Minimalist exploration strategies for robot swarms at the edge of chaos

TL;DR

This study explores how random walks that present chaotic or edge-of-chaos dynamics can be generated and demonstrates how chaotic dynamics are beneficial to maximise exploration effectiveness.

Abstract

Effective exploration abilities are fundamental for robot swarms, especially when small, inexpensive robots are employed (e.g., micro- or nano-robots). Random walks are often the only viable choice if robots are too constrained regarding sensors and computation to implement state-of-the-art solutions. However, identifying the best random walk parameterisation may not be trivial. Additionally, variability among robots in terms of motion abilities-a very common condition when precise calibration is not possible-introduces the need for flexible solutions. This study explores how random walks that present chaotic or edge-of-chaos dynamics can be generated. We also evaluate their effectiveness for a simple exploration task performed by a swarm of simulated Kilobots. First, we show how Random Boolean Networks can be used as controllers for the Kilobots, achieving a significant performance improvement compared to the best parameterisation of a Lévy-modulated Correlated Random Walk. Second, we demonstrate how chaotic dynamics are beneficial to maximise exploration effectiveness. Finally, we demonstrate how the exploration behavior produced by Boolean Networks can be optimized through an Evolutionary Robotics approach while maintaining the chaotic dynamics of the networks.

Figures (6)

• Figure 1: Representation of a 6 Node RBN. a) Graphic representation of a RBN showing connections and node states with "011101" initial state values. b) Boolean functions for each node of the network. c) Table showing node state values, robot step length value (in simulator ticks), and robot angle value (in degrees) for each time step (t=0 to t=3). d) RBN representation as an individual of the Genetic Algorithm population.
• Figure 2: Performance in terms of average first passage time $t_f$ obtained with the LMCRW approach systematically varying the value of the parameters $\rho$ and $\alpha$. The reported values correspond to the mean over 20 independent evaluations.
• Figure 3: Comparison between LMCRW method with the RBN in terms of the average first passage time $t_f$, computed over 20 independent evaluations. For the RBNs, all the 100 created networks are grouped on their respective boxplots. The y axis is in log scale and the dashed line represents the LMCRW median.
• Figure 4: Comparison between RBNs and all 6 EBNs runs for $N=20,30$ with the LMCRW method. The y axis is in log scale and the dashed line represents the LMCRW median.
• Figure 5: Correlation between performance ($t_f$) and sensitivity to initial conditions ($\Delta$, top panels) and average straight motion duration ($\overline{D}$, bottom panels) for RBNs and EBNs with $N\in\{18, 20, 22, 24, 26, 30\}$.