arXiv subjects

Kooktae Lee

Publications and source records attributed to Kooktae Lee.

At least 19 recordsLinked to original sources

arXiv2026

Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems

This paper addresses the decentralized non-uniform area coverage problem for multi-agent systems, a critical task in missions with high spatial priority and resource constraints. While existing density-based methods often rely on computationally heavy Eulerian PDE solvers or heuristic planning, we propose Stochastic Density-Driven Optimal Control (D$^2$OC). This is a rigorous Lagrangian framework that bridges the gap between individual agent dynamics and collective distribution matching. By formulating a stochastic MPC-like problem that minimizes the Wasserstein distance as a running cost, our approach ensures that the time-averaged empirical distribution converges to a non-parametric target density under stochastic LTI dynamics. A key contribution is the formal convergence guarantee established via reachability analysis, providing a bounded tracking error even in the presence of process and measurement noise. Numerical results verify that Stochastic D$^2$OC achieves robust, decentralized coverage while outperforming previous heuristic methods in optimality and consistency.

math.OC↗

arXiv2026

Feedforward Density-Driven Optimal Control for Tracking Time-Varying Distributions with Guaranteed Stability

This paper addresses the spatiotemporal mismatch in multi-agent distribution tracking within time-varying environments. While recent advancements in Density-Driven Optimal Control (D$^2$OC) have enabled finite-time distribution matching using Optimal Transport theory, existing formulations primarily assume a stationary reference density. In dynamic scenarios, such as tracking evolving wildfires or moving plumes, this assumption leads to a structural tracking lag where the agent configuration inevitably falls behind the shifting reference flow. To resolve this, we propose a feedforward-augmented D$^2$OC framework that explicitly incorporates the reference velocity field, modeled via the continuity equation, into the control law. We provide a formal mathematical quantification of the induced tracking lag and analytically prove that the proposed predictive mechanism effectively reduces the cumulative tracking error. Furthermore, an analytical ultimate bound for the local Wasserstein distance is established under discretization errors and transport jitter. Theoretical analysis and numerical results demonstrate that our approach significantly mitigates tracking latency, ensuring robust and high-fidelity tracking performance in rapidly changing environments.

eess.SY↗

arXiv2026

Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC

Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems. Prior research on Density-Driven Optimal Control (D2OC) established a framework to match agent trajectories to a desired spatial distribution. However, implementing this as a predictive controller requires solving a large-scale Karush-Kuhn-Tucker (KKT) system, whose computational complexity grows cubically with the prediction horizon. To resolve this, we propose an analytical structural reduction that transforms the T-horizon KKT system into a condensed quadratic program (QP). This formulation achieves O(T) linear scalability, significantly reducing the online computational burden compared to conventional O(T^3) approaches. Furthermore, to ensure rigorous convergence in dynamic environments, we incorporate a contractive Lyapunov constraint and prove the Input-to-State Stability (ISS) of the closed-loop system against reference propagation drift. Numerical simulations verify that the proposed method facilitates rapid density coverage with substantial computational speed-up, enabling long-horizon predictive control for large-scale multi-agent swarms.

math.OC↗

arXiv2026

AI-Augmented Density-Driven Optimal Control (D2OC) for Decentralized Environmental Mapping

This paper presents an AI-augmented decentralized framework for multi-agent (multi-robot) environmental mapping under limited sensing and communication. While conventional coverage formulations achieve effective spatial allocation when an accurate reference map is available, their performance deteriorates under uncertain or biased priors. The proposed method introduces an adaptive and self-correcting mechanism that enables agents to iteratively refine local density estimates within an optimal transport-based framework, ensuring theoretical consistency and scalability. A dual multilayer perceptron (MLP) module enhances adaptivity by inferring local mean-variance statistics and regulating virtual uncertainty for long-unvisited regions, mitigating stagnation around local minima. Theoretical analysis rigorously proves convergence under the Wasserstein metric, while simulation results demonstrate that the proposed AI-augmented Density-Driven Optimal Control consistently achieves robust and precise alignment with the ground-truth density, yielding substantially higher-fidelity reconstruction of complex multi-modal spatial distributions compared with conventional decentralized baselines.

