Aircraft loss-of-control prevention and recovery: a hybrid control strategy

The Complexity of modern commercial and military aircrafts has necessitated better protection and recovery systems. With the tremendous advances in computer technology, control theory and better mathematical models, a number of issues (Prevention, Recon guration, Recovery, Operation near critical points, ... etc) moderately addressed in the past have regained interest in the aeronautical industry.Flight envelope is essential in all ying aerospace vehicles. Typically, ying the vehicle means remaining within the ight envelope at all times. Operation outside the normal ight regime is usually subject to failure of components (Actuators, Engines, Deection Surfaces) , pilots's mistakes, maneuverability near critical points and environmental conditions(crosswinds...) and in general characterized as Loss-Of-Control (LOC) because the aircraft no longer responds to pilot's inputs as expected.For the purpose of this work,(LOC) in aircraft is de ned as the departure from the safe set (controlled flight) recognized as the maximum controllable (reachable) set in the initial ight envelope. The LOC can be reached either through failure, unintended maneuvers, evolution near irregular points and disturbances. A coordinated strategy is investigated and designed to ensure that the aircraft can maneuver safely in their constraint domain and can also recover from abnormal regime. The procedure involves the computation of the largest controllable (reachable) set (Safe set) contained in the initial prescribed envelope. The problem is posed as a reachability problem using Hamilton-Jacobi Partial Di erential Equation(HJ - PDE) where a cost function is set to be minimized along trajectory departing from the given set. Prevention is then obtained by computing the controller which would allow the flight vehicle to remain in the maximum controlled set in a multi-objective set up. Then the recovery procedure is illustrated with a two - point boundary value problem. Once illustrate, a set of control strategies is designed for recovery purpose ranging from nonlinear smooth regulators with Hamilton Jacobi-Bellman (HJB) formulation to the switching controllers with High Order Sliding Mode Controllers (HOSMC). A coordinated strategy known as a high level supervisor is then implemented using the multi-models concept where models operate in specified safe regions of the state space.Ph.D., Mechanical Engineering and Mechanics -- Drexel University, 201

Symbolic models for incrementally stable singularly perturbed hybrid affine systems

International audienceIn this paper, we consider the problem of symbolic models design for the class of incrementally stable singularly perturbed hybrid affine systems. Contrarily to the existing results in the literature where only switching are taken into account, here we consider a more general class of hybridsystems including switches, impulsions and dynamics evolving in different timescales. Firstly, a discussion about incremental stability of the considered class of systems is given. Secondly, a new method for designing symbolic models for incrementally stable singularly perturbed hybrid affine systems is proposed. Inspired from singularly perturbed techniques based on decoupling the slow dynamics from the fast ones,the obtained symbolic abstraction is designed by discretizing only a part of the state space representing the slow dynamics. An e -approximate bisimulation relation between the original singularly perturbed hybrid affine system and the symbolic model obtained by discretizing the slow dynamics is provided. Indeed, since the discrete abstraction is designed for a system of lower dimension, the number of its transitions is drasticallyreduced. Finally, an example is proposed in order to illustrate the efficiency of the proposed results

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Kinodynamic planning and control of closed-chain robotic systems

