arXiv subjects

Solmaz S. Kia

Publications and source records attributed to Solmaz S. Kia.

At least 37 records · Page 2Linked to original sources

arXiv2021

Learning-based Measurement Scheduling for Loosely-Coupled Cooperative Localization

In cooperative localization, communicating mobile agents use inter-agent relative measurements to improve their dead-reckoning-based global localization. Measurement scheduling enables an agent to decide which subset of available inter-agent relative measurements it should process when its computational resources are limited. Optimal measurement scheduling is an NP-hard combinatorial optimization problem. The so-called sequential greedy (SG) algorithm is a popular suboptimal polynomial-time solution for this problem. However, the merit function evaluation for the SG algorithms requires access to the state estimate vector and error covariance matrix of all the landmark agents (teammates that an agent can take measurements from). This paper proposes a measurement scheduling for CL that follows the SG approach but reduces the communication and computation cost by using a neural network-based surrogate model as a proxy for the SG algorithm's merit function. The significance of this model is that it is driven by local information and only a scalar metadata from the landmark agents. This solution addresses the time and memory complexity issues of running the SG algorithm in three ways: (a) reducing the inter-agent communication message size, (b) decreasing the complexity of function evaluations by using a simpler surrogate (proxy) function, (c) reducing the required memory size.Simulations demonstrate our results.

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arXiv2021

Privacy preservation in continuous-time average consensus algorithm via deterministic additive obfuscation signals

This paper considers the problem of privacy preservation against passive internal and external malicious agents in the continuous-time Laplacian average consensus algorithm over strongly connected and weight-balanced digraphs. For this problem, we evaluate the effectiveness of use of additive perturbation signals as a privacy preservation measure against malicious agents that know the graph topology. Our results include (a) identifying the necessary and sufficient conditions on admissible additive perturbation signals that do not perturb the convergence point of the algorithm from the average of initial values of the agents; (b) obtaining the necessary and sufficient condition on the knowledge set of a malicious agent that enables it to identify the initial value of another agent; (c) designing observers that internal and external malicious agents can use to identify the initial conditions of another agent when their knowledge set on that agent enables them to do so. We demonstrate our results through a numerical example.

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arXiv2021

Distributed Strategy Selection: A Submodular Set Function Maximization Approach

Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain. Submodular set function optimization problems, however, are known to be NP-hard. This paper considers a class of submodular optimization problems that consist of maximization of a monotone and submodular set function subject to a uniform matroid constraint over a group of networked agents that communicate over a connected undirected graph. We work in the value oracle model where the only access of the agents to the utility function is through a black box that returns the utility function value. We propose a distributed suboptimal polynomial-time algorithm that enables each agent to obtain its respective strategy via local interactions with its neighboring agents. Our solution is a fully distributed gradient-based algorithm using the submodular set functions' multilinear extension followed by a distributed stochastic Pipage rounding procedure. This algorithm results in a strategy set that when the team utility function is evaluated at worst case, the utility function value is in 1/c(1-e^(-c)-O(1/T)) of the optimal solution with c to be the curvature of the submodular function. An example demonstrates our results.

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arXiv2021

A Distributed Continuous-time Modified Newton-Raphson Algorithm

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the continuous-time Newton-Raphson method, however structurally, it is amenable to a more efficient distributed implementation. We present a distributed implementation of our proposed optimization algorithm and prove its convergence via Lyapunov analysis. A numerical example demonstrates our results.

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arXiv2021

Cluster-based Distributed Augmented Lagrangian Algorithm for a Class of Constrained Convex Optimization Problems

We propose a distributed solution for a constrained convex optimization problem over a network of clustered agents each consisted of a set of subagents. The communication range of the clustered agents is such that they can form a connected undirected graph topology. The total cost in this optimization problem is the sum of the local convex costs of the subagents of each cluster. We seek a minimizer of this cost subject to a set of affine equality constraints, and a set of affine inequality constraints specifying the bounds on the decision variables if such bounds exist. We design our distributed algorithm in a cluster-based framework which results in a significant reduction in communication and computation costs. Our proposed distributed solution is a novel continuous-time algorithm that is linked to the augmented Lagrangian approach. It converges asymptotically when the local cost functions are convex and exponentially when they are strongly convex and have Lipschitz gradients. Moreover, we use an $ε$-exact penalty function to address the inequality constraints and derive an explicit lower bound on the penalty function weight to guarantee convergence to $ε$-neighborhood of the global minimum value of the cost. A numerical example demonstrates our results.

