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We present AVOCADO (AdaptiVe Optimal Collision Avoidance Driven by Opinion), a novel navigation approach to address holonomic robot collision avoidance when the degree of cooperation of the other agents in the environment is unknown. AVOCADO departs from a Velocity Obstacle's formulation akin to the Optimal Reciprocal Collision Avoidance method. However, instead of assuming reciprocity, AVOCADO poses an adaptive control problem that aims at adapting in real-time to the cooperation degree of other robots and agents. Adaptation is achieved through a novel nonlinear opinion dynamics design that relies solely on sensor observations. As a by-product, based on the nonlinear opinion dynamics, we propose a novel method to avoid the deadlocks under geometrical symmetries among robots and agents. Extensive numerical simulations show that AVOCADO surpasses existing geometrical, learning and planning-based approaches in mixed cooperative/non-cooperative navigation environments in terms of success rate, time to goal and computational time. In addition, we conduct multiple real experiments that verify that AVOCADO is able to avoid collisions in environments crowded with other robots and humans.

This paper presents a novel accelerated distributed algorithm for unconstrained consensus optimization over static undirected networks. The proposed algorithm combines the benefits of acceleration from momentum, the robustness of the alternating direction method of multipliers, and the computational efficiency of gradient tracking to surpass existing state-of-the-art methods in convergence speed, while preserving their computational and communication cost. First, we prove that, by applying momentum on the average dynamic consensus protocol over the estimates and gradient, we can study the algorithm as an interconnection of two singularly perturbed systems: the outer system connects the consensus variables and the optimization variables, and the inner system connects the estimates of the optimum and the auxiliary optimization variables. Next, we prove that, by adding momentum to the auxiliary dynamics, our algorithm always achieves faster convergence than the achievable linear convergence rate for the non-accelerated alternating direction method of multipliers gradient tracking algorithm case. Through simulations, we numerically show that our accelerated algorithm surpasses the existing accelerated and non-accelerated distributed consensus first-order optimization protocols in convergence speed., Comment: This paper has been accepted for publication at IEEE Control Systems Letters

This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. The ellipsoids are defined as time-varying positive definite matrices. On the other hand, given an undirected network, each node is equipped with one of these ellipsoids. The solution is based on a novel distributed reformulation of the original centralized semi-definite outer L\"owner-John program, characterized by a non-separable objective function and global constraints. We prove finite-time convergence to the global minima of the centralized problem in the static case and finite-time bounded tracking error in the dynamic case. Moreover, we prove boundedness of estimation in the tracking of the global optimum and robustness in the estimation against time-varying inputs. As a by-product, the proposed algorithm extends min/max dynamic consensus algorithms to positive definite matrices. We illustrate the properties of the algorithm with different simulated examples, including a distributed estimation showcase where our proposal is integrated into a distributed Kalman filter to surpass the state-of-the-art in mean square error performance., Comment: This work is currently under review

The networked nature of multi-robot systems presents challenges in the context of multi-agent reinforcement learning. Centralized control policies do not scale with increasing numbers of robots, whereas independent control policies do not exploit the information provided by other robots, exhibiting poor performance in cooperative-competitive tasks. In this work we propose a physics-informed reinforcement learning approach able to learn distributed multi-robot control policies that are both scalable and make use of all the available information to each robot. Our approach has three key characteristics. First, it imposes a port-Hamiltonian structure on the policy representation, respecting energy conservation properties of physical robot systems and the networked nature of robot team interactions. Second, it uses self-attention to ensure a sparse policy representation able to handle time-varying information at each robot from the interaction graph. Third, we present a soft actor-critic reinforcement learning algorithm parameterized by our self-attention port-Hamiltonian control policy, which accounts for the correlation among robots during training while overcoming the need of value function factorization. Extensive simulations in different multi-robot scenarios demonstrate the success of the proposed approach, surpassing previous multi-robot reinforcement learning solutions in scalability, while achieving similar or superior performance (with averaged cumulative reward up to x2 greater than the state-of-the-art with robot teams x6 larger than the number of robots at training time)., Comment: This paper is under review at IEEE T-RO

