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

TL;DR

The paper addresses computing the probability mass over a buffered 2D path via $I(f,H) = \int_H f(\vec{x}) dH$, where $f$ is a PDM defined over a polygon $H$. It benchmarks two numerical integration approaches—cubature and sampling-based—within a Martian rover search-planning scenario using a Gaussian-mixture PDM and a five-rover team with sensor footprint $d_{rover}=1\,\mathrm{m}$. Results show cubature is both more accurate and faster across the tested conditions, with a crossover near $N \approx 16.8$ where sampling catches up in speed but incurs substantially higher error (e.g., $14.75\%$ at the crossover) and much steeper runtime growth (up to $\sim 2.5 \times 10^{4}\%$). These findings have practical implications for RL training efficiency and onboard navigation in autonomous planetary rovers.

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.

Figures (8)

• Figure 1: 3D terrain model of the selected mission site
• Figure 2: Traversability analysis of the selected mission site. Traversable terrain is shown in white, high-risk terrain is shown in red, and impassable terrain is shown in black.
• Figure 3: Ray casting method to check if a point (geometry A) is within a non-convex polygon (geometry B). If the ray originating from A intersects B an odd amount of times (three, in this example), then A is within B.
• Figure 4: Subdivision of the unit triangle into four smaller triangles.
• Figure 5: Rover trajectories over the area given the mission planned by LHC_GW_CONV with a random PDM $p(\vec{x})$. $N=16$ was selected to emphasize the issue with sampling-based integration methods.