Gaussian Processes for Modelling Spatial Fields with Robot Swarms

Summary

Robot swarms, by virtue of their decentralised architecture, are a natural tool for scalable, robust modelling of spatial fields, such as water temperature, wind velocity, or terrain elevation.

Abstract Summary

Robot swarms, by virtue of their decentralised architecture, are a natural tool for scalable, robust modelling of spatial fields, such as water temperature, wind velocity, or terrain elevation. However, existing methods rely on external positioning systems that allow each robot to determine its own position in space. Here, we introduce location-unaware Gaussian process regression (LU-GPR) as a solution to the modelling of spatial fields in the absence of such positioning systems. LU-GPR allows each robot to infer the posterior mean and variance of the field in space, while simultaneously agreeing on a common frame of reference with its peers, using only local sensing and communication. We propose an online algorithm that allows each robot to consistently infer local estimates as its local frame of reference converges to the common one. By means of a product of experts model, each robot also combines the estimates of its peers with its own to obtain a global model. Our results show that LU-GPR scales well with the number of robots and is robust to limited communication ranges. We also demonstrate how it can be used in real-world monitoring scenarios to estimate the flow of an evacuating crowd.

Key Points

Robot swarms, by virtue of their decentralised architecture, are a natural tool for scalable, robust modelling of spatial fields, such as water temperature, wind velocity, or terrain elevation.
However, existing methods rely on external positioning systems that allow each robot to determine its own position in space.
Here, we introduce location-unaware Gaussian process regression (LU-GPR) as a solution to the modelling of spatial fields in the absence of such positioning systems.
LU-GPR allows each robot to infer the posterior mean and variance of the field in space, while simultaneously agreeing on a common frame of reference with its peers, using only local sensing and communication.
We propose an online algorithm that allows each robot to consistently infer local estimates as its local frame of reference converges to the common one.

SPATIAL FIELD MODELLING

We now introduce LU-GPR, our proposed approach to modelling spatial fields with a robot swarm, where the robots have no knowledge of their position in space, and can only communicate within a limited range. Each robot runs the GBP algorithm of Jones et al. [ 17 ] , while simultaneously updating its GP model using data collected in time, as we describe in Section III-A .

To build a global model of the latent function, robots collect the models of their peers and fuse them with their own, as we describe in Section III-B .

SPATIAL FIELD MODELLING — Gaussian Processes for Modelling Spatial Fields with Robot Swarms — Fig. 2: Estimation of a spatial field. (a) Function with zero mean to be estimated. (b) Environmental setup, where a fixed number of robots (here, four) with a limited communication range (here, 1 m, as shown by the blue rings) sample the field as they perform a random walk.

EXPERIMENTAL VALIDATION

We validate LU-GPR using two different scenarios. First, using a randomly generated synthetic function, we study how the number of robots and the communication range affect estimation quality. Then, we demonstrate how LU-GPR can be used to model the behaviour of an evacuating crowd. For simplicity, we follow the common practice of assuming that the means of the GPs are zero in both scenarios [ 4 ] .

Sources and Demonstrations

Figures are reproduced from Herranz et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.