilize a scalar plant communicating with an energy harvesting sensor over a wireless communication channel. We prove that a particular greedy... more
In this paper, we study the problem of computing the minimum battery capacity required to stabilize a scalar plant communicating with an energy harvesting sensor over a wireless communication channel. We prove that a particular greedy battery management policy suffices to stabilize the plant, and demonstrate that stability of the system under the greedy policy can be checked by a linear program. Moreover, we show that a critical battery capacity exists, below which no policy can stabilize the system, which itself can be computed by solving a sequence of linear programs which grows logarithmically with respect to the maximum allowed storage capacity. The first of these results address an open question pertaining to the stability of energy harvesting control systems. The last allows us to efficiently compute the smallest battery capacity required to stabilize a given system, which addresses a problem of importance when device size or cost are significant concerns.
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This article provides an introduction to event-triggered coordination for multi-agent average consensus. We provide a comprehensive account of the motivations behind the use of event-triggered strategies for consensus, the methods for... more
This article provides an introduction to event-triggered coordination for multi-agent average consensus. We provide a comprehensive account of the motivations behind the use of event-triggered strategies for consensus, the methods for algorithm synthesis, the technical challenges involved in establishing desirable properties of the resulting implementations, and their applications in distributed control. We pay special attention to the assumptions on the capabilities of the network agents and the resulting features of the algorithm execution, including the interconnection topology, the evaluation of triggers, and the role of imperfect information. The issues raised in our discussion transcend the specific consensus problem and are indeed characteristic of cooperative algorithms for networked systems that solve other coordination tasks. As our discussion progresses, we make these connections clear, highlighting general challenges and tools to address them widespread in the event-trig...
This paper considers event-triggered strategies for the well-known multi-agent average consensus problem. While many results on this topic either require global knowledge of the network topology or cannot guarantee a positive minimum... more
This paper considers event-triggered strategies for the well-known multi-agent average consensus problem. While many results on this topic either require global knowledge of the network topology or cannot guarantee a positive minimum inter-event time, more recent works have been able to establish a positive minimum inter-event time using a fully distributed dynamic triggering mechanism. However, these results only apply to undirected communication networks and are tied to specific Lyapunov functions. This paper presents two different novel distributed dynamic event-triggered algorithms with designable positive minimum inter-event times for directed communication networks. We show that both algorithms have the same asymptotic convergence properties and compare their transient properties through simulations.
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This paper studies a pursuit-evasion problem involving a single pursuer and a single evader, where we are interested in developing a pursuit strategy that doesn't require continuous, or even periodic, information about the position of... more
This paper studies a pursuit-evasion problem involving a single pursuer and a single evader, where we are interested in developing a pursuit strategy that doesn't require continuous, or even periodic, information about the position of the evader. We propose a self-triggered control strategy that allows the pursuer to sample the evader's position autonomously, while satisfying desired performance metric of evader capture. The work in this paper builds on the previously proposed self-triggered pursuit strategy which guarantees capture of the evader in finite time with a finite number of evader samples. However, this algorithm relied on the unrealistic assumption that the evader's exact position was available to the pursuer. Instead, we extend our previous framework to develop an algorithm which allows for uncertainties in sampling the information about the evader, and derive tolerable upper-bounds on the error such that the pursuer can guarantee capture of the evader. In a...
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Swarms of autonomous agents are useful in many applications due to their ability to accomplish tasks in a decentralized manner, making them more robust to failures. Due to the difficulty in running experiments with large numbers of... more
Swarms of autonomous agents are useful in many applications due to their ability to accomplish tasks in a decentralized manner, making them more robust to failures. Due to the difficulty in running experiments with large numbers of hardware agents, researchers typically resort to simulations with simplifying assumptions. While some assumptions are tolerable, we feel that two assumptions have been overlooked: one, that agents take up physical space, and two, that a collision avoidance algorithm is available to add safety to an existing algorithm. While there do exist minimally invasive collision avoidance algorithms designed to add safety while minimizing interference in the intended behavior, we show they can still cause unexpected interference. We use an illustrative example with a double-milling behavior and show, through simulations, that the collision avoidance can still cause unexpected interference and careful parameter tuning is needed.
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We develop a robust moment closure for a general class of continuous-time epidemic spreading processes, the elements of which are prevalent in the literature. Our moment closure method takes as input a general stochastic compartmental... more
We develop a robust moment closure for a general class of continuous-time epidemic spreading processes, the elements of which are prevalent in the literature. Our moment closure method takes as input a general stochastic compartmental spreading process defined for $n$ agents and $m$ compartments, and produces a system of 2nm differential equations whose solutions provide nontrivial approximations to the marginal compartmental membership probabilities for each agent. This is an improvement over the commonly used mean-field type approximation, which provides no such guarantee. We demonstrate that our results provide useful predictions with examples performed on two models of competitive spreading processes, and find the developed closure to be more informative than mean-field approximations.
