Enhancing Reinforcement Learning in Sensor Fusion: A Comparative Analysis of Cubature and Sampling-based Integration Methods for Rover Search Planning

TL;DR

This paper compares cubature and sampling-based numerical integration methods for rover search planning, finding cubature more efficient and accurate for reinforcement learning applications on Martian surface exploration.

Contribution

It provides a detailed analysis of the computational trade-offs between cubature and sampling-based methods in a robotic search context, highlighting cubature's advantages.

Findings

Sampling-based method has 14.75% higher error at equal speed.

Achieving <1% error requires 100x more time with sampling.

Cubature method is preferred for high-iteration reinforcement learning.

Abstract

This study investigates the computational speed and accuracy of two numerical integration methods, cubature and sampling-based, for integrating an integrand over a 2D polygon. Using a group of rovers searching the Martian surface with a limited sensor footprint as a test bed, the relative error and computational time are compared as the area was subdivided to improve accuracy in the sampling-based approach. The results show that the sampling-based approach exhibits a $14.75\%$ deviation in relative error compared to cubature when it matches the computational performance at $100\%$. Furthermore, achieving a relative error below $1\%$ necessitates a $10000\%$ increase in relative time to calculate due to the $\mathcal{O}(N^2)$ complexity of the sampling-based method. It is concluded that for enhancing reinforcement learning capabilities and other high iteration algorithms, the cubature method is preferred over the sampling-based method.