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.

In this article, we consider a large-scale instance of the classical pickup-and-delivery vehicle routing problem that must be solved by a network of mobile cooperating robots. Robots must self-coordinate and self-allocate a set of pickup/delivery tasks while minimizing a given cost figure. This results in a large, challenging mixed-integer linear problem that must be cooperatively solved without a central coordinator. We propose a distributed algorithm based on a primal decomposition approach that provides a feasible solution to the problem in finite time. An interesting feature of the proposed scheme is that each robot computes only its own block of solution, thereby preserving privacy of sensible information. The algorithm also exhibits attractive scalability properties that guarantee solvability of the problem even in large networks. To the best of our knowledge, this is the first attempt to provide a scalable distributed solution to the problem. The algorithm is first tested through Gazebo simulations on a ROS 2 platform, highlighting the effectiveness of the proposed solution. Finally, experiments on a real testbed with a team of ground and aerial robots are provided.

In this article, we consider a network of agents that has to self-assign a set of tasks while respecting resource constraints. One possible formulation is the generalized assignment problem, where the goal is to find a maximum payoff while satisfying capability constraints. We propose a purely distributed branch-and-price algorithm to solve this problem in a cooperative fashion. Inspired by classical (centralized) branch-and-price schemes, in the proposed algorithm, each agent locally solves small linear programs, generates columns by solving simple knapsack problems, and communicates to its neighbors a fixed number of basic columns. We prove finite-time convergence of the algorithm to an optimal solution of the problem. Then, we apply the proposed scheme to a generalized assignment scenario, in which a team of robots has to serve a set of tasks. We implement the proposed algorithm in a Robot Operating System testbed and provide experiments for a team of heterogeneous robots solving the assignment problem.

We present an algorithm for multi-robot coverage of an initially unknown spatial scalar field characterized by a density function, whereby a team of robots simultaneously estimates and optimizes its coverage of the density function over the domain. The proposed algorithm borrows powerful concepts from Bayesian Optimization with Gaussian Processes that, when combined with control laws to achieve centroidal Voronoi tessellation, give rise to an adaptive sequential sampling method to explore and cover the domain. The crux of the approach is to apply a control law using a surrogate function of the true density function, which is then successively refined as robots gather more samples for estimation. The performance of the algorithm is justified theoretically under slightly idealized assumptions, by demonstrating asymptotic no-regret with respect to the coverage obtained with a known density function. The performance is also evaluated in simulation and on the Robotarium with small teams of robots, confirming the good performance suggested by the theoretical analysis.

In this paper, we propose a distributed version of the Hungarian method to solve the well-known assignment problem. In the context of multirobot applications, all robots cooperatively compute a common assignment that optimizes a given global criterion (e.g., the total distance traveled) within a finite set of local computations and communications over a peer-to-peer network. As a motivating application, we consider a class of multirobot routing problems with “spatiotemporal” constraints, i.e., spatial targets that require servicing at particular time instants. As a means of demonstrating the theory developed in this paper, the robots cooperatively find online suboptimal routes by applying an iterative version of the proposed algorithm in a distributed and dynamic setting. As a concrete experimental test bed, we provide an interactive “multirobot orchestral” framework, in which a team of robots cooperatively plays a piece of music on a so-called orchestral floor.

In this paper we present a maneuver regulation scheme for Vertical Take-Off and Landing (VTOL) micro aerial vehicles (MAV). Differently from standard trajectory tracking, maneuver regulation has an intrinsic robustness due to the fact that the vehicle is not required to chase a virtual target, but just to stay on a (properly designed) desired path with a given velocity profile. In this paper we show how a robust maneuver regulation controller can be easily designed by converting an existing tracking scheme. The resulting maneuvering controller has three main appealing features, namely it: (i) inherits the robustness properties of the tracking controller, (ii) gains the appealing features of maneuver regulation, and (iii) does not need any additional tuning with respect to the tracking controller. We prove the correctness of the proposed scheme and show its effectiveness in experiments on a nano-quadrotor. In particular, we show on a nontrivial maneuver how external disturbances acting on the quadrotor cause instabilities in the standard tracking, while marginally affect the maneuver regulation scheme.

In this paper we consider a network of agents monitoring a spatially distributed traffic process. Each node measures the number of arrivals seen at its monitoring point in a given time-interval. We propose an asynchronous distributed approach based on a hierarchical Bayes model with unknown hyperparameter, which allows each node to compute the minimum mean square error (MMSE) estimator of the local arrival rate by suitably fusing the information from the whole network. Simulation results show that the distributed scheme improves the estimation accuracy compared to a purely decentralized setup and is reliable even in presence of limited local data. An ad-hoc algorithm with reduced complexity is also proposed, which performs very closely to the optimal MMSE estimator.