Aplicat embargament des de la data de defensa fins el dia 1/6/2022This work proposes a methodology for kinodynamic planning and trajectory control in robots with closed kinematic chains. The ability to plan trajectories is key in a robotic system, as it provides a means to convert high-level task commands¾like “move to that location'', or “throw the object at such a speed''¾into low-level controls to be followed by the actuators. In contrast to purely kinematic planners, which only generate collision-free paths in configuration space, kinodynamic planners compute state-space trajectories that also account for the dynamics and force limits of the robot. In doing so, the resulting motions are more realistic and exploit gravity, inertia, and centripetal forces to the benefit of the task. Existing kinodynamic planners are fairly general and can deal with complex problems, but they require the state coordinates to be independent. Therefore, they are hard to apply to robots with loop-closure constraints whose state space is not globally parameterizable. These constraints define a nonlinear manifold on which the trajectories must be confined, and they appear in many systems, like parallel robots, cooperative arms manipulating an object, or systems that keep multiple contacts with the environment. In this work, we propose three steps to generate optimal trajectories for such systems. In a first step, we determine a trajectory that avoids the collisions with obstacles and satisfies all kinodynamic constraints of the robot, including loop-closure constraints, the equations of motion, or any limits on the velocities or on the motor and constraint forces. This is achieved with a sampling-based planner that constructs local charts of the state space numerically, and with an efficient steering method based on linear quadratic regulators. In a second step, the trajectory is optimized according to a cost function of interest. To this end we introduce two new collocation methods for trajectory optimization. While current methods easily violate the kinematic constraints, those we propose satisfy these constraints along the obtained trajectories. During the execution of a task, however, the trajectory may be affected by unforeseen disturbances or model errors. That is why, in a third step, we propose two trajectory control methods for closed-chain robots. The first method enjoys global stability, but it can only control trajectories that avoid forward singularities. The second method, in contrast, has local stability, but allows these singularities to be traversed robustly. The combination of these three steps expands the range of systems in which motion planning can be successfully applied.Aquest treball proposa una metodologia per a la planificació cinetodinàmica i el control de trajectòries en robots amb cadenes cinemàtiques tancades. La capacitat de planificar trajectòries és clau en un robot, ja que permet traduir instruccions d'alt nivell com ara ¿mou-te cap aquella posició'' o ¿llença l'objecte amb aquesta velocitat'' en senyals de referència que puguin ser seguits pels actuadors. En comparació amb els planificadors purament cinemàtics, que només generen camins lliures de col·lisions a l'espai de configuracions, els planificadors cinetodinàmics obtenen trajectòries a l'espai d'estats que són compatibles amb les restriccions dinàmiques i els límits de força del robot. Els moviments que en resulten són més realistes i aprofiten la gravetat, la inèrcia i les forces centrípetes en benefici de la tasca que es vol realitzar. Els planificadors cinetodinàmics actuals són força generals i poden resoldre problemes complexos, però assumeixen que les coordenades d'estat són independents. Per tant, no es poden aplicar a robots amb restriccions de clausura cinemàtica en els quals l'espai d'estats no admeti una parametrització global. Aquestes restriccions defineixen una varietat diferencial sobre la qual cal mantenir les trajectòries, i apareixen en sistemes com ara els robots paral·lels, els braços que manipulen objectes coordinadament o els sistemes amb extremitats en contacte amb l'entorn. En aquest treball, proposem tres passos per generar trajectòries òptimes per a aquests sistemes. En un primer pas, determinem una trajectòria que evita les col·lisions amb els obstacles i satisfà totes les restriccions cinetodinàmiques, incloses les de clausura cinemàtica, les equacions del moviment o els límits en les velocitats i en les forces d'actuació o d'enllaç. Això s'aconsegueix mitjançant un planificador basat en mostratge aleatori que utilitza cartes locals construïdes numèricament, i amb un mètode eficient de navegació local basat en reguladors quadràtics lineals. En un segon pas, la trajectòria s'optimitza segons una funció de cost donada. A tal efecte, introduïm dos nous mètodes de col·locació per a l'optimització de trajectòries. Mentre els mètodes existents violen fàcilment les restriccions cinemàtiques, els que proposem satisfan aquestes restriccions al llarg de les trajectòries obtingudes. Durant l'execució de la tasca, tanmateix, la trajectòria pot veure's afectada per pertorbacions imprevistes o per errors deguts a incerteses en el model dinàmic. És per això que, en un tercer pas, proposem dos mètodes de control de trajectòries per robots amb cadenes tancades. El primer mètode gaudeix d'estabilitat global, però només permet controlar trajectòries que no travessin singularitats directes del robot. El segon mètode, en canvi, té estabilitat local, però permet travessar aquestes singularitats de manera robusta. La combinació d'aquests tres passos amplia el ventall de sistemes en els quals es pot aplicar amb èxit la planificació cinetodinàmica.Postprint (published version

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version