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A k-order coverage control problem is studied where a network of agents must deploy over a desired area. The objective is to deploy all the agents in a decentralized manner such that a certain coverage performance metric of the network is... more
A k-order coverage control problem is studied where a network of agents must deploy over a desired area. The objective is to deploy all the agents in a decentralized manner such that a certain coverage performance metric of the network is maximized. Unlike many prior works that consider multiagent deployment, we explicitly consider applications where more than one agent may be required to service an event that randomly occurs anywhere in the domain. The proposed method ensures the distributed agents autonomously cover the area while simultaneously relaxing the requirement of constant communication among the agents. In order to achieve the stated goals, a self-triggered coordination method is developed that both determines how agents should move without having to continuously acquire information from other agents, as well as exactly when to communicate and acquire new information. Through analysis, the proposed strategy is shown to provide asymptotic convergence similar to that of co...
This paper revisits the multi-agent average consensus problem on weight-balanced directed graphs. In order to reduce communication among the agents, many recent works have considered event-triggered communication and control as a method... more
This paper revisits the multi-agent average consensus problem on weight-balanced directed graphs. In order to reduce communication among the agents, many recent works have considered event-triggered communication and control as a method to reduce communication while still ensuring that the entire network converges to the desired state. One common way to do this is to design events such that a specifically chosen Lyapunov function is monotonically decreasing; however, depending on the chosen Lyapunov function the transient behaviors can be very different. Consequently, we are instead interested in considering a class of Lyapunov functions such that each Lyapunov function produces a different event-triggered coordination algorithm to solve the multi-agent average consensus problem. The proposed class of algorithms all guarantee exponential convergence of the resulting network and exclusion of Zeno behavior. This allows us to easily consider the implementation of different algorithms t...
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We propose a mathematical framework, based on conic geometric programming, to control a susceptible-infected-susceptible viral spreading process taking place in a directed contact network with unknown contact rates. We assume that we have... more
We propose a mathematical framework, based on conic geometric programming, to control a susceptible-infected-susceptible viral spreading process taking place in a directed contact network with unknown contact rates. We assume that we have access to time series data describing the evolution of the spreading process observed by a collection of sensor nodes over a finite time interval. We propose a data-driven robust convex optimization framework to find the optimal allocation of protection resources (e.g., vaccines and/or antidotes) to eradicate the viral spread at the fastest possible rate. In contrast to current network identification heuristics, in which a single network is identified to explain the observed data, we use available data to define an uncertainty set containing all networks that are coherent with empirical observations. Our characterization of this uncertainty set of networks is tractable in the context of conic geometric programming, recently proposed by Chandrasekar...
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Swarms of autonomous agents, through their decentralized and robust nature, show great promise as a future solution to the myriad missions of business, military, and humanitarian relief. The diverse nature of mission sets creates the need... more
Swarms of autonomous agents, through their decentralized and robust nature, show great promise as a future solution to the myriad missions of business, military, and humanitarian relief. The diverse nature of mission sets creates the need for swarm algorithms to be deployed on a variety of hardware platforms. Certain swarm behaviors have been demonstrated on platforms where collisions between agents are harmless, but on many platforms collisions are prohibited since they would damage the agents involved. The available literature typically assumes that collisions can be avoided by adding a collision avoidance algorithm on top of an existing swarm behavior. Through an illustrative example in our experience replicating a particular behavior, we show that this can be difficult to achieve since the swarm behavior can be disrupted by the collision avoidance. We introduce metrics quantifying the level of disruption in our swarm behavior and propose a technique that is able to assist in tun...
In this paper we consider an online planning problem for unmanned aerial vehicle (UAV) operations. Specifically, a UAV has the task of reaching a goal from a set of possible goals while minimizing the amount of energy required. Due to... more
In this paper we consider an online planning problem for unmanned aerial vehicle (UAV) operations. Specifically, a UAV has the task of reaching a goal from a set of possible goals while minimizing the amount of energy required. Due to unforeseen disturbances, it is possible that initially attractive goals might end up being very expensive during the execution. Thus, two main problems are investigated here: i) how to predict and plan the motion of the UAV at run time to minimize its energy consumption and ii) when to schedule next replanning time to avoid unnecessary periodic re-evaluation executions. Our approach considers a nonlinear model of the system for which a model predictive controller is used to determine the desired control inputs for each possible goal. These control inputs are then used to estimate the energy required to reach the different goals. Finally, a self-triggered scheduling policy determines how long to wait before replanning the goal to aim for. The proposed f...
