Interacting Particles with Lévy Strategies: Limits of Transport Equations for Swarm Robotic Systems

Abstract

Lévy 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 descriptions from the movement strategies of the individual robots. Starting from a kinetic equation which describes the movement of robots based on alignment, collisions and occasional long distance runs according to a Lévy distribution, we obtain a system of evolution equations for the fractional diffusion for long times. We show that the system allows efficient parameter studies for a search problem, addressing basic questions like the optimal number of robots needed to cover an area in a certain time. For shorter times, in the hyperbolic limit of the kinetic equation, the PDE model is dominated by alignment, irrespective of the long range movement. This is in agreement with previous results in swarming of self-propelled particles. The article indicates the novel and quantitative modeling opportunities which swarm robotic systems provide for the study of both emergent collective behaviour and anomalous diffusion, on the respective time scales.

Intrinsic and environmental factors modulating autonomous robotic search under high uncertainty

“…Likewise, autonomous robotic search problems always face some level of uncertainty regarding the environment, sensor performance and reliability, the motor plant function, the possible location of the search targets, the latency in which they may appear/disappear, or move, etc. In those problems where uncertainty is large, and partial or no information is available to implement algorithmic or heuristic searches, strategies inspired in biology have been proposed to address them, both in single robots 18 – 21 and in swarm strategies 22 – 27 .…”

Distribution and pressure of active Lévy swimmers under confinement

“…Instead, a power-law distribution of run-times that leads to Lévy motion has been shown to explain the observed persistent motion [11]. Lévy motions are understood as a more advantageous foraging or search strategy than Brownian motion in many settings [22][23][24][25][26][27], leading to applications in robotics and artificial intelligence for better search pattern design [28][29][30][31].…”

Moment-Driven Predictive Control of Mean-Field Collective Dynamics

“…Classical examples in socio-economy, biology and robotics are given by self-propelled particles, such animals and robots, see e.g. [2,14,25,30,52,50,37]. Those particles interact according to a nonlinear model encoding various social rules as for example attraction, repulsion and alignment.…”