This paper presents ECO-DKF, the first Event-Triggered and Certifiable Optimal Distributed Kalman Filter. Our algorithm addresses two major issues inherent to Distributed Kalman Filters: (i) fully distributed and scalable optimal estimation and (ii) reduction of the communication bandwidth usage. The first requires to solve an NP-hard optimisation problem, forcing relaxations that lose optimality guarantees over the original problem. Using only information from one-hop neighbours, we propose a tight Semi-Definite Programming relaxation that allows to certify locally and online if the relaxed solution is the optimum of the original NP-hard problem. In that case, ECO-DKF is optimal in the square error sense under scalability and event-triggered one-hop communications restrictions. Additionally, ECO-DKF is a globally asymptotically stable estimator. To address the second issue, we propose an event-triggered scheme from the relaxed optimisation output. The consequence is a broadcasting-based algorithm that saves communication bandwidth, avoids individual communication links and multiple information exchanges within instants, and preserves the optimality and stability properties of the filter., Comment: This paper has been accepted for publication at IEEE Transactions on Automatic Control

The optimal design of power converters requires accurate knowledge of the dissipation elements of its system to achieve the desired performance and security requirements. Calorimetric methods have surpassed classical electrical methods for the estimation of semiconductor power losses but have mechanical limitations and resort to analytical electrothermal equivalent circuits for this task. These electrothermal models are highly dependent on the topology and technology used on the power converter leading to either simplifications that underestimate the thermal effects or intractable sets of differential equations. To overcome these issues, we propose a novel data-driven identification method to characterize the thermal dynamics of power converters allowing the designer to obtain semiconductor total power losses only by means of temperature measurements without the need of a calorimeter. Given a set of power vs.temperature profiles, our solution identifies the linear model that best fits the data. The solution is based on an optimization problem that allows not only accurate identification but also coding of the desired modeling requirements, such as dynamics' invertibility to allow the estimation of power losses from the temperature profiles. The proposed methodology can be applied to any power converter topology. Furthermore, by obtaining a linear model, standard control theory techniques can be exploited to analyze and control the thermal dynamics. Real experiments validate the generality and accuracy of the proposal.

The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the unknown interaction model. Besides, high-dimensional and nonlinear state trajectories make it difficult to identify if two nodes are connected. Current solutions rely on prior knowledge of the graph topology and the dynamic behavior of the nodes, and hence, have poor generalization to other network configurations. To address these issues, we propose a novel learning-based approach that combines (i) a strongly convex program that efficiently uncovers graph topologies with global convergence guarantees and (ii) a self-attention encoder that learns to embed the original state trajectories into a feature space and predicts appropriate regularizers for the optimization program. In contrast to other works, our approach can identify the graph topology of unseen networks with new configurations in terms of number of nodes, connectivity or state trajectories. We demonstrate the effectiveness of our approach in identifying graphs in multi-robot formation and flocking tasks., Comment: Accepted at IEEE MRS 2023

The outer Lowner-John method is widely used in sensor fusion applications to find the smallest ellipsoid that can approximate the intersection of a set of ellipsoids, described by positive definite covariance matrices modeling the quality of each sensor. We propose a distributed algorithm to solve this problem when these matrices are defined over the network's nodes. This is of particular significance as it is the first decentralized algorithm capable of computing the covariance intersection ellipsoid by combining information from the entire network using only local interactions. The solution is based on a reformulation of the centralized problem, leading to a local protocol based on exact dynamic consensus tools. After reaching consensus, the protocol converges to an outer Lowner-John ellipsoid in finite time, and to the global optimum asymptotically. Formal convergence analysis and numerical experiments are provided to validate the proposal's advantages., Comment: This is the accepted version of the manuscript: "Distributed outer approximation of the intersection of ellipsoids," Rodrigo Aldana-Lopez, Eduardo Sebastian, Rosario Aragues, Eduardo Montijano and Carlos Sagues, in IEEE Control Systems Letters, 2023, DOI: 10.1109/LCSYS.2023.3280259

