Joint velocity redistribution for fault tolerant manipulators

If the end-effector of a robotic manipulator moves on a specified trajectory, then for the fault tolerant operation, it is required that the end-effector continues the trajectory with a minimum velocity jump when a fault occurs within a joint. This problem is addressed in the paper. A way to tolerate the fault is to find new joint velocities for the faulty manipulator in which results into the same end-effector velocity provided by the healthy manipulator. The aim of this study is to find a strategy which optimally redistributes the joint velocities for the remained healthy joints of the manipulators. The optimality is defined by the minimum end-effector velocity jump. A solution of the problem is presented and it is applied to a robotics manipulator. Then through a case study and a simulation study it is validated. The paper shows that if would be possible the joint velocity redistribution results into a zero velocity jump

On the effort of task completion for partially-failed manipulators

Adding to a previous work of the authors for task completion for partially failed manipulator, other aspects of the effort are discussed. The paper aims to investigate on the strategies of maximum effort for maintaining the availability of partially failed manipulators. The failures are assumed as the joint lock failures of the manipulators. The main objective is to facilitate the existing manipulators to continue their tasks even if a non catastrophic fault occurs into their joints. The tasks includes motion tasks and force tasks. For each group of tasks a constrained optimality problem is introduced. Then in a case study a required force profile on a desired trajectory using a 3DOF planar manipulator is indicated. Through this study the joint angles and joint torques for a healthy manipulator and a faulty manipulator are shown. It is illustrated that a failure in the second joint is tolerated on the trajectory of end-effector

Kinematic design and motion planning of fault tolerant robots with locked joint failures

2019 Summer.Includes bibliographical references.The problem of kinematic design and motion planning of fault tolerant robots with locked joint failure is studied in this work. In kinematic design, the problem of designing optimally fault tolerant robots for equal joint failure probabilities is first explored. A measure of local fault tolerance for equal joint failure probabilities has previously been defined based on the properties of the singular values of the Jacobian matrix. Based on this measure, one can determine a Jacobian that is optimal. Because these measures are solely based on the singular values of the Jacobian, permutation of the columns does not affect the optimality. Therefore, when one generates a kinematic robot design from this optimal Jacobian, there will be 7! robot designs with the same locally optimal fault tolerant property. This work shows how to analyze and organize the kinematic structure of these 7! designs in terms of their Denavit and Hartenberg (DH) parameters. Furthermore, global fault tolerant measures are defined in order to evaluate the different designs. It is shown that robot designs that are very similar in terms of DH parameters, e.g., robots generated from Jacobians where the columns are in reverse order, can have very different global properties. Finally, a computationally efficient approach to calculate the global pre- and post-failure dexterity measures is presented and used to identify two Pareto optimal robot designs. The workspaces for these optimal designs are also shown. Then, the problem of designing optimally fault tolerant robots for different joint failure probabilities is considered. A measure of fault tolerance for different joint failure probabilities is defined based on the properties of the singular values of the Jacobian after failures. Using this measure, methods to design optimally fault tolerant robots for an arbitrary set of joint failure probabilities and multiple cases of joint failure probabilities are introduced separately. Given an arbitrary set of joint failure probabilities, the optimal null space that optimizes the fault tolerant measure is derived, and the associated isotropic Jacobians are constructed. The kinematic parameters of the optimally fault tolerant robots are then generated from these Jacobians. One special case, i.e., how to construct the optimal Jacobian of spatial 7R robots for both positioning and orienting is further discussed. For multiple cases of joint failure probabilities, the optimal robot is designed through optimizing the sum of the fault tolerant measures for all the possible joint failure probabilities. This technique is illustrated on planar 3R robots, and it is shown that there exists a family of optimal robots. After the optimally fault tolerant robots are designed, the problem of planning the optimal trajectory with minimum probability of task failure for a set of point-to-point tasks, after experiencing locked joint failures, is studied. The proposed approach first develops a method to calculate the probability of task failure for an arbitrary trajectory, where the trajectory is divided into small segments, and the probability of task failure of each segment is calculated based on its failure scenarios. Then, a motion planning algorithm is proposed to find the optimal trajectory with minimum probability of task failure. There are two cases. The trajectory in the first case is the optimal trajectory from the start configuration to the intersection of the bounding boxes of all the task points. In the other case, all the configurations along the self-motion manifold of task point 1 need to be checked, and the optimal trajectory is the trajectory with minimum probability of task failure among them. The proposed approach is demonstrated on planar 2R redundant robots, illustrating the effectiveness of the algorithm

