Nicolas Léchevin

Trajectory tracking of leader-follower formations characterized by constant line-of-sight angles

A group of identical unicycles is controlled by means of local feedback laws that require measurements of the unicycles relative positions and speeds. Vehicle interconnections are considered unilateral and are modeled by means of a directed acyclic graph. Although not needed for the implementation of the controllers, the desired trajectory of each vehicle is derived from the requirement that the formation must rotate with the leader while ensuring that the relative positions and line-of-sight angles between unicycles are time-invariant. Exponential convergence of the actual trajectories to a ball centered on the desired trajectories is obtained by computing the Jacobian of the nonlinear dynamics and using results from contraction theory. Instrumental to this derivation is the subsystem feedback decomposition interpretation of the plant model. In this context, convergence depends on the uniform negative definiteness and strict positive realness of the forward and feedback subsystems. Such properties are obtained provided a set of linear and bilinear matrix inequalities as well as kinematic constraints are satisfied. A numerical example illustrates the convergence property of a leader-follower formation.

A solution to simultaneous arrival of multiple UAVs using Pythagorean hodograph curves

This paper presents a solution to the problem of simultaneous arrival of a swarm of UAVs by safe and continuously flyable paths. Continuously flyable-paths are generated by satisfying the curvature constraint throughout the path-length. The flyable paths ensure the safety of the UAVs by changing the shape of the flyable-paths by adjusting curvature of the paths. The main idea used in this paper is that a specific type of path is used in the first place for path planning and the shape of the path is varied to meet the multiple constraints. Pythagorean hodograph curves are used for the path planning algorithm. The principle of differential geometry that a planar curve is completely determined by its curvature is used for changing the shape of the path. The multiple constraints are: (i) curvature constraints (ii) minimum-separation-distance and (iii) non-intersection of paths at equal length

Decentralized Detection of a Class of Non-Abrupt Faults With Application to Formations of Unmanned Airships

We propose a decentralized non-abrupt fault detection (DNaFD) scheme for leader-to-follower formations of unmanned airships. Non-abrupt faults are those that result in slow performance degradation and in undesirable drift, which can propagate from one vehicle to another, and therefore can adversely affect mission integrity, potentially destabilizing multivehicle formations, while being difficult to detect. As opposed to model-based fault detectors, which are typically insensitive to non-abrupt faults, the proposed signal-based DNaFD enables the detection of slowly degrading vehicle performance by performing a statistical test on heading angle trajectories. Here, the formation of unmanned airships is assumed stabilized by a distributed formation guidance scheme that uses neighboring vehicle information. High-fidelity, nonlinear 6-degrees-of-freedom (DOF) simulations of formation flying airships show that the proposed DNaFD scheme combined with a simple guidance adaptation technique enable detection of a class of non-abrupt faults and formation recovery, despite mild winds and parametric uncertainties, while preserving a requirement on formation geometry.

Convergence of sampled-data models in digital redesign

This note proposes sufficient conditions that guarantee uniform-in-time convergence, as the sampling period approaches zero, of the control input to and the controlled output of a plant under sampled-data control to those corresponding signals of the same plant under continuous-time control. Sampled-data control systems exhibiting such behavior are formally defined as sampled-data models, which can be very convenient in the analysis and design of sampled-data systems since they can warn the engineer if a known limiting closed-loop behavior is likely to be violated. This practical consideration often occurs in digital redesign, where an analog control law is implemented digitally, with the objective of preventing intersample ripples.

Health-Aware Coverage Control With Application to a Team of Small UAVs

This paper studies the problem of controlling a team of vehicles in order to cover a region with their onboard sensors. The goal is to perform such a coverage task when the capability of the vehicles to carry out the task varies through time. We consider variable sensing performance and the loss of vehicles. Algorithms are proposed to enable coverage despite such variable health conditions. These algorithms are validated through experiments with quad-rotor unmanned air vehicles. Since these algorithms require communication among the vehicles, simulations are carried out to show that the proposed algorithms degrade nicely when perfect communication is not possible.

