Eduardo Montijano

Distributed attitude synchronization control of multi-agent systems with switching topologies

This paper addresses the attitude synchronization problem in multi-agent systems with directed and switching interconnection topologies. Two cases for the synchronization problem are discussed under different assumptions about the measurable information. In the first case the agents can measure their rotations relative to a global reference coordinate frame, whilst in the second case they can only measure the relative rotations between each other. Two intuitive distributed control laws based on the axis-angle representations of the rotations are proposed for the two cases, respectively. The invariance of convex balls in SO(3) is guaranteed. Moreover, attitude synchronization is ensured under the well-known mild switching assumptions, the joint strong connection for the first case and joint quasi-strong connection for the second case. To show the effectiveness of the proposed control schemes, illustrative examples are provided.

Human-Computer Interaction Based on Hand Gestures Using RGB-D Sensors

In this paper we present a new method for hand gesture recognition based on an RGB-D sensor. The proposed approach takes advantage of depth information to cope with the most common problems of traditional video-based hand segmentation methods: cluttered backgrounds and occlusions. The algorithm also uses colour and semantic information to accurately identify any number of hands present in the image. Ten different static hand gestures are recognised, including all different combinations of spread fingers. Additionally, movements of an open hand are followed and 6 dynamic gestures are identified. The main advantage of our approach is the freedom of the users hands to be at any position of the image without the need of wearing any specific clothing or additional devices. Besides, the whole method can be executed without any initial training or calibration. Experiments carried out with different users and in different environments prove the accuracy and robustness of the method which, additionally, can be run in real-time.

Distributed formation control without a global reference frame

This paper presents a decentralized controller to drive a team of agents to reach a desired formation in the absence of a global reference frame. Each agent is able to measure its relative position and orientation with respect to its neighbors. The different orientations imply that the relative positions between pairs of agents are sensed differently for each agent. In order to reach the desired configuration, the agents use two simultaneous consensus controllers, one to control their relative orientations, and another for their relative positions. The convergence to the desired configuration is shown by comparing the system with time-varying orientations with the equivalent approach with fixed rotations, showing that their difference vanishes as time goes to infinity. While the analysis in the paper is performed in a 2-dimensional space with orientations belonging to SO(2), our approach can be extended to handle 3 dimensions and orientations in SO(3). Simulation results, as well as hardware experiments with two quadrotor UAVs, corroborate the theoretical findings of the paper.

Consistent data association in multi-robot systems with limited communications.

In this paper we address the data association problem of features observed by a robot team with limited communications. At every time instant, each robot can only exchange data with a subset of the robots, its neighbors. Initially, each robot solves a local data association with each of its neighbors. After that, the robots execute the proposed algorithm to agree on a data association between all their local observations which is globally consistent. One inconsistency appears when chains of local associations give rise to two features from one robot being associated among them. The contribution of this work is the decentralized detection and resolution of these inconsistencies. We provide a fully decentralized solution to the problem. This solution does not rely on any particular communication topology. Every robot plays the same role, making the system robust to individual failures. Information is exchanged exclusively between neighbors. In a finite number of iterations, the algorithm finishes with a data association which is free of inconsistent associations. In the experiments, we show the performance of the algorithm under two scenarios. In the first one, we apply the resolution and detection algorithm for a set of stochastic visual maps. In the second, we solve the feature matching between a set of images taken by a robotic team.

Distributed attitude synchronization control

In this paper we consider the problem of constructing feedback control laws for a system of n agents that shall synchronize their attitudes in SO(3). We propose distributed controllers for two synchronization problems, in which the objective is the same, to synchronize the orientations, but what the agents can perceive or communicate differs. In the first problem the agents can measure their orientation to a common reference object, and either communicate with the neighbors or estimate the relative orientation to their neighbors. In the second problem the agents can, without communication, only measure the relative orientation to the neighbors. For the first problem we present a controller which will lead to synchronization, provided the neighborhood graph is connected. For the second problem we present a controller that will lead to synchronization provided the neighborhood graph is connected and the agents initially are contained within a geodesic ball of radius πover2 , which is the maximal convex set in SO(3).