observer and energy-balance based approaches

Due to the increasing complexity of modern technical processes, the most critical issues in the design of an automated system nowadays are safety/reliability, higher performance and cost efficiency. Faults in process components can lead to a considerable reduce of the efficiency of the process, quality of the product and in some cases even result in fatalities. In order to avert these losses, an efficient diagnosis of the faults plays a central role. Therefore, fault diagnosis is becoming an essential part of modern control systems. Fault diagnosis of linear dynamical systems has been extensively studied since decades and well-established techniques exist in the literature. However, fault diagnosis for nonlinear dynamical systems is yet an active field of research. Since most of real systems are nonlinear in nature, classically, linear fault diagnosis techniques have been applied to nonlinear systems based on the linearized system model around an operating point. The drawback of this approach is the limited fault diagnosis performance. In order to fulfill the increasing demand of more effective fault diagnosis systems for nonlinear processes, a lot of attention has been paid to nonlinear fault diagnosis techniques, which is the major topic of this thesis. Different from linear systems, there is no uniform solution for the fault diagnosis of general nonlinear systems. Various schemes have been proposed for nonlinear systems with special structures. Among them, Lipschitz nonlinear systems have been intensively studied, since on one hand more general nonlinear systems can be transformed into Lipschitz nonlinear systems, and on the other hand, many linear fault diagnosis approaches can be extended to this kind of nonlinear systems. For Lipschitz nonlinear systems, observer-based fault detection approach has been mostly applied, which consists of an observer-based residual generator and a residual evaluator. Classically, residual generator and residual evaluator are designed separately. Since the performance of fault detection system is decided by residual generator and evaluator together, it can be expected that, higher fault detection performance can be achieved by designing these two units in an integrated manner instead of separate handling of them. Motivated by this fact, an integrated design approach of observer-based residual generator and evaluator is proposed for Lipschitz nonlinear systems. Besides the schemes extended from linear methods (i.e. observer-based approach, parity space approach etc.), new nonlinear fault diagnosis techniques have also been studied recently, which can be effectively applied to complex nonlinear systems i.e. switched nonlinear systems, hybrid nonlinear systems etc. Among them, new fault diagnosis schemes based on passivity and energy-balance which are closely related to system “energy” have a great potential due to their clear physical meanings. In this thesis, this approach is extended to a complete fault detection and isolation framework with the focus on passive nonlinear systems. The fault diagnosis methodologies proposed in this thesis are tested with the design examples in the respective chapters and with the robot manipulator benchmark problem. The simulation results show the effectiveness of the proposed schemes.Aufgrund der zunehmenden Komplexität moderner technischer Verfahren sind heutzutage Sicherheit/Zuverlässigkeit, höhere Leistung und Kosteneffizienz wichtige Probleme bei der Gestaltung eines automatisierten Systems. Fehler in Prozesskomponenten führen zu einer erheblichen Reduzierung im Wirkungsgrad des Prozesses, in der Qualität des Produktes und können im schlimmsten Fall sogar katastrophale Folgen haben. Um dies zu vermeiden ist eine effiziente Diagnose der Fehler von zentraler Bedeutung. Fehlerdiagnose ist daher ein wesentlicher Bestandteil von modernen Steuerungssystemen geworden. Die Fehlerdiagnose bei linearen dynamischen Systemen wurde seit Jahrzehnten ausführlich untersucht und gut etablierte Techniken existieren in der Literatur, dagegen ist die Fehlerdiagnose für nichtlineare dynamische Systeme noch ein aktives Forschungsfeld. Da die meisten realen Systemen nichtlineare sind, werden lineare Fehlerdiagnosetechniken meistens auf ein linearisiertes Systemmodell angewendet, was sich jedoch nachteilig auf die Leistung auswirkt. Deshalb gewinnt nichtlineare Fehlerdiagnosetechnik zur Erfüllung der wachsenden Nachfrage nach einer besseren Fehlerdiagnose für nichtlineare Prozesse immer mehr an Bedeutung und ist daher das Hauptthema dieser Dissertation. Da es keine einheitliche Lösung für die Fehlerdiagnose allgemeiner nichtlinearer Systeme gibt werden bestimmte nichtlineare Systeme mit speziellen Strukturen untersucht. Unter ihnen sind besonders die Lipschitz Systeme intensiv untersucht worden, da einerseits viele allgemeine nichtlineare Systeme in Lipschitz Systeme umgewandelt werden können und andererseits viele lineare Fehlerdiagnose Ansätze für diese Art von nichtlinearen Systemen erweitert werden können. Für Lipschitz Systeme werden meist beobachtergestützte Fehlerdetektionsverfahren verwendet, die aus einem Residuengenerator und einer Residuenauswertung bestehen. Klassischerweise werden Residuengenerator und Residuenauswertung getrennt entworfen. Da die Leistung der Fehlerdetektion sowohl von Residuengenerator als auch von Residuenauswertung gemeinsam abhängt, ist zu erwarten, dass eine höhere Fehlererkennungsleistung erreicht werden kann, wenn der Entwurf dieser beiden Einheiten integriert erfolgt. Deshalb wird hier ein integrierter Design-Ansatz zur beobachtergestützten Fehlererkennung für Lipschitz Systeme vorgeschlagen. Neben der Erweiterung von linearen Methoden (beobachtergestützter Ansatz, Paritäts Raum Ansatz usw.) werden neue, nichtlineare Fehlerdiagnosetechniken seit kurzem untersucht, die auch auf komplexe, nichtlineare Systeme (geschaltete nichtlineare Systeme, hybride nichtlineare Systeme usw.) angewendet werden können. Unter ihnen besonders Passivitäts- und Energie-Bilanz- gestützte Verfahren, die eng mit der " Systemenergien" verbunden sind, ein großes Potenzial durch ihre klare physikalische Bedeutung. Diese Verfahren werden in dieser Dissertation zu einer vollständigen Fehlererkennungs- und Isolationsmethodik mit dem Fokus auf passive nichtlineare Systeme erweitert. Die gezeigten Algorithmen werden in den entsprechenden Kapiteln anhand von numerischen Beispielen getestet. Weiterhin wird die Verwendung der Algorithmen an dem geläufigen Beispielprozess eines Roboter Manipulators gezeigt um deren Nutzen und Anwendbarkeit zu demonstrieren

Fault Detection and Identification for Robot Manipulators ∗

Abstract: Several factors must be considered for robotic task execution in the presence of a fault, including: detection, identification, and accommodation for the fault. In this paper, a prediction error based dead-zone residual function and a nonlinear observer are used to detect and identify a class of actuator faults. Advantages of the proposed fault detection and identification methods are that they are based on the nonlinear dynamic model of a robot manipulator (and hence, can be extended to a number of general Euler Lagrange systems), they do not require acceleration measurements, and they are independent from the controller. A Lyapunov-based analysis is provided to prove that the developed fault observer converges to the actual fault. Simulation results are provided to illustrate the performance of the detection and identification methods.