Recent advancements in Multi-Robot Systems (MRS) and mesh network technologies pave the way for innovative approaches to explore extreme environments. The Artemis Accords, a series of international agreements, have further catalyzed this progress by fostering cooperation in space exploration, emphasizing the use of cutting-edge technologies. In parallel, the widespread adoption of the Robot Operating System 2 (ROS 2) by companies across various sectors underscores its robustness and versatility. This paper evaluates the performances of available ROS 2 MiddleWare (RMW), such as FastRTPS, CycloneDDS and Zenoh, over a mesh network with a dynamic topology. The final choice of RMW is determined by the one that would fit the most the scenario: an exploration of the extreme extra-terrestrial environment using a MRS. The conducted study in a real environment highlights Zenoh as a potential solution for future applications, showing a reduced delay, reachability, and CPU usage while being competitive on data overhead and RAM usage over a dynamic mesh topology

We consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable partial derivatives of order m. A natural candidate for the estimator of f* in such a case is the best fit to the data set that satisfies a certain smoothness condition. This estimator can be seen as a least squares estimator subject to an upper bound on some measure of smoothness. Another useful estimator is the one that minimizes the degree of smoothness subject to an upper bound on the average of squared errors. We prove that these two estimators are computable as solutions to quadratic programs, establish the consistency of these estimators and their partial derivatives, and study the convergence rate as n increases to infinity. The effectiveness of the estimators is illustrated numerically in a setting where the value of a stock option and its second derivative are estimated as functions of the underlying stock price.