Distributed Simultaneous Localisation and Auto-Calibration using Gaussian Belief Propagation

TL;DR

This work presents a novel scalable, fully distributed, and online method for simultaneous localisation and extrinsic calibration for multi-robot setups that not only yields accurate robot localisation and auto-calibration but also is able to perform under challenging circumstances.

Abstract

We present a novel scalable, fully distributed, and online method for simultaneous localisation and extrinsic calibration for multi-robot setups. Individual a priori unknown robot poses are probabilistically inferred as robots sense each other while simultaneously calibrating their sensors and markers extrinsic using Gaussian Belief Propagation. In the presented experiments, we show how our method not only yields accurate robot localisation and auto-calibration but also is able to perform under challenging circumstances such as highly noisy measurements, significant communication failures or limited communication range.

Figures (5)

• Figure 1: Overview of the proposed auto-calibrating localisation system for three heterogeneous robots (top). Each robot observes the markers $M$ placed on its peers to establish measurement $\bar{{{\mathbf {z}}}}_{SM}$ using sensor $S$ mounted on top of a moving base $B$. Using the proposed methodology, the robots' relative positions and their calibration parameters can be retrieved in a distributed and asynchronous fashion performing probabilistic inference on a factor graph. We refer to ${{\mathbf T}}_{WB}$ as ${{\mathbf W}}{{\mathbf B}}$ for clarity.
• Figure 2: Example of calibration of the extrinsic of the sensors' pose and markers' position using the proposed method, where we artificially set the ground-truth extrinsics to be the same for visual clarity. We overlay the calibration estimates of 64 robots from randomly initialised states (left), and visualise the estimated extrinsics after the calibration (right).
• Figure 3: Reducing the inter-robot communication by restructuring the factor graph. We refer to ${{\mathbf T}}_{WB}$ as ${{\mathbf W}}{{\mathbf B}}$ for clarity. Left: The inter-robot factor (range bearing) depends on four variables: the poses of the robots, the marker $M$, and the sensor $S$ pose with respect to the robot base $B$. Right We introduce the marker and sensor variable in the world coordinate frame using Eq. \ref{['eq.calibration_likelihood']}. While the total number of variables increases, the inter-robot factors depend on fewer variables, thus reducing the communication requirements.
• Figure 4: From top to bottom: RMSE ATE for ${{\mathbf T}}_{WB}$, ${{\mathbf T}}_{BS}$, ${{\mathbf {t}}}_{BM}$. RMSE ARE omitted as it follows the same trend. Left: Comparison of different distributed alternatives (Final RMSE ATE of global, non-distributed LM shown for reference). Right: Analysis of robustness regarding communication failures by randomly dropping a percentage of the inter-robot GBP messages in each iteration. 100% indicates that all inter-robot messages are dropped, preventing co-localisation.
• Figure 5: From top to bottom: RMSE ATE for ${{\mathbf T}}_{WB}$, ${{\mathbf T}}_{BS}$, ${{\mathbf {t}}}_{BM}$. RMSE ARE omitted as it follows the same trend. Left: Effect of increasing the fraction of outlier noise. Non-Gaussian noise is added to the inter-robot sensor measurement to simulate outliers. Right: Impact on the overall accuracy when robots are limited to only communicating with peers within the specified range.