On the control of the algebraic connectivity and clustering of a mobile robotic network

International audienceIn this paper two related problems are studied: the control of the algebraic connectivity and clustering of a network of single-integrator agents. A steepest-descent algorithm is presented for the first problem, so that a smooth approximation of the algebraic connectivity of the underlying undirected communication graph converges to an assigned value. For the second problem, a new gradient-based control strategy is proposed to automatically partition the mobile robotic network into two predefined groups: our spectral clustering method leverages a continuous-time power-iteration algorithm on the normalized Laplacian matrix which provides an estimate of its Fiedler vector at each time instant. The results of numerical simulations are provided to illustrate our theoretical findings

The Second-order Parametric Consensus Protocol

International audienceIn this paper we extend the parametric consensus protocol recently introduced by the author, to more realistic agents modeled as double integrators and interacting over an undirected communication network. The stability properties of the new protocol in terms of the real parameter "s" are studied for some relevant graph topologies, and the connection with the notion of bipartite consensus is highlighted. The theory is illustrated with the help of two worked examples, dealing with the coordination of a team of quadrotor UAVs and with cooperative temperature measurement in an indoor environment

The Second-order Parametric Consensus Protocol

International audienceIn this paper we extend the parametric consensus protocol recently introduced by the author, to more realistic agents modeled as double integrators and interacting over an undirected communication network. The stability properties of the new protocol in terms of the real parameter "s" are studied for some relevant graph topologies, and the connection with the notion of bipartite consensus is highlighted. The theory is illustrated with the help of two worked examples, dealing with the coordination of a team of quadrotor UAVs and with cooperative temperature measurement in an indoor environment

Visibility maintenance via controlled invariance for leader-follower Dubins-like vehicles

The paper studies the visibility maintenance problem (VMP) for a leader-follower pair of Dubins-like vehicles with input constraints, and proposes an original solution based on the notion of controlled invariance. The nonlinear model describing the relative dynamics of the vehicles is interpreted as linear uncertain system, with the leader robot acting as an external disturbance. The VMP is then reformulated as a linear constrained regulation problem with additive disturbances (DLCRP). Positive D-invariance conditions for linear uncertain systems with parametric disturbance matrix are introduced and used to solve the VMP when box bounds on the state, control input and disturbance are considered. The proposed design procedure is shown to be easily adaptable to more general working scenarios. Extensive simulation results are provided to illustrate the theory and show the effectiveness of our approachComment: 17 pages, 24 figures, extended version of the journal paper of the authors submitted to Automatic

A Distributed Solution to the Network Reconstruction Problem

International audienceIt has been recently shown in Ren et al. (2010) that by collecting noise-contaminated time series generated by a coupled-oscillator system at each node of a network, it is possible to robustly reconstruct its topology, i.e. determine the graph Laplacian. Restricting ourselves to linear consensus dynamics over undirected communication networks, in this paper we introduce a new dynamic average consensus least-squares algorithm to locally estimate these time series at each node, thus making the reconstruction process fully distributed and more easily applicable in the real world. We also propose a novel efficient method for separating the off-diagonal entries of the reconstructed Laplacian, and examine several concepts related to the trace of the dynamic correlation matrix of the coupled single integrators, which is a distinctive element of our network reconstruction method. The theory is illustrated with examples from computer, power and transportation systems

The Deformed Consensus Protocol

International audienceThis paper studies a generalization of the standard continuous-time consensus protocol, obtained by replacing the Laplacian matrix of the communication graph with the so-called deformed Laplacian. The deformed Laplacian is a second-degree matrix polynomial in the real variable s which reduces to the standard Laplacian for s equal to unity. The stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs, and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems. Examples and simulation results are provided to illustrate our theoretical findings

Uncalibrated Visual Compass from Omnidirectional Line Images with Application to Attitude MAV Estimation

International audienceThis paper presents a new algorithm based on previous results of the authors, for the estimation of the yaw angle of an omnidirectional camera robot undergoing a 6-DoF rigid motion. Our real-time algorithm is uncalibrated, robust to noisy data, and it only relies on the projection of 3-D parallel lines as image features. Numerical and real-world experiments conducted with an eye-in-hand robot manipulator, which we used to simulate the 3-D motion of a Micro unmanned Aerial Vehicle (MAV), show the accuracy and reliability of our estimation algorithm

Decentralized optimal control of a vehicle platoon with guaranteed string stability

International audienceThis paper presents new decentralized optimal strategies for Cooperative Adaptive Cruise Control (CACC) of a car platoon under string-stability constraints. Two related scenarios are explored in the article: in the first one, a linear-quadratic regulator in the presence of measurable disturbances is synthesized, and the string-stability of the platoon is enforced over the controller's feedback and feedforward gains. In the second scenario, H2- and Hinf-performance criteria, respectively accounting for the desired group behavior and the string-stability of the platoon, are simultaneously achieved using the recently-proposed compensator blending method. An analytical study of the impact of actuation/communication delays and uncertain model parameters on the stability of the multi-vehicle system, is also conducted. The theory is illustrated via numerical simulations

Cooperative human-robot haptic navigation

International audienceThis paper proposes a novel use of haptic feedback for human navigation with a mobile robot. Assuming that a path-planner has provided a mobile robot with an obstacle-free trajectory, the vehicle must steer the human from an initial to a desired target position by only interacting with him/her via a custom-designed vibro-tactile bracelet. The subject is free to decide his/her own pace and a warning vibrational signal is generated by the bracelet only when a large deviation with respect to the planned trajectory is detected by the vision sensor on-board the robot. This leads to a cooperative navigation system that is less intrusive, more flexible and easy-to-use than the ones existing in literature. The effectiveness of the proposed system is demonstrated via extensive real-world experiments