Optimal mapping of joint faults into healthy joint velocity space for fault-tolerant redundant manipulators

redundant manipulator

A Kinematic Analysis and Evaluation of Planar Robots Designed From Optimally Fault-Tolerant Jacobians Khaled M. Ben-Gharbia, Student Member, IEEE,

Abstract—It is common practice to design a robot’s kinematics from the desired properties that are locally specified by a manipulator Jacobian. In this work, the desired property is fault tolerance, defined as the postfailure Jacobian possessing the largest possible minimum singular value over all possible locked-joint failures. A mathematical analysis based on the Gram matrix that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. It is shown that rearranging the columns of the Jacobian or multiplying one or more of the columns of the Jacobian by ±1 will not affect local fault tolerance; however, this will typically result in a very different manipulator. Two examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are analyzed. This analysis shows that there is a large variability in the global kinematic properties of these designs, despite being generated from the same Jacobian. It is especially surprising that major differences in global behavior occurs for manipulators that are identical in the working area. Index Terms—Fault-tolerant robots, robot kinematics, redundant robots. I

Fast and Accurate Computation of the Round-Off Noise of LTI Systems

From its introduction in the last decade, affine arithmetic (AA) has shown beneficial properties to speed up the time of computation procedures in a wide variety of areas. In the determination of the optimum set of finite word-lengths of the digital signal processing systems, the use of AA has been recently suggested by several authors, but the existing procedures provide pessimistic results. The aim is to present a novel approach to compute the round-off noise (RON) using AA which is both faster and more accurate than the existing techniques and to justify that this type of computation is restricted to linear time-invariant systems. By a novel definition of AA-based models, this is the first methodology that performs interval-based computation of the RON. The provided comparative results show that the proposed technique is faster than the existing numerical ones with an observed speed-up ranging from 1.6 to 20.48, and that the application of discrete noise models leads to results up to five times more accurate than the traditional estimations

Fault Tree Analysis: a survey of the state-of-the-art in modeling, analysis and tools

Fault tree analysis (FTA) is a very prominent method to analyze the risks related to safety and economically critical assets, like power plants, airplanes, data centers and web shops. FTA methods comprise of a wide variety of modelling and analysis techniques, supported by a wide range of software tools. This paper surveys over 150 papers on fault tree analysis, providing an in-depth overview of the state-of-the-art in FTA. Concretely, we review standard fault trees, as well as extensions such as dynamic FT, repairable FT, and extended FT. For these models, we review both qualitative analysis methods, like cut sets and common cause failures, and quantitative techniques, including a wide variety of stochastic methods to compute failure probabilities. Numerous examples illustrate the various approaches, and tables present a quick overview of results

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

Towards a framework for architecting heterogeneous teams of humans and robots for space exploration

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 113-121).Human-robotic systems will play a critical role in space exploration, should NASA embark on missions to the Moon and Mars. A unified framework to optimally leverage the capabilities of humans and robots in space exploration will be an invaluable tool for mission planning. Although there is a growing body of literature on human robotic interactions (HRI), there is not yet a framework that lends itself both to a formal representation of heterogeneous teams of humans and robots, and to an evaluation of such teams across a series of common, task-based metrics. My objective in this thesis is to lay the foundations of a unified framework for architecting human-robotic systems for optimal task performance given a set of metrics. First, I review literature from different fields including HRI and human-computer interaction, and synthesize multiple considerations for architecting heterogeneous teams of humans and robots. I then present methods to systematically and formally capture the characteristics that describe a human-robotic system to provide a basis for evaluating human-robotic systems against a common set of metrics.(cont.) I propose an analytical formulation of common metrics to guide the design and evaluate the performance of human-robot systems, and I then apply the analytical formulation to a case study of a multi-agent human-robot system developed at NASA. Finally, I discuss directions for further research aimed at developing this framework.by Julie Ann Arnold.S.M

Integrated maintenance model based on establishment of principles of mechanical vibrations change and its impact on prognostics of condition of rotor engines

Osnovni cilj ove disertacije je da se razvije Integrisani model odrţavanja zasnovan na vibracijama sloţenih rotacionih tehniĉkih sistema, odnosno da se uspostavi sprovoĊenje dijagnostiĉkih provera stanja sklopova rotacionih mašina (kontrola vibracija). Zatim da se definišu optimalne periodiĉnosti vibracija kao i identifikacija ocena i rangiranja rizika sa stanovišta prekida rada mašina. Na taj naĉin potvrdiće se glavna hipoteza koja glasi: „Razvijanjem integrisanog modela odrţavanja zasnovanog na uspostavljanju zakonitosti promene mehaniĉkih vibracija moći će da se preventivno predvide pojave neispravnosti i prognozira stanje rotacionih mašina.The basic goal of this dissertation is the development of an Integrated Maintenance Model based on vibrations of complex rotational technical systems, in other words, the establishment of implementation of diagnostic checks of rotating machinery compositions condition (control of vibrations). Afterwards, the definition of optimal periodicity of vibrations, as well as identification of estimations and ranking of risks from the stand point of disruption of work of operational processes. This is the way to confirm the main hypothesis which reads: “Development of an Integrated Maintenance Model based on the establishment of legality of change of mechanical vibrations will enable preventive predicting of malfunction occurrence, as well as prognosis of rotating machinery health