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arXiv2020

An IMM-based Decentralized Cooperative Localization with LoS and NLoS UWB Inter-agent Ranging

This paper investigates an infra-structure free global localization of a group of communicating mobile agents (e.g., first responders or exploring robots) via an ultra-wideband (UWB) inter-agent ranging aided dead-reckoning. We propose a loosely coupled cooperative localization algorithm that acts as an augmentation atop the local dead-reckoning system of each mobile agent. This augmentation becomes active only when an agent wants to process a relative measurement it has taken. The main contribution of this paper is addressing the challenges in the proper processing of the UWB range measurements in the framework of a loosely coupled cooperative localization. Even though UWB offers a decimeter level accuracy in line-of-sight (LoS) ranging, its accuracy degrades significantly in non-line-of-sight (NLoS) due to the significant unknown positive bias in the measurements. Thus, the measurement models for the UWB LoS and NLoS ranging conditions are different, and proper processing of NLoS measurements requires a bias compensation measure. We also show that, in practice, the measurement modal discriminators determine the type of UWB range measurements should be probabilistic. To take into account the probabilistic nature of the NLoS identifiers when processing UWB inter-agent ranging feedback, we employ an interacting multiple model (IMM) estimator in our localization filter. We also propose a bias compensation method for NLoS UWB measurements. The effectiveness of our cooperative localization is demonstrated via an experiment for a group of pedestrians who use UWB relative range measurements among themselves to improve their shoe-mounted INS geolocation.

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arXiv2020

Deterministic Privacy Preservation in Static Average Consensus Problem

In this paper we consider the problem of privacy preservation in the static average consensus problem. This problem normally is solved by proposing privacy preservation augmentations for the popular first order Laplacian-based algorithm. These mechanisms however come with computational overhead, may need coordination among the agents to choose their parameters and also alter the transient response of the algorithm. In this paper we show that an alternative iterative algorithm that is proposed in the literature in the context of dynamic average consensus problem has intrinsic privacy preservation and can be used as a privacy preserving algorithm that yields the same performance behavior as the well-known Laplacian consensus algorithm but without the overheads that come with the existing privacy preservation methods.

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arXiv2020

Multi-Agent Maximization of a Monotone Submodular Function via Maximum Consensus

Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain. However, submodular set function optimization problems are known to be NP-hard. In this paper, we consider a class of submodular optimization problems that consists of maximization of a monotone and submodular set function subject to a uniform matroid constraint over a group of networked agents that communicate over a connected undirected graph. Our objective is to obtain a distributed suboptimal polynomial-time algorithm that enables each agent to obtain its respective policy via local interactions with its neighboring agents. Our solution is a fully distributed gradient-based algorithm using the multilinear extension of the submodular set functions and exploiting a maximum consensus scheme. This algorithm results in a policy set that when the team objective function is evaluated at worst case the objective function value is in $1-1/e-O(1/T)$ of the optimal solution. An example demonstrates our results.