This paper solves the problem of herding countless evaders by means of a few robots. The objective is to steer all the evaders towards a desired tracking reference while avoiding escapes. The problem is very challenging due to the highly complex repulsive evaders' dynamics and the underdetermined states to control. We propose a solution that is based on Implicit Control and a novel dynamic assignment strategy to select the evaders to be directly controlled. The former is a general technique that explicitly computes control inputs even in highly complex input-nonaffine dynamics. The latter is built upon a convex-hull dynamic clustering inspired by the Voronoi tessellation problem. The combination of both allows to choose the best evaders to directly control, while the others are indirectly controlled by exploiting the repulsive interactions among them. Simulations show that massive herds can be herd throughout complex patterns by means of a few herders., Comment: E. Sebastian, E. Montijano and C. Sagues,"Multi-robot Implicit Control of Massive Herds'', Fifth Iberian Robotics Conference (ROBOT22), 2022

This paper presents LEMURS, an algorithm for learning scalable multi-robot control policies from cooperative task demonstrations. We propose a port-Hamiltonian description of the multi-robot system to exploit universal physical constraints in interconnected systems and achieve closed-loop stability. We represent a multi-robot control policy using an architecture that combines self-attention mechanisms and neural ordinary differential equations. The former handles time-varying communication in the robot team, while the latter respects the continuous-time robot dynamics. Our representation is distributed by construction, enabling the learned control policies to be deployed in robot teams of different sizes. We demonstrate that LEMURS can learn interactions and cooperative behaviors from demonstrations of multi-agent navigation and flocking tasks., Comment: Accepted for publication at IEEE International Conference on Robotics and Automation 2023

This paper presents a novel control strategy to herd groups of non-cooperative evaders by means of a team of robotic herders. In herding problems, the motion of the evaders is typically determined by strongly nonlinear and heterogeneous reactive dynamics, which makes the development of flexible control solutions a challenging problem. In this context, we propose Implicit Control, an approach that leverages numerical analysis theory to find suitable herding inputs even when the nonlinearities in the evaders' dynamics yield to implicit equations. The intuition behind this methodology consists in driving the input, rather than computing it, towards the unknown value that achieves the desired dynamic behavior of the herd. The same idea is exploited to develop an adaptation law, with stability guarantees, that copes with uncertainties in the herd's models. Moreover, our solution is completed with a novel caging technique based on uncertainty models and Control Barrier Functions (CBFs), together with a distributed estimator to overcome the need of complete perfect measurements. Different simulations and experiments validate the generality and flexibility of the proposal., Comment: This paper has been accepted for publication in the IEEE Transactions on Robotics

The optimal fusion of estimates in a Distributed Kalman Filter (DKF) requires tracking of the complete network error covariance, problematic in terms of memory and communication. A scalable alternative is to fuse estimates under unknown correlations, doing the update by solving an optimisation problem. Unfortunately, this problem is NP-hard, forcing relaxations that lose optimality guarantees. Motivated by this, we present the first Certifiable Optimal DKF (CO-DKF). Using only information from one-hop neighbours, CO-DKF solves the optimal fusion of estimates under unknown correlations by a particular tight Semidefinite Programming (SDP) relaxation which allows to certify, locally and in real time, if the relaxed solution is the actual optimum. In that case, we prove optimality in the Mean Square Error (MSE) sense. Additionally, we demonstrate the global asymptotic stability of the estimator. CO-DKF outperforms other state-of-the-art DKF algorithms, specially in sparse, highly noisy setups., Comment: This paper has been accepted at 60th 2021 IEEE Conference on Decision and Control (CDC)

This paper presents a novel control strategy to herd a group of non-cooperative evaders by means of a team of robotic herders. In herding problems, the motion of the evaders is typically determined by strong nonlinear reactive dynamics, escaping from the herders. Many applications demand the herding of numerous and/or heterogeneous entities, making the development of flexible control solutions challenging. In this context, our main contribution is a control approach that finds suitable herding actions even when the nonlinearities in the evaders' dynamics yield to implicit equations. We resort to numerical analysis theory to characterise the existence conditions of such actions and propose two design methods to compute them, one transforming the continuous time implicit system into an expanded explicit system, and the other applying a numerical method to find the action in discrete time. Simulations and real experiments validate the proposal in different scenarios., Comment: Accepted at ICRA 2021