Markovian robots: minimal navigation strategies for active particles

Abstract

We explore minimal navigation strategies for active particles in complex, dynamical, external fields, introducing a class of autonomous, self-propelled particles which we call Markovian robots (MR). These machines are equipped with a navigation control system (NCS) that triggers random changes in the direction of self-propulsion of the robots. The internal state of the NCS is described by a Boolean variable that adopts two values. The temporal dynamics of this Boolean variable is dictated by a closed Markov chain -- ensuring the absence of fixed points in the dynamics -- with transition rates that may depend exclusively on the instantaneous, local value of the external field. Importantly, the NCS does not store past measurements of this value in continuous, internal variables. We show that, despite the strong constraints, it is possible to conceive closed Markov chain motifs that lead to nontrivial motility behaviors of the MR in one, two and three dimensions. By analytically reducing the complexity of the NCS dynamics, we obtain an effective description of the long-time motility behavior of the MR that allows us to identify the minimum requirements in the design of NCS motifs and transition rates to perform complex navigation tasks such as adaptive gradient following, detection of minima or maxima, or selection of a desired value in a dynamical, external field. We put these ideas in practice by assembling a robot that operates by the proposed minimalistic NCS to evaluate the robustness of MR, providing a proof-of-concept that is possible to navigate through complex information landscapes with such a simple NCS whose internal state can be stored in one bit. These ideas may prove useful for the engineering of miniaturized robots.

arXiv comment19 pages, 7 figures

References in corpus (21)

• Collective motion
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Emergence of macroscopic directed motion in populations of motile colloids
• Designing phoretic micro- and nano-swimmers
• Collective Motion of Vibrated Polar Disks
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• Swarming and swirling in self-propelled polar granular rods
• Boltzmann and hydrodynamic description for self-propelled particles
• Tuned, driven, and active soft matter
• Emergent vortices in populations of colloidal rollers
• Diffusion, subdiffusion, and trapping of active particles in heterogeneous media
• Self-propelled particles with fluctuating speed and direction of motion
• The Bacterial Chemotactic Response Reflects a Compromise Between Transient and Steady State Behavior
• Steering chiral swimmers along noisy helical paths
• Engineering sensorial delay to control phototaxis and emergent collective behaviors
• Self-propelled particles with selective attraction-repulsion interaction - From microscopic dynamics to coarse-grained theories
• Diffusion properties of active particles with directional reversal
• Signalling noise enhances chemotactic drift of E. coli
• Chemotaxis When Bacteria Remember: Drift versus Diffusion
• A geometric approach to self-propelled motion in isotropic and anisotropic environments
• Hydrodynamic Equations for Flocking Models without Velocity Alignment

Cited by in corpus (16)

• Run-and-tumble particles in two-dimensions : Marginal position distributions
• Optimal steering of a smart active particle
• Information and motility exchange in collectives of active particles
• Run-and-Tumble particle in inhomogeneous media in one dimension
• The random walk of intermittently self-propelled particles
• Epidemic processes on self-propelled particles: continuum and agent-based modelling
• Hunting active Brownian particles: Learning optimal behavior
• Chemokinetic scattering, trapping, and avoidance of active Brownian particles
• A novel approach to chemotaxis: active particles guided by internal clocks
• Kinematics of Persistent Random Walkers with Two Distinct Modes of Motion
• Biohybrid active matter -- the emergent properties of cell-mediated microtransport
• Active Crowds
• Effect of speed fluctuations on the collective dynamics of active disks
• Kinetic theory of decentralized learning for smart active matter
• Kinetic and macroscopic models for active particles exploring complex environments with an internal navigation control system
• Active stop and go motion: a strategy to improve spatial exploration and survival