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arXiv2020

A sub-modular receding horizon solution for mobile multi-agent persistent monitoring

We study the problem of persistent monitoring of a finite number of inter-connected geographical nodes by a group of heterogeneous mobile agents. We assign to each geographical node a concave and increasing reward function that resets to zero after an agent's visit. Then, we design the optimal dispatch policy of which nodes to visit at what time and by what agent by finding a policy set that maximizes a utility that is defined as the total reward collected at visit times. We show that this optimization problem is NP-hard and its computational complexity increases exponentially with the number of the agents and the length of the mission horizon. By showing that the utility function is a monotone increasing and submodular set function of agents' policy, we proceed to propose a suboptimal dispatch policy design with a known optimality gap. To reduce the time complexity of constructing the feasible search set and also to induce robustness to changes in the operational factors, we perform our suboptimal policy design in a receding horizon fashion. Then, to compensate for the shortsightedness of the receding horizon approach for reward distribution beyond the feasible policies of the agents over the receding horizon, we add a new term to our utility, which provides a measure of nodal importance beyond the receding horizon's sight. This term gives the policy design an intuition to steer the agents towards the nodes with higher rewards on the patrolling graph. Finally, we discuss how our proposed algorithm can be implemented in a decentralized manner. A simulation study demonstrates our results.

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arXiv2020

A distributed service-matching coverage via heterogeneous mobile agents

We propose a distributed deployment solution for a group of mobile agents that should provide a service for a dense set of targets. The agents are heterogeneous in a sense that their quality of service (QoS), modeled as a spatial Gaussian distribution, is different. To provide the best service, the objective is to deploy the agents such that their collective QoS distribution is as close as possible to the density distribution of the targets. We propose a distributed consensus-based expectation-maximization (EM) algorithm to estimate the target density distribution, modeled as a Gaussian mixture model (GMM). The GMM not only gives an estimate of the targets' distribution, but also partitions the area to subregions, each of which is represented by one of the GMM's Gaussian bases. We use the Kullback-Leibler divergence (KLD) to evaluate the similarity between the QoS distribution of each agent and each Gaussian basis/subregion. Then, a distributed assignment problem is formulated and solved as a discrete optimal mass transport problem that allocates each agent to a subregion by taking the KLD as the assignment cost. We demonstrate our results by a sensor deployment for event detection where the sensor's QoS is modeled as an anisotropic Gaussian distribution.

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arXiv2020

Dynamic Active Average Consensus and its Application in Containment Control

This paper proposes a continuous-time dynamic active weighted average consensus algorithm in which the agents can alternate between active and passive modes depending on their ability to access to their reference input. The objective is to enable all the agents, both active and passive, to track the weighted average of the reference inputs of the active agents. The algorithm is modeled as a switched linear system whose convergence properties are carefully studied considering the agents' piece-wise constant access to the reference signals and possible piece-wise constant weights of the agents. We also study the discrete-time implementation of this algorithm. Next, we show how a containment control problem, in which a group of followers should track the convex hull of a set of observed leaders, can be cast as an active average consensus problem, and solved efficiently by our proposed dynamic active average consensus algorithm. Numerical examples demonstrate our results.

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arXiv2019

A Study on Accelerating Average Consensus Algorithms Using Delayed Feedback

In this paper, we study accelerating a Laplacian-based dynamic average consensus algorithm by splitting the conventional delay-free disagreement feedback into weighted summation of a current and an outdated term. We determine for what weighted sum there exists a range of time delay that results in the higher rate of convergence for the algorithm. For such weights, using the Lambert W function, we obtain the rate increasing range of the time delay, the maximum reachable rate and comment on the value of the corresponding maximizer delay. We also study the effect of use of outdated feedback on the control effort of the agents and show that only for some specific affine combination of the immediate and outdated feedback the control effort of the agents does not go beyond that of the delay-free algorithm. Additionally, we demonstrate that using outdated feedback does not increase the steady state tracking error of the average consensus algorithm. Lastly, we determine the optimum combination of the current and the outdated feedback weights to achieve the maximum increase in the rate of convergence without increasing the control effort of the agents. We demonstrate our results through a numerical example.

