We design a distributed feedback optimization strategy, embedded into a modular ROS 2 control architecture, which allows a team of heterogeneous robots to cooperatively monitor and encircle a target while patrolling points of interest. By relying on the aggregative feedback optimization framework, we handle multi-robot dynamics while minimizing a global performance index depending on both microscopic (e.g., the location of single robots) and macroscopic variables (e.g., the spatial distribution of the team). The proposed distributed policy allows the robots to cooperatively address the global problem by employing only local measurements and neighboring data exchanges. These exchanges are performed through an asynchronous communication protocol ruled by locally-verifiable triggering conditions. We formally prove that our strategy steers the robots to a set of configurations representing stationary points of the considered optimization problem. The effectiveness and scalability of the overall strategy are tested via Monte Carlo campaigns of realistic Webots ROS 2 virtual experiments. Finally, the applicability of our solution is shown with real experiments on ground and aerial robots.

Model-free optimization methods typically rely on cost samples gathered by perturbing the current solution estimate along a finite and fixed set of directions. However, at each iteration, only the current cost samples are used, while potentially informative, previously collected samples are discarded. In this work, we challenge this conventional approach by introducing a simple yet effective memory mechanism that maintains an auxiliary vector of iteratively updated cost samples. By leveraging this stored information, our method estimates descent directions through an averaging of all perturbing directions weighted by the auxiliary vector components. This results in faster convergence without increasing the number of function queries. By interpreting the resulting algorithm as a time-varying dynamical system, we are able to establish its convergence properties in the strongly convex case. In particular, by using tools from system theory based on timescale separation, we are able to guarantee a linear convergence rate toward an arbitrarily small neighborhood of the optimal solution. Numerical simulations on regression problems demonstrate that the proposed approach significantly outperforms existing model-free optimization methods.

Several interesting problems in multirobot systems can be cast in the framework of distributed optimization. Examples include multirobot task allocation, vehicle routing, target protection, and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this article, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss its implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots.

Sparse convex optimization involves optimization problems where the decision variables are constrained to have a certain number of entries equal to zero. In this paper, we consider the case in which the objective function is decomposed into a sum of different local objective functions and propose a novel fully-distributed scheme to address the problem over a network of cooperating agents. Specifically, by taking advantage of a suitable problem reformulation, we define an Augmented Lagrangian function associated with the reformulated problem. Then, we address such an Augmented Lagrangian by suitably interlacing the Gradient Tracking distributed algorithm and the Block Coordinated Descent method giving rise to a novel fully-distributed scheme. The effectiveness of the proposed algorithm is corroborated through some numerical simulations of problems considering both synthetic and real-world data sets.

In this paper, we propose a distributed algorithm to control a team of cooperating robots aiming to protect a target from a set of intruders. Specifically, we model the strategy of the defending team by means of an online optimization problem inspired by the emerging distributed aggregative framework. In particular, each defending robot determines its own position depending on (i) the relative position between an associated intruder and the target, (ii) its contribution to the barycenter of the team, and (iii) collisions to avoid with its teammates. We highlight that each agent is only aware of local, noisy measurements about the location of the associated intruder and the target. Thus, in each robot, our algorithm needs to (i) locally reconstruct global unavailable quantities and (ii) predict its current objective functions starting from the local measurements. The effectiveness of the proposed methodology is corroborated by simulations and experiments on a team of cooperating quadrotors.