This paper explores decision-making processes in robotic systems tasked with reconstructing scalar fields through sensing in uncertain environments. Each robot must handle noisy perception and operate within specific environmental and physical constraints. The complexity increases in multiagent scenarios, where robots must not only plan their actions but also anticipate the movements and strategies of other agents. Effective coordination is crucial to prevent collisions and minimize redundant tasks. To address this challenge, we propose an online, distributed multi-robot sampling algorithm that combines Monte Carlo Tree Search (MCTS) with Gaussian regression. In this approach, each robot iteratively selects its next sampling point while exchanging limited information with other robots and predicting their future actions. Predictions about other robots future actions are computed with a MCTS that is recomputed at each iteration to incorporate all information collected up to that point. We evaluate the performance of our method across diverse environments and team sizes, comparing it to algorithmic alternatives.

In multi-robot informative path planning the problem is to find a route for each robot in a team to visit a set of locations that can provide the most useful data to reconstruct an unknown scalar field. In the budgeted version, each robot is subject to a travel budget limiting the distance it can travel. Our interest in this problem is motivated by applications in precision agriculture, where robots are used to collect measurements to estimate domain-relevant scalar parameters such as soil moisture or nitrates concentrations. In this paper, we propose an online, distributed multi-robot sampling algorithm based on Monte Carlo Tree Search (MCTS) where each robot iteratively selects the next sampling location through communication with other robots and considering its remaining budget.We evaluate our proposed method for varying team sizes and in different environments, and we compare our solution with four different baseline methods. Our experiments show that our solution outperforms the baselines when the budget is tight by collecting measurements leading to smaller reconstruction errors.

In this paper we consider the information path-planning problem for a single robot in a stochastic environment with static obstacles subject to a preassigned constraint on the distance it can travel. Given a set of candidate sampling locations, the objective is to determine a path for the robot that allows to visit as many sampling locations as possible to accurately reconstruct an unknown underlying scalar field while not exceeding the assigned travel budget. Starting from the assumption that the phenomenon being measured can be modeled by a Gaussian Process, our algorithm balances exploration and exploitation to determine a sequence of locations ensuring that a preassigned final site is reached before the budget is consumed. Using mutual information as a reward criterion, as well as a generative model to predict consumed energy, the algorithm iteratively determines where to sample next, and when to end the mission. Our findings are validated in simulation in various scenarios and lead to a better reconstruction with less failures when compared with other methods.