Optimal Mass Transport and Kernel Density Estimation for State-Dependent Networked Dynamic Systems

Badyn, Mathias Hudoba de; Eren, Utku; Açıkmeşe, Behçet; Mesbahi, Mehran

doi:10.1109/cdc.2018.8619808

Cited by 22 publications

(14 citation statements)

References 34 publications

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“…(0, T )), then the system (2) under (8) satisfies the regularity conditions (10) and (11). These requirements are mild and can be easily satisfied in practice.…”

Section: Robustness Of the Control Lawmentioning

confidence: 98%

“…The problem of field estimation and deployment has also been studied in recent works [11], [7], [8], [12]. In [8], [12], the authors also consider a field estimation problem followed by an optimal control formulation for swarm deployment.…”

Section: Introductionmentioning

confidence: 99%

“…However, the numerical solutions are usually open-loop and have robustness issues due to environmental uncertainty. In [11], [7], the authors formulate an optimal mass transport problem followed by mean-field feedback strategies. Our work differs in that we not only design closed-loop control laws but also study their robustness property.…”

Section: Introductionmentioning

confidence: 99%

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Field Estimation using Robotic Swarms through Bayesian Regression and Mean-Field Feedback

Zheng¹,

Lin²

2021

Preprint

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Recent years have seen an increased interest in using mean-field density based modelling and control strategy for deploying robotic swarms. In this paper, we study how to dynamically deploy the robots subject to their physical constraints to efficiently measure and reconstruct certain unknown spatial field (e.g. the air pollution index over a city). Specifically, the evolution of the robots' density is modelled by mean-field partial differential equations (PDEs) which are uniquely determined by the robots' individual dynamics. Bayesian regression models are used to obtain predictions and return a variance function that represents the confidence of the prediction. We formulate a PDE constrained optimization problem based on this variance function to dynamically generate a reference density signal which guides the robots to uncertain areas to collect new data, and design mean-field feedback-based control laws such that the robots' density converges to this reference signal. We also show that the proposed feedback law is robust to density estimation errors in the sense of input-to-state stability. Simulations are included to verify the effectiveness of the algorithms.

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“…(0, T )), then the system (2) under (8) satisfies the regularity conditions (10) and (11). These requirements are mild and can be easily satisfied in practice.…”

Section: Robustness Of the Control Lawmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Field Estimation using Robotic Swarms through Bayesian Regression and Mean-Field Feedback

Zheng¹,

Lin²

2021

Preprint

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“…Optimal transport [298] allows to achieve spatiallyorganizing behavior by transporting a swarm of agents, represented as a probability distribution, from its current distribution to a desired distribution while optimizing a cost function [206], [299], [300].…”

Section: Optimal Transport Based Algorithmmentioning

confidence: 99%

Review of Multi-Agent Algorithms for Collective Behavior: a Structural Taxonomy

et al. 2018

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In this paper, we review multi-agent collective behavior algorithms in the literature and classify them according to their underlying mathematical structure. For each mathematical technique, we identify the multi-agent coordination tasks it can be applied to, and we analyze its scalability, bandwidth use, and demonstrated maturity. We highlight how versatile techniques such as artificial potential functions can be used for applications ranging from low-level position control to high-level coordination and task allocation, we discuss possible reasons for the slow adoption of complex distributed coordination algorithms in the field, and we highlight areas for further research and development.

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“…More recently, researchers have studied real-time deployment (RTD) of multi-agent systems which is also called optimal mass transport (OMT) in the literature. In the OMT problem, agent coordination is governed by the continuity PDE and assigned by finding the optimal transformation between two arbitrary distributions with an equal mass [13], [14]. The existing OMT work assures convergence of agent deployment from an initial distribution to a target configuration.…”

Section: Introductionmentioning

confidence: 99%

Real-Time Deployment of a Large-Scale Multi-Quadcopter System (MQS)

Rastgoftar¹

2022

Preprint

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This paper presents a continuum mechanics-based approach for real-time deployment (RTD) of a multi-quadcopter system between moving initial and final configurations arbitrarily distributed in a 3-D motion space. The proposed RTD problem is decomposed into spatial planning, temporal planning and acquisition sub-problems. For the spatial planning, the RTD desired coordination is defined by integrating (i) rigid-body rotation, (ii) one-dimensional homogeneous deformation, and (ii) one-dimensional heterogeneous coordination such that necessary conditions for inter-agent collision avoidance between every two quadcopter UAVs are satisfied. By the RTD temporal planning, this paper suffices the inter-agent collision avoidance between every two individual quadcopters, and assures the boundedness of the rotor angular speeds for every individual quadcopter. For the RTD acquisition, each quadcopter modeled by a nonlinear dynamics applies a nonlinear control to stably and safely track the desired RTD trajectory such that the angular speeds of each quadcopter remain bounded and do not exceed a certain upper limit.

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Optimal Mass Transport and Kernel Density Estimation for State-Dependent Networked Dynamic Systems

Cited by 22 publications

References 34 publications

Field Estimation using Robotic Swarms through Bayesian Regression and Mean-Field Feedback

Field Estimation using Robotic Swarms through Bayesian Regression and Mean-Field Feedback

Review of Multi-Agent Algorithms for Collective Behavior: a Structural Taxonomy

Real-Time Deployment of a Large-Scale Multi-Quadcopter System (MQS)

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