Application of a differentiator-based adaptive super-twisting controller for a redundant cable-driven parallel robot

In this paper we present preliminary, experimental results of an Adaptive Super-Twisting Sliding-Mode Controller with time-varying gains for redundant Cable-Driven Parallel Robots. The sliding-mode controller is paired with a feed-forward action based on dynamics inversion. An exact sliding-mode differentiator is implemented to retrieve the velocity of the end-effector using only encoder measurements with the properties of finite-time convergence, robustness against perturbations and noise filtering. The platform used to validate the controller is a robot with eight cables and six degrees of freedom powered by 940 W compact servo drives. The proposed experiment demonstrates the performance of the controller, finite-time convergence and robustness in tracking a trajectory while subject to external disturbances up to approximately 400% the mass of the end-effector

Observability studies for spacecraft attitude determination based on temperature data

Die Schätzung und Steuerung der Fluglage ist elementar für jede Raumfahrzeugmission. Die erforderliche Genauigkeit hängt von der jeweiligen Mission und ihren Nutzlasten ab. Ein funktionierendes Lageregelungssystem ist jedoch immer unverzichtbar, um die Zielgenauigkeit und Stabilität der Nutzlasten zu gewährleisten, die für den Erfolg der Mission entscheidend sind. Daher ist es sinnvoll, redundante Methoden zur Schätzung und Regelung der aktuellen Fluglage einzusetzen. Diese Arbeit fokussiert sich primär auf die Lageschätzung. Hierbei wird untersucht ob und wie Temperaturmessungen für die Lagebestimmung genutzt werden können. Diese Untersuchung wird durchgeführt, indem die zugrundeliegenden mathematischen Beschreibungen der Fluglage sowie der Temperaturdynamik betrachtet werden. Auf deren Grundlage wird dann ein Beobachter zur Lageschätzung entwickelt, der sich hauptsächlich auf die Temperaturdaten von zwei verschiedenen Sensorkonfigurationen stützt. In der ersten Konfiguration wird nur ein einziger Temperatursensor verwendet, dessen Informationen mit Gyroskopmessungen fusioniert werden, um die Lage zu bestimmen. Dies wird durch eine Transformation in Normalform und eine neuartige Lagebeschreibung erreicht. Auftretende Mehrdeutigkeiten bei der Lagebestimmung sowie alternative Beobachterdesigns werden vorgestellt. Die Analyse zeigt, dass mit dem vorgeschlagenen Beobachter lokale Aussagen zur Lageschätzung getroffen werden können - vorausgesetzt, die verwendeten Modelle und Messungen sind ausreichend genau und es steht genügend Rechenleistung zur Verfügung. In der zweiten Konfiguration werden sechs Paare von Temperatursensoren betrachtet. Jedes Paar besteht aus zwei Sensoren mit unterschiedlichen physikalischen Eigenschaften und zeigt in Richtung einer anderen Raumfahrzeugachse. Diese Sensorsignale enthalten genügend Informationen, um die Fluglage zu rekonstruieren, ohne dass die Verwendung von Ableitungen höherer Ordnung erforderlich ist. Es wird ein Algorithmus vorgeschlagen, der die Position der Sonne und der Erde schätzt und diese zur Bestimmung der Lage verwendet. Die Beobachter für beide Konfigurationen verwenden eine Transformation in eine kanonische Form, um ihre Schätzungen zu erhalten. Die resultierenden Beobachter sind daher sowohl in den transformierten als auch in den ursprünglichen Koordinaten formuliert. Während diese Beobachter unter Annahmen die häufig in der Literatur verwendeten werden äquivalent sind, kann es, sobald diese Annahmen fallengelassen werden, zu einer Reihe interessanter Phänomene wie Mehrdeutigkeit der Lösungen und sogar Instabilität kommen. Diese Phänomene werden an unserem vorgestellten System veranschaulicht und es werden Methoden vorgeschlagen, um sie zu bewältigen. Die für die zweite Konfiguration entworfenen Beobachter werden auf die von der Raumsondenmission GRACE erhaltenen Daten angewandt. Dabei hat sich gezeigt, dass die vorgeschlagenen Modelle für die Temperaturschätzung mit einem R2-Wert zwischen 78,8 % und 99,9 % gut geeignet sind. Die vorgeschlagenen Algorithmen erlauben eine Genauigkeit mit einem mittleren Fehler über eine Umlaufbahn von weniger als fünf Grad und lassen sich nachweislich leicht durch zusätzliche Messungen ergänzen.Attitude estimation and control is fundamental for every spacecraft mission. Accuracy requirements are strongly dependant on mission level goals and the respective payloads and experiments. However, it is always essential for the mission success to have a functioning attitude control system to allow a high pointing accuracy and stability of the payloads. Therefore, it is useful to employ redundant means to estimate and control the current attitude. The estimation of the attitude is the main topic of this work in which the information contained in temperature measurements for attitude estimation is investigated. This investigation is carried out by providing the underlying mathematical descriptions of the attitude as well as temperature dynamics. Different observer designs are considered based on these models to estimate the attitude relying mostly on the temperature data obtained from two different sensor configurations. In the first configuration, only a single temperature sensor is employed and the information is fused with gyroscope measurements to determine the attitude. This is achieved based on a transformation into normal form and a novel attitude description. Arising ambiguities in the attitude estimation, as well as alternative observer designs are presented. The analysis shows that with the proposed observer, it is possible to estimate the attitude provided that the employed models and measurements are sufficiently accurate and that enough computational power is available. The second configuration considers six pairs of temperature sensors. Each pair consists of two sensors with different physical properties and every pair points into a different body axis. These sensor signals contain enough information to reconstruct the attitude without requiring the usage of higher-order derivatives. An algorithm is proposed that estimates the position of the Sun and Earth and uses these to estimate the attitude. The observers for both configurations use a transformation of the system dynamics into canonical form to obtain a formulation of the problem that allows for estimation. The resulting observers are therefore formulated in transformed and original coordinates. While these observers are equivalent under assumptions widely used in literature, the moment these assumptions are dropped, a number of interesting phenomena such as ambiguity of the solutions and even instability can occur. These phenomena are illustrated by the system of interest and methods are proposed to deal with them. The designed observers for the second configuration are applied to the data obtained from the spacecraft mission GRACE. The results indicate that the proposed models are well suited for the temperature estimation with a R2 value between 78.8% and 99.9%. The proposed algorithms admit an accuracy with a mean error over an orbit of less than five degrees and are shown to be easily augmented with additional measurements