cs.MA↗

arXiv2026

Optimal Transport-Based Decentralized Multi-Agent Distribution Matching

This paper presents a decentralized control framework for distribution matching in multi-agent systems (MAS), where agents collectively achieve a prescribed terminal spatial distribution. The problem is formulated using optimal transport (Wasserstein distance), which provides a principled measure of distributional discrepancy and serves as the basis for the control design. To avoid solving the global optimal transport problem directly, the distribution-matching objective is reformulated into a tractable per-agent decision process, enabling each agent to identify its desired terminal locations using only locally available information. A sequential weight-update rule is introduced to construct feasible local transport plans, and a memory-based correction mechanism is incorporated to maintain reliable operation under intermittent and range-limited communication. Convergence guarantees are established, showing cycle-wise improvement of a surrogate transport cost under both linear and nonlinear agent dynamics. Simulation results demonstrate that the proposed framework achieves effective and scalable distribution matching while operating fully in a decentralized manner.

eess.SY↗

arXiv2025

Breaking Symmetry-Induced Degeneracy in Multi-Agent Ergodic Coverage via Stochastic Spectral Control

Multi-agent ergodic coverage via Spectral Multiscale Coverage (SMC) provides a principled framework for driving a team of agents so that their collective time-averaged trajectories match a prescribed spatial distribution. While classical SMC has demonstrated empirical success, it can suffer from gradient cancellation, particularly when agents are initialized near symmetry points of the target distribution, leading to undesirable behaviors such as stalling or motion constrained along symmetry axes. In this work, we rigorously characterize the initial conditions and symmetry-induced invariant manifolds that give rise to such directional degeneracy in first-order agent dynamics. To address this, we introduce a stochastic perturbation combined with a contraction term and prove that the resulting dynamics ensure almost-sure escape from zero-gradient manifolds while maintaining mean-square boundedness of agent trajectories. Simulations on symmetric multi-modal reference distributions demonstrate that the proposed stochastic SMC effectively mitigates transient stalling and axis-constrained motion, while ensuring that all agent trajectories remain bounded within the domain.

eess.SY↗

arXiv2025

Collision-Aware Density-Driven Control of Multi-Agent Systems via Control Barrier Functions

This paper tackles the problem of safe and efficient area coverage using a multi-agent system operating in environments with obstacles. Applications such as environmental monitoring and search and rescue require robot swarms to cover large domains under resource constraints, making both coverage efficiency and safety essential. To address the efficiency aspect, we adopt the Density-Driven Control (D$^2$C) framework, which uses optimal transport theory to steer agents according to a reference distribution that encodes spatial coverage priorities. To ensure safety, we incorporate Control Barrier Functions (CBFs) into the framework. While CBFs are commonly used for collision avoidance, we extend their applicability by introducing obstacle-specific formulations for both circular and rectangular shapes. In particular, we analytically derive a unit normal vector based on the agent's position relative to the nearest face of a rectangular obstacle, improving safety enforcement in environments with non-smooth boundaries. Additionally, a velocity-dependent term is incorporated into the CBF to enhance collision avoidance. Simulation results validate the proposed method by demonstrating smoother navigation near obstacles and more efficient area coverage than the existing method, while still ensuring collision-free operation.

eess.SY↗

arXiv2025

On the Convergence of Density-Based Predictive Control for Multi-Agent Non-Uniform Area Coverage

This paper presents Density-based Predictive Control (DPC), a novel multi-agent control strategy for efficient non-uniform area coverage, grounded in optimal transport theory. In large-scale scenarios such as search and rescue or environmental monitoring, traditional uniform coverage fails to account for varying regional priorities. DPC leverages a pre-constructed reference distribution to allocate agents' coverage efforts, spending more time in high-priority or densely sampled regions. We analyze convergence conditions using the Wasserstein distance, derive an analytic optimal control law for unconstrained cases, and propose a numerical method for constrained scenarios. Simulations on first-order dynamics and linearized quadrotor models demonstrate that DPC achieves trajectories closely matching the non-uniform reference distribution, outperforming existing coverage methods.

eess.SY↗

arXiv2025

Connectivity-Preserving Multi-Agent Area Coverage via Optimal-Transport-Based Density-Driven Optimal Control (D2OC)

Multi-agent systems play a central role in area coverage tasks across search-and-rescue, environmental monitoring, and precision agriculture. Achieving non-uniform coverage, where spatial priorities vary across the domain, requires coordinating agents while respecting dynamic and communication constraints. Density-driven approaches can distribute agents according to a prescribed reference density, but existing methods do not ensure connectivity. This limitation often leads to communication loss, reduced coordination, and degraded coverage performance. This letter introduces a connectivity-preserving extension of the Density-Driven Optimal Control (D2OC) framework. The coverage objective, defined using the Wasserstein distance between the agent distribution and the reference density, admits a convex quadratic program formulation. Communication constraints are incorporated through a smooth connectivity penalty, which maintains strict convexity, supports distributed implementation, and preserves inter-agent communication without imposing rigid formations. Simulation studies show that the proposed method consistently maintains connectivity, improves convergence speed, and enhances non-uniform coverage quality compared with density-driven schemes that do not incorporate explicit connectivity considerations.

