Probabilistic network topology prediction for active planning:An adaptive algorithm and application

TL;DR

This paper introduces an adaptive algorithm for predicting the probability of future network connections in multi-robot systems, enhancing active planning accuracy under measurement uncertainty and noisy conditions.

Contribution

The paper develops the APSE algorithm using power series expansion for probabilistic topology prediction, with theoretical error bounds and practical approximation methods.

Findings

The APSE algorithm accurately predicts future network edges.

Predictions improve active planning performance under uncertainty.

Simulation results validate the method's effectiveness in multi-robot scenarios.

Abstract

This paper tackles the problem of active planning to achieve cooperative localization for multi-robot systems (MRS) under measurement uncertainty in GNSS-limited scenarios. Specifically, we address the issue of accurately predicting the probability of a future connection between two robots equipped with range-based measurement devices. Due to the limited range of the equipped sensors, edges in the network connection topology will be created or destroyed as the robots move with respect to one another. Accurately predicting the future existence of an edge, given imperfect state estimation and noisy actuation, is therefore a challenging task. An adaptive power series expansion (or APSE) algorithm is developed based on current estimates and control candidates. Such an algorithm applies the power series expansion formula of the quadratic positive form in a normal distribution. Finite-term approximation is made to realize the computational tractability. Further analyses are presented to show that the truncation error in the finite-term approximation can be theoretically reduced to a desired threshold by adaptively choosing the summation degree of the power series. Several sufficient conditions are rigorously derived as the selection principles. Finally, extensive simulation results and comparisons, with respect to both single and multi-robot cases, validate that a formally computed and therefore more accurate probability of future topology can help improve the performance of active planning under uncertainty.