*Article* **Experimental Validation of Entropy-Driven Swarm Exploration under Sparsity Constraints with Sparse Bayesian Learning**

**Christoph Manss 1,2,\*, Isabel Kuehner <sup>2</sup> and Dmitriy Shutin <sup>2</sup>**


**Abstract:** Increasing the autonomy of multi-agent systems or swarms for exploration missions requires tools for efficient information gathering. This work studies this problem from theoretical and experimental perspectives and evaluates an exploration system for multiple ground robots that cooperatively explore a stationary spatial process. For the distributed model, two conceptually different distribution paradigms are considered. The exploration is based on fusing distributively gathered information using Sparse Bayesian Learning (SBL), which permits representing the spatial process in a compressed manner and thus reduces the model complexity and communication load required for the exploration. An entropy-based exploration criterion is formulated to guide the agents. This criterion uses an estimation of a covariance matrix of the model parameters, which is then quantitatively characterized using a D-optimality criterion. The new sampling locations for the agents are then selected to minimize this criterion. To this end, a distributed optimization of the D-optimality criterion is derived. The proposed entropy-driven exploration is then presented from a system perspective and validated in laboratory experiments with two ground robots. The experiments show that SBL together with the distributed entropy-driven exploration is real-time capable and leads to a better performance with respect to time and accuracy compared with similar state-of-the-art algorithms.

**Keywords:** distributed estimation; Sparse Bayesian Learning; exploration; swarm; multi-agent systems; consensus; D-optimal design
