Simulated Annealing for Multi-Robot Ergodic Information Acquisition Using Graph-Based Discretization

TL;DR

Simulated annealing is used to generate the target sampling distribution, starting from uniform and gradually shifting to an estimated optimal distribution, by varying the coldness parameter of a Boltzmann distribution with the estimated sampling entropy as energy.

Abstract

One of the goals of active information acquisition using multi-robot teams is to keep the relative uncertainty in each region at the same level to maintain identical acquisition quality (e.g., consistent target detection) in all the regions. To achieve this goal, ergodic coverage can be used to assign the number of samples according to the quality of observation, i.e., sampling noise levels. However, the noise levels are unknown to the robots. Although this noise can be estimated from samples, the estimates are unreliable at first and can generate fluctuating values. The main contribution of this paper is to use simulated annealing to generate the target sampling distribution, starting from uniform and gradually shifting to an estimated optimal distribution, by varying the coldness parameter of a Boltzmann distribution with the estimated sampling entropy as energy. Simulation results show a substantial improvement of both transient and asymptotic entropy compared to both uniform and direct-ergodic searches. Finally, a demonstration is performed with a TurtleBot swarm system to validate the physical applicability of the algorithm.

Figures (7)

• Figure 1: Example information gathering task of locating survivors in a map $\mathcal{G}$ with regions $\mathcal{R}$ and edges $\mathcal{E}$ caused by blockage of trees. The regions containing various amount of rubble, which causes differences in information quality i.e., noise levels $\sigma_i^2$, across the regions.
• Figure 2: Flowchart of the annealed ergodic information gathering algorithm.
• Figure 3: Example distribution of 30 robots (black markers) with various coldness $\beta$. The color of the border of the region represents the relative variance $\sigma^2$, the inner color represents the target distribution $\bar{\rho}(\beta)$. (a) the robots are equally spread out regardless of the variance; (b) the robots are somewhat between the uniform distribution and the optimal distribution; (c) the distribution of robots are proportional to the variance, which is the optimal for information gathering; (d) the robots are concentrated at the two regions with the highest variance, this causes severe under-sampling in the rest of the regions.
• Figure 4: Comparison of maximum posterior entropy between uniform, direct ergodic, and annealed ergodic over 100 trials. With the solid line representing the median and the shaded region bounded by the dash line representing the first to third quartile region. top row shows the true entropy obtained from external oracle. This shows that annealing is consistently performing better both transiently and asymptotically. bottom row shows the estimated entropy from the internal believe of the robots. This shows that when compared to the true entropy, direct ergodic method has a problem of overestimating the information it has.
• Figure 5: Example space average $\bar{\rho}$ and time average $\hat{\rho}$ of each region shown in different color, with the optimal distribution shown in dashed-line. The left column shows the result using annealing and right column shows the result of direct ergodic. Annealing shows a smooth transition from uniform to the optimal solution which is trackable for the time average; while the direct ergodic method produced a fluctuating space average that causes an extreme time average.