eess.SY↗

arXiv2025

Density-Driven Multi-Agent Coordination for Efficient Farm Coverage and Management in Smart Agriculture

The growing scale of modern farms has increased the need for efficient and adaptive multi-agent coverage strategies for pest, weed, and disease management. Traditional methods such as manual inspection and blanket pesticide spraying often lead to excessive chemical use, resource waste, and environmental impact. While unmanned aerial vehicles (UAVs) offer a promising platform for precision agriculture through targeted spraying and improved operational efficiency, existing UAV-based approaches remain limited by battery life, payload capacity, and scalability, especially in large fields where single-UAV or uniformly distributed spraying is insufficient. Although multi-UAV coordination has been explored, many current frameworks still assume uniform spraying and do not account for infestation severity, UAV dynamics, non-uniform resource allocation, or energy-efficient coordination. To address these limitations, this paper proposes a Density-Driven Optimal Control (D2OC) framework that integrates Optimal Transport (OT) theory with multi-UAV coverage control for large-scale agricultural spraying. The method supports non-uniform, priority-aware resource allocation based on infestation intensity, reducing unnecessary chemical application. UAVs are modeled as a linear time-varying (LTV) system to capture variations in mass and inertia during spraying missions. The D2OC control law, derived using Lagrangian mechanics, enables efficient coordination, balanced workload distribution, and improved mission duration. Simulation results demonstrate that the proposed approach outperforms uniform spraying and Spectral Multiscale Coverage (SMC) in coverage efficiency, chemical reduction, and operational sustainability, providing a scalable solution for smart agriculture.

eess.SY↗

arXiv2025

Density-Driven Optimal Control for Non-Uniform Area Coverage in Decentralized Multi-Agent Systems Using Optimal Transport

This paper addresses the fundamental problem of non-uniform area coverage in multi-agent systems, where different regions require varying levels of attention due to mission-dependent priorities. Existing uniform coverage strategies are insufficient for realistic applications, and many non-uniform approaches either lack optimality guarantees or fail to incorporate crucial real-world constraints such as agent dynamics, limited operation time, the number of agents, and decentralized execution. To resolve these limitations, we propose a novel framework called Density-Driven Optimal Control (D2OC). The central idea of D2OC is the integration of optimal transport theory with multi-agent coverage control, enabling each agent to continuously adjust its trajectory to match a mission-specific reference density map. The proposed formulation establishes optimality by solving a constrained optimization problem that explicitly incorporates physical and operational constraints. The resulting control input is analytically derived from the Lagrangian of the objective function, yielding closed-form optimal solutions for linear systems and a generalizable structure for nonlinear systems. Furthermore, a decentralized data-sharing mechanism is developed to coordinate agents without reliance on global information. Comprehensive simulation studies demonstrate that D2OC achieves significantly improved non-uniform area coverage performance compared to existing methods, while maintaining scalability and decentralized implementability.

eess.SY↗

arXiv2020

Ergodic Control Strategy for Multi-Agent Environment Exploration

In this study, an ergodic environment exploration problem is introduced for a centralized multi-agent system. Given the reference distribution represented by the Mixture of Gaussian (MoG), the ergodicity is achieved when the time-averaged robot distribution is identical to the given reference distribution. The major challenge associated with this problem is to determine proper timing for a team of agents (robots) to visit each Gaussian component in the reference MoG for ergodicity. The ergodic function is defined as a measure of ergodicity and the condition for convergence is derived based on timing analysis. The proposed control strategy provides relatively reasonable performance to achieve the ergodicity. We provide the formal algorithm for centralized multi-agent control to achieve the ergodicity and simulation results are presented for the validation of the proposed algorithm.

eess.SY↗

arXiv2020

Efficient, Decentralized, and Collaborative Multi-Robot Exploration using Optimal Transport Theory

An Optimal Transport (OT)-based decentralized collaborative multi-robot exploration strategy is proposed in this paper. This method is to achieve an efficient exploration with a predefined priority in the given domain. In this context, the efficiency indicates how a team of robots (agents) cover the domain reflecting the corresponding priority map (or degrees of importance) in the domain. The decentralized exploration implies that each agent carries out their exploration task independently in the absence of any supervisory agent/computer. When an agent encounters another agent within a communication range, each agent receives the information about which areas are already covered by other agents, yielding a collaborative exploration. The OT theory is employed to quantify the difference between the distribution formed by the robot trajectories and the given reference spatial distribution indicating the priority. A computationally feasible way is developed to measure the performance of the proposed exploration scheme. Further, the formal algorithm is provided for the efficient, decentralized, and collaborative exploration plan. Simulation results are presented to validate the proposed methods.

