Simulation and time series analysis of responsive active Brownian particles (rABPs) with memory

To realise the goals of active matter at the micro- and nano-scale, the next generation of microrobots must be capable of autonomously sensing and responding to their environment to carry out pre-programmed tasks. Memory effects are proposed to have a significant effect on the dynamics of responsive robotic systems, drawing parallels to strategies used in nature across all length-scales. Inspired by the integral feedback control mechanism by which Escherichia coli (<i>E. coli</i>) are proposed to sense their environment, we develop a numerical model for responsive active Brownian particles (rABP) in which the rABPs continuously react to changes in the physical parameters dictated by their local environment. The resulting time series, extracted from their dynamic diffusion coefficients, velocity or from their fluctuating position with time, are then used to classify and characterise their response, leading to the identification of conditional heteroscedasticity in their physics. We then train recurrent neural networks (RNNs) capable of quantitatively describing the responsiveness of rABPs using their 2D trajectories. We believe that our proposed strategy to determine the parameters governing the dynamics of rABPs can be applied to guide the design of microrobots with physical intelligence encoded during their fabrication.