A Decision Policy for the Routing and Munitions Management of Multiformations of Unmanned Combat Vehicles in Adversarial Urban Environments

The control and management of unmanned combat vehicles (UCVs) operating in an adversarial urban environment is a challenging task due, in part, to the imperfect and incomplete information available, the conflicting objectives of opposing teams, the uncertain stochastic dynamics, and the limitation in computational capability. In this paper, a decision policy built upon Markov decision processes is proposed to provide optimal routing and munitions management despite the conflicting objectives of the adversaries and the stochastic dynamics. The main novelty of the proposed decision policy lies in its handling of multiple UCV formations of varying dimensions. This multiformations capability is explicitly accounted for in the proposed formulation of the optimization problem. The UCVs, which constitute the blue team, have for objective to reach prescribed tactical target locations from a common starting point by following possibly different paths across an adversarial urban environment, within prescribed time windows and with maximum lethality. On their way, the UCVs will face an adversarial red team, which is composed of ground units that can engage any nearby UCV. The rendezvous objective of the blue team can be interpreted as a constraint in an optimization problem, aimed at minimizing damage while maximizing the total number of remaining munitions at the time the multiformations reach the targets. The blue and red teams play the roles of cost-function minimizer and maximizer, respectively. The worst-case minimization objective of the blue team is formulated as a finite-time optimization, which is solved by means of a dynamic programming equation with value function evolving according to a graph of feasible UCV paths. The resulting decision policy takes the form of a lookup table, which is ideal for online implementations. The practical case of imperfect information on the classification and the location of the adversarial ground units is addressed by means of a one-step lookahead rollout policy using estimates provided by a recursive Bayesian filter. Simulation results show that the concept of multiformations provides, on average, an improvement in performance when compared with single-formation routing.

Safety and Reliability in Cooperating Unmanned Aerial Systems

This book provides a comprehensive overview of recent advances in the analysis and design of health management systems for cooperating unmanned aerial vehicles. Such systems rely upon monitoring and fault adaptation schemes. Motivation for their study comes from the fact that, despite the use of fault-tolerant control software and hardware embedded onboard air vehicles, overall fleet performance may still be degraded after the occurrence of anomalous events such as systems faults and failures. Cooperative health management (CHM) systems seek to provide adaptation to the presence of faults by capitalizing on the availability of interconnected computing, sensing and actuation resources.This monograph complements the proposed CHM concepts by means of case studies and application examples. It presents fundamental principles and results encompassing optimization, systems theory, information theory, dynamics, modeling and simulation. Written by pioneers in cooperative control, health management and fault-tolerant control for unmanned systems, this book is a unique source of information for designers, researchers and practitioners interested in the field.

Optimizing the location of sensors subject to health degradation

One of the main hypotheses supporting the development of cooperative unmanned systems is that the deployment of mobile assets (sensors, weapons) in groups is expected to result in a more effective mission than if conducted with a single asset. Few researches have tackled the design of autonomous decision making for teaming UxVs (unmanned air and ground vehicles) operating under degraded conditions, even though it is common knowledge that real operations are more often than not conducted in less-than-ideal conditions. We consider a team of UxVs that have for mission to persistently monitor an area. We want to ensure they perform as best as possible assuming they are subject to a limited set of degraded conditions. We propose a model to account for variable sensor effectiveness as well as a method to optimize their placement based on a cost balancing heuristic. Numerical simulation suggests accounting for sensor effectiveness improves their placement.

Transportation risk analysis using probabilistic model checking

Elaboration of an approach for transportation risk assessment and contingency evaluation.Modeling risk prone transportation tasks as composed Markov Decision Process (MDP).Assessment of transportation tasks expressed as MDP via probabilistic model checking.Provision of decision making support via decision trees built from the model checking output.Evaluation of risk related properties expressed in probabilistic temporal logic. Transportation and supply chain activities represent essential components in many endeavors covering both public and private domains. However, the underlying transport networks are complex and potentially fragile due to weather, natural disasters or other risk factors. Thus, assessing transportation related risk represents a key decision support capability along with the ability to evaluate contingency options for risk mitigation. In this paper, we address these issues by adopting probabilistic model checking to evaluate the risk and contingency options related to transportation tasks. In this pursuit, risk related properties are assessed for behavioral models capturing the transport system. Moreover, we show the usefulness of constructing decision trees that can provide insightful means of risk appraisal. The proposed approach can help decision makers evaluate contingency options and determine lower and upper cost bounds for risky transportation tasks such as those involved in humanitarian aid provision. The proposed approach is also illustrated with a case study.

A digital control perspective for real-time modeling of electrical switching systems - a case study of linear circuits with diodes

The article describes a digital control technique for real-time modeling and simulation of hybrid systems. The performance of the closed-loop real-time model is close to that of the original continuous-time model. To illustrate the technique, linear circuits equipped with diodes were considered. A voltage source model of the diode is represented as an analog controller in feedback with a linear, time-invariant system and serves as a starting point to a global digital redesign strategy. The objective of digital redesign is to obtain a discrete-time control system that behaves as closely as possible to the LTI continuous-time closed-loop system. The procedure was validated through real-time and off-line simulations of a three-phase diode rectifier.