A class of optimal fault tolerant Jacobian for minimal redundant manipulators based on symmetric geometries

Design of locally optimal fault tolerant manipulators has been recently addressed via using the constraints of the desired null space for the Jacobian matrix of the manipulators. In the present paper the Jacobian matrices for optimal fault tolerance are presented based on geometric properties of column vectors instead of the null space. They are equally fault tolerant to a single joint failure from the worst-case relative manipulability and worst-case dexterity points of view. The optimality is achieved through a symmetric distribution of points on spheres.

A hybrid approach for fault tolerance in robotics

This paper studies the difference between the human behaviours for fault tolerance with a pseudo inverse reconfiguration approach for fault tolerance of robotic arms. If this difference is well understood then it can be used to introduce a hybrid approach for fault tolerant motion of robotic arms. The proposed approach is expected to combine human fault-tolerance dexterity and advantages of a model based fault tolerance. The main aim is to add human dexterity for fault tolerance of robotic arms.

Multiple actuator fault tolerance for static nonlinear systems based on minimum velocity jump

Static nonlinear systems are common when the model of the kinematics of mechanical or civil structures is analyzed for instance kinematics of robotic manipulators. This paper addresses the maximum effort toward fault tolerance for any number of the locked actuators failures in static nonlinear systems. It optimally reconfigures the inputs via a mapping that maximally accommodates the failures. The mapping maps the failures to an extra action of healthy actuators that results to a minimum jump for the velocity of the output variables. Then from this mapping, the minimum jump of the velocity of the output is calculated. The conditions for a zero velocity jump of the output variables are discussed. This shows that, when the conditions of fault tolerance are maintained, the proposed framework is capable of fault recovery not only at fault instances but also at the whole output trajectory. The proposed mapping is validated by three case studies.

Optimal fault tolerant Jacobian matrix generators for redundant manipulators

The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian matrix is obtained. In this study, an optimal fault-tolerant Jacobian matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

Optimal fault-tolerant robotic manipulators

This thesis addresses “Optimal Fault-Tolerant Robotic Manipulators” for locked-joint failures and consists of three components. It begins by investigating the regions of workspace where the manipulator can operate with high reliability. It then continues with an efficient deployment of kinematic redundancies for fault-tolerant operation. Finally, it presents a novel method for design of optimal fault-tolerant manipulators.

Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For fault-tolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump, because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of the condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator's locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. Then, it is observed that the condition number provides an upper bound of the required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. A solution is for selected optimization problem is presented. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.

A hybrid intelligent system and its application to fault detection and diagnosis

This paper proposes a hybrid system that integrates the SOM (Self Organizing Map) neural network, the kMER (kernel-based Maximum Entropy learning Rule) algorithm and the Probabilistic Neural Network (PNN) for data visualization and classification. The rationales of this hybrid SOM-kMER-PNN model are explained, and the applicability of the proposed model is demonstrated using two benchmark data sets and a real-world application to fault detection and diagnosis. The outcomes show that the hybrid system is able to achieve comparable classification rates when compared to those from a number of existing classifiers and, at the same time, to produce meaningful visualization of the data sets.

A hybrid neural classifier for dimensionality reduction and data visualization and its application to fault detection and classification of induction motors

In this paper, a hybrid neural classifier combining the auto-encoder neural network and the Lattice Vector Quantization (LVQ) model is described. The auto-encoder network is used for dimensionality reduction by projecting high dimensional data into the 2D space. The LVQ model is used for data visualization by forming and adapting the granularity of a data map. The mapped data are employed to predict the target classes of new data samples. To improve classification accuracy, a majority voting scheme is adopted by the hybrid classifier. To demonstrate the applicability of the hybrid classifier, a series of experiments using simulated and real fault data from induction motors is conducted. The results show that the hybrid classifier is able to outperform the Multi-Layer Perceptron neural network, and to produce very good classification accuracy rates for various fault conditions of induction motors.