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arXiv2019

Distributed Leader Following of an Active Leader for Linear Heterogeneous Multi-Agent Systems

This paper considers a leader-following problem for a group of heterogeneous linear time invariant (LTI) followers that are interacting over a directed acyclic graph. Only a subset of the followers has access to the state of the leader in specific sampling times. The dynamics of the leader that generates its sampled states is unknown to the followers. For interaction topologies in which the leader is a global sink in the graph, we propose a distributed algorithm that allows the followers to arrive at the sampled state of the leader by the time the next sample arrives. Our algorithm is a practical solution for a leader-following problem when there is no information available about the state of the leader except its instantaneous value at the sampling times. Our algorithm also allows the followers to track the sampled state of the leader with a locally chosen offset that can be time-varying. When the followers are mobile agents whose state or part of their state is their position vector, the offset mechanism can be used to enable the followers to form a transnational invariant formation about the sampled state of the leader. We prove that the control input of the followers to take them from one sampled state to the next one is minimum energy. We also show in case of the homogeneous followers, after the first sampling epoch the states and inputs of all the followers are synchronized with each other. Numerical examples demonstrate our results.

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arXiv2019

Cooperative Localization under Limited Connectivity

We report two decentralized multi-agent cooperative localization algorithms in which, to reduce the communication cost, inter-agent state estimate correlations are not maintained but accounted for implicitly. In our first algorithm, to guarantee filter consistency, we account for unknown inter-agent correlations via an upper bound on the joint covariance matrix of the agents. In the second method, we use an optimization framework to estimate the unknown inter-agent cross-covariance matrix. In our algorithms, each agent localizes itself in a global coordinate frame using a local filter driven by local dead reckoning and occasional absolute measurement updates, and opportunistically corrects its pose estimate whenever it can obtain relative measurements with respect to other mobile agents. To process any relative measurement, only the agent taken the measurement and the agent the measurement is taken from need to communicate with each other. Consequently, our algorithms are decentralized algorithms that do not impose restrictive network-wide connectivity condition. Moreover, we make no assumptions about the type of agents or relative measurements. We demonstrate our algorithms in simulation and a robotic~experiment.

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arXiv2019

On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems

This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems the delay can lead to increase in the rate of convergence, (b) the exact range of time delay for which the rate of convergence is greater than that of the delay free system, and (c) an estimate on the value of the delay that leads to the maximum rate of convergence. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. We demonstrate our results through a numerical example on the practical application in accelerating an agreement algorithm for networked~systems by use of a delayed feedback.

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arXiv2018

On Robustness Analysis of a Dynamic Average Consensus Algorithm to Communication Delay

This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents' reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of the SCWB digraphs. We also show that for delays in the admissible bound, for static signals the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results.

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arXiv2018

Tutorial on dynamic average consensus: the problem, its applications, and the algorithms

This paper considers the problem of dynamic average consensus algorithm design for a group of communicating agents. This problem consists of designing a distributed algorithm that enables a group of agents with communication and computation capabilities to use local interactions to track the average of locally time-varying reference signals at each agent. The objective of this article is to provide an overview of the dynamic average consensus problem that serves as a comprehensive introduction to the problem definition, its applications, and the distributed methods available to solve them. Our primary intention, rather than providing a full account of all the available literature, is to introduce the reader, in a tutorial fashion, to the main ideas behind dynamic average consensus algorithms, the performance trade-offs considered in their design, and the requirements needed for their analysis and convergence guarantees.

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arXiv2017

Server assisted distributed cooperative localization over unreliable communication links

This paper considers the problem of cooperative localization (CL) using inter-robot measurements for a group of networked robots with limited on-board resources. We propose a novel recursive algorithm in which each robot localizes itself in a global coordinate frame by local dead reckoning, and opportunistically corrects its pose estimate whenever it receives a relative measurement update message from a server. The computation and storage cost per robot in terms of the size of the team is of order O(1), and the robots are only required to transmit information when they are involved in a relative measurement. The server also only needs to compute and transmit update messages when it receives an inter-robot measurement. We show that under perfect communication, our algorithm is an alternative but exact implementation of a joint CL for the entire team via Extended Kalman Filter (EKF). The perfect communication however is not a hard requirement. In fact, we show that our algorithm is intrinsically robust with respect to communication failures, with formal guarantees that the updated estimates of the robots receiving the update message are of minimum variance in a first-order approximate sense at that given timestep. We demonstrate the performance of the algorithm in simulation and experiments.

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