In this work, we propose an event-triggered algorithm based on a virtual force deployment approach to address the multi-agent coverage control problem in the presence of obstacles. Unlike most works that consider this problem, we are... more
In this work, we propose an event-triggered algorithm based on a virtual force deployment approach to address the multi-agent coverage control problem in the presence of obstacles. Unlike most works that consider this problem, we are mainly interested in reducing the amount of communication and motion required by the agents to reach a configuration that increases the coverage throughout an environment of interest. In particular, most works that consider this problem assume agents are in constant communication with each other. Instead, the event-triggered algorithm we propose allows agents to decide for themselves when communication is necessary while still achieving the primary goal of covering the environment and ensuring collisions are avoided. Several simulations illustrate the result of our algorithm with and without the presence of an obstacle and compares it against a similar algorithm that does not consider event-triggered communication.
In this paper, we develop robust mechanisms for the prediction and control of a networked epidemic process. The work presented here is significant in that it addresses a long-standing open question in the field of control of networked... more
In this paper, we develop robust mechanisms for the prediction and control of a networked epidemic process. The work presented here is significant in that it addresses a long-standing open question in the field of control of networked epidemic processes by circumventing the need to heuristically approximate the system studied by mean-field models. This enables us to provide rigorous stochastic convergence guarantees on the epidemic model itself, improving over the mean-field type convergence results of most prior work. The prediction dynamics we construct follow from combining a multivariate comparison lemma, and the Frechet approximation of joint probabilities. The controller we construct uses the prediction dynamics to compute control actions which guarantee exponential decay in the level of exposure and infection in the spreading graph, which in simulation are often less costly than heuristic control methods. As an application, we use the developed framework for optimizing the us...
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This paper proposes and analyzes a stochastic Susceptible-Exposed-Infected-Removed (SEIR) spreading model on networks. Imagine a nursing home housing 28 seniors and 7 staff workers, in which one of the staff has tested positive for... more
This paper proposes and analyzes a stochastic Susceptible-Exposed-Infected-Removed (SEIR) spreading model on networks. Imagine a nursing home housing 28 seniors and 7 staff workers, in which one of the staff has tested positive for COVID-19. Unfortunately, the results of this test are 3 days late and the infected person had not been quarantining while waiting for their test results. What is now the individual risk to the different people living in this nursing home? If the home has access to two rapid COVID-19 viral tests, who should they be given to and why? In order to answer questions like this, we need to study stochastic models rather than deterministic ones. Unlike the vast majority of works that analyze various deterministic models, stochastic models are required when analyzing the risk of COVID-19 to individual people rather than tracking aggregate numbers in a given region. More specifically, this paper compares the results provided by analyzing stochastic and deterministic models and investigating when it is suitable to use the different models. In particular, we show why it is not suitable to use deterministic models when analyzing the spread in small communities and how these questions can be better addressed using stochastic ones. Finally, we show the added complications that arise due to the relatively long incubation period of COVID-19, and how it can be addressed. A simulated case study of the spread of COVID-19 in a 35-person nursing home is used to help illustrate our results.
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This paper proposes an asynchronous periodic event-triggered communication and control law to solve the multi-agent consensus problem. In contrast with similar works on periodic event-triggered coordination, we do not assume a common... more
This paper proposes an asynchronous periodic event-triggered communication and control law to solve the multi-agent consensus problem. In contrast with similar works on periodic event-triggered coordination, we do not assume a common sampling period among the agents. Since agents can only take actions (e.g., broadcast a message, update a control signal) at their own sampling times, agents in general do not have the luxury of being able to immediately react to new information received by neighbors as is often assumed in similar works. This type of model is much more pragmatic as it better accounts for different pieces of hardware/software operating at different frequencies. We provide sufficient conditions under which the proposed algorithm guarantees that the agents converge to a consensus state. Numerical experiments illustrate the effectiveness of the proposed strategy.
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— This paper considers a multi-agent consensus problem over strongly connected and balanced directed graphs. Unlike many works that consider continuous or periodic communication and control strategies, we are interested in developing an... more
— This paper considers a multi-agent consensus problem over strongly connected and balanced directed graphs. Unlike many works that consider continuous or periodic communication and control strategies, we are interested in developing an event-triggered algorithm to reduce the overall load of the network in terms of limited communication and control updates. Furthermore, we focus on a sampled-data implementation that allows agents in a communication network to determine whether locally sampled information should be discarded or broadcasted to neighbors. This formulation allows us to automatically rule out Zeno behavior that is often a challenge in distributed event-triggered systems. We show that all agents eventually rendezvous at the centroid of their initial formation given an appropriate selection of the local sampling period and event-triggering parameters. We demonstrate the effectiveness of the proposed communication and control law through simulations.