Robotic Exploration using Generalized Behavioral Entropy

TL;DR

The paper addresses robotic exploration under human-like uncertainty perception by introducing Behavioral Entropy, a generalized entropy operator built from Prelec probability weighting. It analyzes theoretical properties, proves admissibility within the generalized entropy framework, and defines a Behavioral-entropy-based frontier utility for exploration. Empirical results from proof-of-concept simulations and ROS-Unity simulations demonstrate that Behavioral Entropy enables faster and more diverse exploration than Shannon or Renyi entropies, with practical guidance on parameter choices. Overall, the work provides a perceptive uncertainty measure and demonstrates its value for information-driven path planning in uncertain environments.

Abstract

This work presents and evaluates a novel strategy for robotic exploration that leverages human models of uncertainty perception. To do this, we introduce a measure of uncertainty that we term "Behavioral entropy", which builds on Prelec's probability weighting from Behavioral Economics. We show that the new operator is an admissible generalized entropy, analyze its theoretical properties and compare it with other common formulations such as Shannon's and Renyi's. In particular, we discuss how the new formulation is more expressive in the sense of measures of sensitivity and perceptiveness to uncertainty introduced here. Then we use Behavioral entropy to define a new type of utility function that can guide a frontier-based environment exploration process. The approach's benefits are illustrated and compared in a Proof-of-Concept and ROS-Unity simulation environment with a Clearpath Warthog robot. We show that the robot equipped with Behavioral entropy explores faster than Shannon and Renyi entropies.

Figures (6)

• Figure 1: Proposed exploration framework with our contribution in the red cloud. The Omnimapper SLAM system provides a local map $\mathcal{L}$, a global map $\mathcal{M}$ and robot localization $x$. Then, frontiers $f$ and perceived occupancy $\mathcal{W}$ are extracted from $\mathcal{M}$. The frontiers $f$ are clustered ($F$) and Behavioral entropy $H^{\textup{B}}$ is calculated from $\mathcal{W}$. For each cluster in $F$, a behavioral information gain $I^B$ is obtained from $H^{\textup{B}}$ that corresponds to the measurement model. Then, utilities $U$ are calculated from the information $I^B$ and pose estimate $x$. The explorer then picks a suitable goal region $B^x_r$ and sends it to the navigation manager, which in turn sends global and local plans $\eta$ to the controller.
• Figure 2: (Left) Prelec's probability weighting function with a few parameter choices. Y-axis $w(p)$ indicates the perceived uncertainty associated with probability $p$ (X-axis). Dotted line indicates the unity curve $w(p)=p$. (Right) Behavioral entropy variation with $\alpha$ in log scale for a Bernoulli trial. Black curve indicates Shannon's entropy.
• Figure 3: Environments used for simulations
• Figure 4: Violin plots indicating the number of iterations used to complete $99\%$ of exploration under different behavioral exploration strategies, sensing radius and noise conditions
• Figure 5: The unity-ROS environment used in DARPA subterranean challenge. Snapshot of execution shown with map and costmap, frontier clusters (yellow box), laser scans and robot going to region (blue circle), trying to follow a planned path (green line).

Theorems & Definitions (17)

• Definition 1: Generalized entropy
• Proposition 1: Perceived probability SD:16, Prop. $2.11$
• Lemma 1: Maximality of $H^{\textup{S}}$
• Theorem 1
• proof
• Remark 1
• Definition 2: Sensitivity
• Definition 3: Perceptiveness
• Lemma 2
• proof