Exploration is a crucial problem in safety of life applications, such as search and rescue missions. Gaussian processes constitute an interesting underlying data model that leverages the spatial correlations of the process to be explored to reduce the required sampling of data. Furthermore, multiagent approaches offer well known advantages for exploration. Previous decentralized multi-agent exploration algorithms that use Gaussian processes as underlying data model, have only been validated through simulations. However, the implementation of an exploration algorithm brings difficulties that were not tackle yet. In this work, we propose an exploration algorithm that deals with the following challenges: (i) which information to transmit to achieve multi-agent coordination; (ii) how to implement a lightweight collision avoidance; (iii) how to learn the data's model without prior information. We validate our algorithm with two experiments employing real robots. First, we explore the magnetic field intensity with a ground-based robot. Second, two quadcopters equipped with an ultrasound sensor explore a terrain profile. We show that our algorithm outperforms a meander and a random trajectory, as well as we are able to learn the data's model online while exploring.

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In processing spatially distributed data, multi-agent robotic platforms equipped with sensors and computing capabilities are gaining interest for applications in inhospitable environments. In this work an algorithm for a distributed realization of sparse bayesian learning (SBL) is discussed for learning a static spatial process with the splitting-over-features approach over a network of interconnected agents. The observed process is modeled as a superposition of weighted kernel functions, or features as we call it, centered at the agent's measurement locations. SBL is then used to determine which feature is relevant for representing the spatial process. Using upper bounding convex functions, the SBL parameter estimation is formulated as 1-norm constrained optimization, which is solved distributively using alternating direction method of multipliers (ADMM) and averaged consensus. The performance of the method is demonstrated by processing real magnetic field data collected in a laboratory.

This paper focuses on exploration when using different data distribution schemes and ADMM as a solver for swarms. By exploration, we mean the estimation of new measurement locations that are beneficial for the model estimation. In particular, the different distribution schemes are splitting-over-features or heterogeneous learning and splitting-over-examples or homogeneous learning. Each agent contributes a solution to solve the joint optimization problem by using ADMM and the consensus algorithm. This paper shows that some information is unknown to the individual agent, and thus, the estimation of new measurement positions is not possible without further communication. Therefore, this paper shows results for how to distribute only necessary information for a global exploration. We show the benefits between the proposed global exploration scheme and benchmark exploration schemes such as random walk and systematic traversing, i.e., meandering. The proposed waypoint estimation methods are then tested against each other and with other movement methods. This paper shows that a movement method, which considers the current information within the model, is superior to the benchmark movement methods.