Probabilistic Consensus on Feature Distribution for Multi-robot Systems with Markovian Exploration Dynamics

TL;DR

This paper introduces a decentralized multi-robot method for reconstructing feature distributions in a 2D environment, using Markovian exploration and a consensus protocol, with proven convergence and validated through simulations.

Contribution

It presents a novel decentralized fusion protocol for multi-robot feature distribution estimation with theoretical convergence guarantees.

Findings

Feature distribution estimates converge to ground truth.

Hellinger distance decreases to zero over time.

Validated through numerical and SITL simulations.

Abstract

In this paper, we present a consensus-based decentralized multi-robot approach to reconstruct a discrete distribution of features, modeled as an occupancy grid map, that represent information contained in a bounded planar 2D environment, such as visual cues used for navigation or semantic labels associated with object detection. The robots explore the environment according to a random walk modeled by a discrete-time discrete-state (DTDS) Markov chain and estimate the feature distribution from their own measurements and the estimates communicated by neighboring robots, using a distributed Chernoff fusion protocol. We prove that under this decentralized fusion protocol, each robot's feature distribution converges to the ground truth distribution in an almost sure sense. We verify this result in numerical simulations that show that the Hellinger distance between the estimated and ground truth feature distributions converges to zero over time for each robot. We also validate our strategy through Software-In-The-Loop (SITL) simulations of quadrotors that search a bounded square grid for a set of visual features distributed on a discretized circle.