A distributed algorithm for average consensus on strongly connected weighted digraphs

In this work we propose a distributed algorithm to solve the discrete-time average consensus problem on strongly connected weighted digraphs (SCWDs). The key idea is to couple the computation of the average with the estimation of the left eigenvector associated with the zero eigenvalue of the Laplacian matrix according to the protocol described in Qu et al. (2012). The major contribution is the removal of the requirement of the knowledge of the out-neighborhood of an agent, thus paving the way for a simple implementation based on a pure broadcast-based communication scheme.

A decentralized algorithm for balancing a strongly connected weighted digraph

In this work we propose a decentralized algorithm for balancing a strongly connected weighted digraph. This algorithm relies on the decentralized estimation of the left eigenvector associated to the zero structural eigenvalue of the Laplacian matrix. The estimation is performed through the distributed computation of the powers of the Laplacian matrix itself. This information can be locally used by each agent to modify the weights of its incoming edges so that their sum is equal to the sum of the weights outgoing this agent, i.e., the weighted digraph is balanced. Simulation results are proposed to corroborate the theoretical results.

Distributed Data Association in Robotic Networks With Cameras and Limited Communications

We address the data association problem of features that are observed by a robotic network. Every robot in the network has limited communication capabilities and can only exchange local matches with its neighbors. We propose a distributed algorithm that takes these local matches and, by their propagation in the network, computes global correspondences. When the algorithm finishes, each robot knows the correspondences between its features and the features of all the other robots, even if they cannot directly communicate. The presence of spurious local correspondences may produce inconsistent global correspondences, which are association paths between features observed by the same robot. The contributions of this study are the propagation of the local matches and the detection and resolution of these inconsistencies. We formally prove that after executing the algorithm, all the robots finish with a data association that is free of inconsistencies. We provide a fully decentralized solution to the problem that is valid for any fixed communication topology and with bounded communications between the robots. Simulations and experimental results with real images show the performance of the method considering different features, matching functions, and robotic applications.

Vision-Based Distributed Formation Control Without an External Positioning System

In this paper, we present a fully distributed solution to drive a team of robots to reach a desired formation in the absence of an external positioning system that localizes them. Our solution addresses two fundamental problems that appear in this context. First, we propose a 3-D distributed control law, designed at a kinematic level, that uses two simultaneous consensus controllers: one to control the relative orientations between robots, and another for the relative positions. The convergence to the desired configuration is shown by comparing the system with time-varying orientations against the equivalent approach with fixed orientations, showing that their difference vanishes as time goes to infinity. Second, in order to apply this controller to a group of aerial robots, we combine this idea with a novel sensor fusion algorithm to estimate the relative pose of the robots by using onboard cameras and information from the inertial measurement unit. The algorithm removes the influence of roll and pitch from the camera images and estimates the relative pose between robots by using a structure from the motion approach. Simulation results, as well as hardware experiments with a team of three quadrotors, demonstrate the effectiveness of the controller and the vision system working together.

Chebyshev Polynomials in Distributed Consensus Applications

In this paper we analyze the use of Chebyshev polynomials in distributed consensus applications. It is well known that the use of polynomials speeds up the convergence to the consensus in a significant way. However, existing solutions only work for low degree polynomials and require the topology of the network to be fixed and known. We propose a distributed algorithm based on the second order difference equation that describes the Chebyshev polynomials of first kind. The contributions of our algorithm are three: (i) Since the evaluation of Chebyshev polynomials is stable, there is no limitation in the degree of the polynomial. (ii) Instead of the knowledge of the whole network topology, it only requires a partial knowledge or an approximation to it. (iii) It can be applied to time varying topologies. In the paper we characterize the main properties of the algorithm for both fixed and time-varying communication topologies. Theoretical results, as well as experiments with synthetic data, show the benefits of using our algorithm compared to existing methods.