Markovian robots: minimal navigation strategies for active particles

TL;DR

This paper introduces minimalistic Markovian robots with a simple Boolean control system that can perform complex navigation tasks in dynamic external fields, demonstrating their effectiveness through theoretical analysis and practical robot implementation.

Contribution

It presents a novel class of autonomous robots with a Boolean Markov chain-based control system capable of complex navigation without storing past data.

Findings

Markovian robots can perform adaptive gradient following.

They can detect minima or maxima in external fields.

A proof-of-concept robot demonstrates practical navigation capabilities.

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.