eess.SY↗

arXiv2020

Efficient Multi-Robot Exploration with Energy Constraint based on Optimal Transport Theory

This paper addresses an Optimal Transport (OT)-based efficient multi-robot exploration problem, considering the energy constraints of a multi-robot system. The efficiency in this problem implies how a team of robots (agents) covers a given domain, reflecting a priority of areas of interest represented by a density distribution, rather than simply following a preset of uniform patterns. To achieve an efficient multi-robot exploration, the optimal transport theory that quantifies a distance between two density distributions is employed as a tool, which also serves as a means of performance measure. The energy constraints for the multi-robot system is then incorporated into the OT-based multi-robot exploration scheme. The proposed scheme is decoupled from robot dynamics, broadening the applicability of the multi-robot exploration plan to heterogeneous robot platforms. Not only the centralized but also decentralized algorithms are provided to cope with more realistic scenarios such as communication range limits between agents. To measure the exploration efficiency, the upper bound of the performance is developed for both the centralized and decentralized cases based on the optimal transport theory, which is computationally tractable as well as efficient. The proposed multi-robot exploration scheme is also applicable to a time-varying distribution, where the spatio-temporal evolution of the given reference distribution is desired. To validate the proposed method, multiple simulation results are provided.

eess.SY↗

arXiv2020

Asynchronous Distributed Averaging: A Switched System Framework for Average Error Analysis

This paper investigates an expected average error for distributed averaging problems under asynchronous updates. The asynchronism in this context implies no existence of a global clock as well as random characteristics in communication uncertainty such as communication delays and packet drops. Although some previous works contributed to the design of average consensus protocols to guarantee the convergence to an exact average, these methods may increase computational burdens due to extra works. Sometimes it is thus beneficial to make each agent exchange information asynchronously without modifying the algorithm, which causes randomness in the average value as a trade-off. In this study, an expected average error is analyzed based on the switched system framework, to estimate an upper bound of the asynchronous average compared to the exact one in the expectation sense. Numerical examples are provided to validate the proposed results.

eess.SY↗

arXiv2020

On the Ergodicity of an Autonomous Robot for Efficient Environment Explorations

This paper addresses the autonomous robot ergodicity problem for efficient environment exploration. The spatial distribution as a reference is given by a mixture of Gaussian and the mass generation of the robot is assumed to be skinny Gaussian. The main problem to solve is then to find out proper timing for the robot to visit as well as leave each component-wise Gaussian for the purpose of achieving the ergodicity. The novelty of the proposed method is that no approximation is required for the developed method. Given the definition of the ergodic function, a convergence condition is derived based on the timing analysis. Also, a formal algorithm to achieve the ergodicity is provided. To support the validity of the proposed algorithm, simulation results are provided.

eess.SY↗

arXiv2019

A Stabilizing Control Algorithm for Asynchronous Parallel Quadratic Programming via Dual Decomposition

This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data at each iteration step due to the interdependency of data. The synchronization latency may incur a large amount of waiting time caused by an idle process during computation. We aim to mitigate this synchronization penalty in PQP problems by implementing asynchronous updates of the dual variable. The price to pay for adopting asynchronous computing algorithms is the unpredictability of the solution, resulting in a tradeoff between speedup and accuracy. In the worst case, the state of interest may become unstable owing to the stochastic behavior of asynchrony. We investigate the stability condition of asynchronous PQP problems by employing the switched system framework. A formal algorithm is provided to ensure the asymptotic stability of dual variables. Further, it is shown that the implementation of the proposed algorithm guarantees the uniqueness of optimal solutions, irrespective of asynchronous behavior. To verify the validity of the proposed methods, simulation results are presented.

eess.SY↗

arXiv2016

Convergence Analysis of Asynchronous Consensus in Discrete-time Multi-agent Systems with Fixed Topology

In this paper, we study a convergence condition for asynchronous consensus problems in multi-agent systems. The convergence in this context implies the asynchronous consensus value converges to the synchronous one and is unique. Although it is reported in the literature that the consensus value under asynchronous communications may not coincide with the synchronous consensus value, it has not received much attention. In some applications, the discrepancy between them may result in serious consequences. For such applications it is critical to determine under what conditions the asynchronous consensus value is the same as the synchronous consensus value. We illustrate these issues with a few examples and then provide a condition, which guarantees that the asynchronous consensus value converges to the synchronous one. The validity of the proposed result is verified with simulations.

eess.SY↗