A Feasibility assessment of a new navigation system for unmanned underwater vehicles with adaptive gain sliding mode differentiation

In this work, a highly accurate navigation device is proposed for unmanned underwater vehicle navigation. A six degree of freedom, open loop underwater vehicle model is generated and is used as the motion platform in this study. The new navigation system, previously developed at the Rochester Institute of Technology, requires real-time body angular acceleration terms as inputs to the algorithm. To address this requirement, real-time signal differentiation techniques were investigated. The differentiation of real-world, noisy signals is a difficult task due to the inherent numerical differentiation and subsequent noise amplification. A sliding mode differentiation scheme is proposed with a fuzzy adaptive controller to aid the accuracy of the signal differentiator and minimize noise amplification. The device algorithms are then implemented in the underwater vehicle model and navigation estimates are compared against theoretical motion. The result is an accurate representation of underwater vehicle attitude and velocity without the aid of global positioning satellite data. Although inertial position estimates obtained from noisy signals suffer from drifting, the filtering techniques used in this work minimize this effect. The navigation estimates show the best results on dynamic maneuvers which do not induce a rolling motion as the underdamped rolling motion requires higher steady state noise for estimation. When assessed against current technologies for underwater vehicle navigation that do not use GPS, the proposed system provides comparable estimation results while creating a reduction of cost, weight and removing the dependence on the speed of sound in water

Fixed-time sliding mode based observer for nonlinear systems with unknown parameters and unknown inputs

International audienceIt is of importance to design observers for multi-variable nonlinear systems with unknown parameters and partially driven by unknown inputs. Such a problem arises in systems subject to disturbances or with inaccessible inputs and in many applications such as parameter identification, fault detection and isolation or cryptography. In this paper, the problem of fixed-time observation for nonlinear dynamical systems with unknown parameter and inputs is studied. Conditions on full/partial state and parameters identification are provided by the the way of an observation algorithm based on differential geometry theory. Then, an uniform differentiator for estimating simultaneously the states and unknown parameters in fixed-time while avoiding observability singularities is designed. An example on topology identification of network systems is described to show the effectiveness of the proposed method

Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article

Control Theory in Engineering

The subject matter of this book ranges from new control design methods to control theory applications in electrical and mechanical engineering and computers. The book covers certain aspects of control theory, including new methodologies, techniques, and applications. It promotes control theory in practical applications of these engineering domains and shows the way to disseminate researchers’ contributions in the field. This project presents applications that improve the properties and performance of control systems in analysis and design using a higher technical level of scientific attainment. The authors have included worked examples and case studies resulting from their research in the field. Readers will benefit from new solutions and answers to questions related to the emerging realm of control theory in engineering applications and its implementation

Advanced Mathematics and Computational Applications in Control Systems Engineering

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering