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In this paper, we propose a computationally efficient, robust density control strategy for the mean-field model of a robotic swarm. We formulate a static optimal control problem (OCP) that computes a robot velocity field which drives the…

Optimization and Control · Mathematics 2022-12-06 Carlo Sinigaglia , Andrea Manzoni , Francesco Braghin , Spring Berman

This study investigates the use of global control strategies to enhance the directed migration of swarms of interacting self-propelled particles confined in a channel. Uncontrolled dynamics naturally leads to wall accumulation, clogging,…

Soft Condensed Matter · Physics 2025-12-03 Chiara Calascibetta , Laëtitia Giraldi , Jérémie Bec

In this paper, we consider the problem of optimally guiding a large-scale swarm of underwater vehicles that is tasked with the indirect control of an advection-diffusion environmental field. The microscopic vehicle dynamics are governed by…

Optimization and Control · Mathematics 2022-02-21 Carlo Sinigaglia , Andrea Manzoni , Francesco Braghin , Spring Berman

This paper presents a novel density control framework for multi-robot systems with spatial safety and energy sustainability guarantees. Stochastic robot motion is encoded through the Fokker-Planck Partial Differential Equation (PDE) at the…

Systems and Control · Electrical Eng. & Systems 2026-05-25 Longchen Niu , Andrew Nasif , Gennaro Notomista

This paper introduces a safety-critical optimization-based control strategy that leverages control Lyapunov and control barrier functions to guide the spatial density of robotic swarms governed by the Fokker-Planck equation to a predefined…

Systems and Control · Electrical Eng. & Systems 2026-05-04 Longchen Niu , Gennaro Notomista

This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage…

Systems and Control · Computer Science 2017-11-30 Karthik Elamvazhuthi , Hendrik Kuiper , Spring Berman

We study the problem of distributed control of large-scale robotic swarms which can be modeled as continuum densities evolving under the continuity equation. We propose a formalization of distributed controllers as (generally nonlinear)…

Systems and Control · Electrical Eng. & Systems 2026-05-01 Max Emerick , Saroj Prasad Chhatoi , Bassam Bamieh

Optimal control of large particle systems with collective dynamics by few agents is a subject of high practical importance (e.g. in evacuation dynamics), but still limited mathematical basis. In particular the transition from discrete…

Optimization and Control · Mathematics 2016-10-06 Martin Burger , René Pinnau , Andreas Roth , Claudia Totzeck , Oliver Tse

L\'{e}vy robotic systems combine superdiffusive random movement with emergent collective behaviour from local communication and alignment in order to find rare targets or track objects. In this article we derive macroscopic fractional PDE…

Robotics · Computer Science 2020-03-06 Gissell Estrada-Rodriguez , Heiko Gimperlein

We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…

Optimization and Control · Mathematics 2021-02-01 Simone Göttlich , Claudia Totzeck

With the rapid development of AI and robotics, transporting a large swarm of networked robots has foreseeable applications in the near future. Existing research in swarm robotics has mainly followed a bottom-up philosophy with predefined…

Systems and Control · Electrical Eng. & Systems 2022-10-04 Tongjia Zheng , Qing Han , Hai Lin

Classical flocking models demonstrate how local interactions generate emergent order, but real-world multi-agent deployments are bound by severe constraints: limited actuator availability, heterogeneous communication latencies, and…

Optimization and Control · Mathematics 2026-05-04 Jiguang Yu

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

Numerical Analysis · Mathematics 2021-09-09 Mildred Aduamoah , Benjamin D. Goddard , John W. Pearson , Jonna C. Roden

We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…

Optimization and Control · Mathematics 2021-08-18 Yongxin Chen

Modern applications, such as orchestrating the collective behavior of robotic swarms or traffic flows, require the coordination of large groups of agents evolving in unstructured environments, where disturbances and unmodeled dynamics are…

Systems and Control · Electrical Eng. & Systems 2026-02-11 Gian Carlo Maffettone , Davide Salzano , Mario di Bernardo

This paper investigates efficient techniques to collect and concentrate an under-actuated particle swarm despite obstacles. Concentrating a swarm of particles is of critical importance in health-care for targeted drug delivery, where…

Robotics · Computer Science 2017-01-03 Arun V. Mahadev , Dominik Krupke , Jan-Marc Reinhardt , Sándor P. Fekete , Aaron T. Becker

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's…

Systems and Control · Computer Science 2018-10-02 Bryce Doerr , Richard Linares

Micro- and nanorobots are often controlled by global input signals, such as an electromagnetic or gravitational field. These fields move each robot maximally until it hits a stationary obstacle or another stationary robot. This paper…

Robotics · Computer Science 2014-02-18 Aaron Becker , Erik D. Demaine , Sándor P. Fekete , James McLurkin

In the present paper we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with…

Optimization and Control · Mathematics 2016-09-26 Mattia Bongini , Giuseppe Buttazzo

Manipulation of large systems of active particles is a serious challenge across diverse domains, including crowd management, control of robotic swarms, and coordinated material transport. The development of advanced control strategies for…

Robotics · Computer Science 2025-12-15 Albina Klepach , Egor E. Nuzhin , Alexey A. Tsukanov , Nikolay V. Brilliantov
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