Quantifying Robotic Swarm Coverage

Abstract

In the field of swarm robotics, the design and implementation of spatial density control laws has received much attention, with less emphasis being placed on performance evaluation. This work fills that gap by introducing an error metric that provides a quantitative measure of coverage for use with any control scheme. The proposed error metric is continuously sensitive to changes in the swarm distribution, unlike commonly used discretization methods. We analyze the theoretical and computational properties of the error metric and propose two benchmarks to which error metric values can be compared. The first uses the realizable extrema of the error metric to compute the relative error of an observed swarm distribution. We also show that the error metric extrema can be used to help choose the swarm size and effective radius of each robot required to achieve a desired level of coverage. The second benchmark compares the observed distribution of error metric values to the probability density function of the error metric when robot positions are randomly sampled from the target distribution. We demonstrate the utility of this benchmark in assessing the performance of stochastic control algorithms. We prove that the error metric obeys a central limit theorem, develop a streamlined method for performing computations, and place the standard statistical tests used here on a firm theoretical footing. We provide rigorous theoretical development, computational methodologies, numerical examples, and MATLAB code for both benchmarks.

Decentralized, Deterministic Robot Swarm Control using Blob Methods for PDEs

“…One way of quantifying the accuracy of the controller is by comparing the swarm blob function ρ against the target distribution ρ using the error metric from [2]: color='C4', alpha=0.5) plt.xlabel(r'$x$') plt.ylabel(r'$\rho(x)$') plt.legend(("Final Robot Position", "Swarm Blob Function", "Target →Distribution"), bbox_to_anchor=(1.04,1), loc="upper left") plt.annotate("$e_1 = {0:.3f}$".format(e1f), xy=(0, 0.245), xycoords='data', xytext=(0.5, 0.2), textcoords='data', arrowprops=dict(arrowstyle="-", connectionstyle="arc3"), ) caption("Visualization of the error metric $e_1$: the absolute area between " "the swarm blob function and target distribution. ")…”