Optimal collision avoidance in swarms of active Brownian particles

Borra, Francesco; Cencini, Massimo; Celani, Antonio

doi:10.1088/1742-5468/ac12c6

Cited by 5 publications

(3 citation statements)

References 39 publications

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“…Control problems of systems with incomplete information and memory limitation appear in many practical situations. These constraints become especially predominant when designing the control of small devices [ 1 , 2 ], and are important for understanding the control mechanisms of biological systems [ 3 , 4 , 5 , 6 , 7 , 8 ] because their sensors are extremely noisy and their controllers can only have severely limited memories.…”

Section: Introductionmentioning

confidence: 99%

Memory-Limited Partially Observable Stochastic Control and Its Mean-Field Control Approach

Tottori

Kobayashi

2022

Entropy

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Control problems with incomplete information and memory limitation appear in many practical situations. Although partially observable stochastic control (POSC) is a conventional theoretical framework that considers the optimal control problem with incomplete information, it cannot consider memory limitation. Furthermore, POSC cannot be solved in practice except in special cases. In order to address these issues, we propose an alternative theoretical framework, memory-limited POSC (ML-POSC). ML-POSC directly considers memory limitation as well as incomplete information, and it can be solved in practice by employing the technique of mean-field control theory. ML-POSC can generalize the linear-quadratic-Gaussian (LQG) problem to include memory limitation. Because estimation and control are not clearly separated in the LQG problem with memory limitation, the Riccati equation is modified to the partially observable Riccati equation, which improves estimation as well as control. Furthermore, we demonstrate the effectiveness of ML-POSC for a non-LQG problem by comparing it with the local LQG approximation.

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Section: Introductionmentioning

confidence: 99%

Memory-Limited Partially Observable Stochastic Control and Its Mean-Field Control Approach

Tottori

Kobayashi

2022

Entropy

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“…As a general outlook, although here we have focused on the situation in which navigation is performed by a single agent, it would be definitely worth studying the optimization of collective processes by including interactions among multiple agents 207,208 . In fact, cooperation between agents has already been proved useful to improve the overall performance 209,210 , even in the presence of just a few leaders 211,212 who efficiently manage to guide the group towards the achievement of common tasks.…”

Section: Discussionmentioning

confidence: 99%

Optimal Navigation in Active Matter

Piro

2024

Springer Theses

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Motile active matter systems are composed by a collection of agents, each of which extracts energy from the surrounding environment in order to convert it into self-driven motion. At the microscopic scale, however, directed motion is hindered by both the presence of stochastic fluctuations. Living microorganisms therefore had to develop simple yet effective propulsion and steering mechanisms in order to survive.We may turn the question of how these processes work in nature around and ask how they should work in order to perform a task in the theoretically optimal way, an issue which falls under the name of the optimal navigation problem. The first formulation of this problem dates back to the seminal work of E. Zermelo in 1931, in which he addressed the question of how to steer a ship in the presence of an external stationary wind so as to reach the destination in the shortest time.Despite the considerable progress made over the years in this context, however, there are still a number of open challenges. In this thesis, we therefore aim to generalize Zermelo's solution by adding more and more ingredients in the description of the optimal navigation problem for microscopic active particles.First, borrowing theoretical tools from differential geometry, we here show how to extend the analytical solution of this problem to when motion occurs on curved surfaces and in the presence of arbitrary flows. Interestingly, we reveal that it can elegantly be solved by finding the geodesics of an asymmetric metric of general relativity, known as the Randers metric.Then, we study the case in which navigation happens in the presence of strong external forces. In this context, route optimization can be crucial as active particles may encounter trapping regions that would substantially slow-down their progress. Comparing the exploration efficiency of Zermelo's solution with a more trivial strategy in which the active agent always points in the same direction, here we highlight the importance of the optimal path stability, which turns out to be fundamental in the design of the proper navigation strategy depending on the task at hand.We then take it a step further and include a key ingredient in the comprehensive study of optimal navigation in active matter, namely stochastic fluctuations. Although methods already exist to obtain both analytically and numerically the optimal strategies even in the presence of noise, their implementation requires the presence of an external interpreter that * Despite this difference, in the following we will actually not make any distinction between these two terms since their observable behavior -when considered individually-is indistinguishable in a homogeneous environment 32 .

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“…In many practical applications of the stochastic optimal control theory, several constraints need to be considered. In the cases of small devices [1,2] and biological systems [3][4][5][6][7][8], for example, incomplete information and memory limitation become predominant because their sensors are extremely noisy and their memory resources are severely limited. To take into account one of these constraints, incomplete information, partially observable stochastic control (POSC) has been extensively studied in the stochastic optimal control theory [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Forward-Backward Sweep Method for the System of HJB-FP Equations in Memory-Limited Partially Observable Stochastic Control

Tottori

Kobayashi

2023

Entropy

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Memory-limited partially observable stochastic control (ML-POSC) is the stochastic optimal control problem under incomplete information and memory limitation. To obtain the optimal control function of ML-POSC, a system of the forward Fokker–Planck (FP) equation and the backward Hamilton–Jacobi–Bellman (HJB) equation needs to be solved. In this work, we first show that the system of HJB-FP equations can be interpreted via Pontryagin’s minimum principle on the probability density function space. Based on this interpretation, we then propose the forward-backward sweep method (FBSM) for ML-POSC. FBSM is one of the most basic algorithms for Pontryagin’s minimum principle, which alternately computes the forward FP equation and the backward HJB equation in ML-POSC. Although the convergence of FBSM is generally not guaranteed in deterministic control and mean-field stochastic control, it is guaranteed in ML-POSC because the coupling of the HJB-FP equations is limited to the optimal control function in ML-POSC.

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Optimal collision avoidance in swarms of active Brownian particles

Cited by 5 publications

References 39 publications

Memory-Limited Partially Observable Stochastic Control and Its Mean-Field Control Approach

Memory-Limited Partially Observable Stochastic Control and Its Mean-Field Control Approach

Optimal Navigation in Active Matter

Forward-Backward Sweep Method for the System of HJB-FP Equations in Memory-Limited Partially Observable Stochastic Control

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