Fault Residual Generation via Nonlinear Analytical Redundancy

Fault detection is critical in many applications, and analytical redundancy (AR) has been the key underlying tool for many approaches to fault detection. However, the conventional AR approach is formally limited to linear systems. In this brief, we exploit the structure of nonlinear geometric control theory to derive a new nonlinear analytical redundancy (NLAR) framework. The NLAR technique is applicable to affine systems and is seen to be a natural extension of linear AR. The NLAR structure introduced in this brief is tailored toward practical applications. Via an example of robot fault detection, we show the considerable improvement in performance generated by the approach compared with the traditional linear AR approach

Robot Reliability Through Fuzzy Markov Models

In the past few years, new applications of robots have increased the importance of robotic reliability and fault tolerance. Standard approaches of reliability engineering rely on the probability model, which is often inappropriate for this task due to a lack of sufficient probabilistic information during the design and prototyping phases. Fuzzy logic offers an alternative to the probability paradigm, possibility, that is much more appropriate to reliability in the robotic context.National Science FoundationNASAOffice of Naval ResearchSandia National Laborator

Robotic Fault Detection Using Nonlinear Analytical Redundancy

In this paper we discuss the application of our recently developed nonlinear analytical redundancy (NLAR) fault detection technique to a two-degree of freedom robot manipulator. NLAR extends the traditional linear AR technique to derive the maximum possible number of fault detection tests into the continuous nonlinear domain. The ability to handle nonlinear systems vastly expands the accuracy and viable applications of the AR technique. The effectiveness of the approach is demonstrated through an example.NASANational Science Foundatio

Experimental AR Fault Detection Methods for a Hydraulic Robot

This paper focuses on practical use and theoretical elaboration of the analytical redundancy technique which is used to efficiently detect faults that have been determined to be mission-hazardous by previous FMECA and fault tree analyses of the Rosie system. We believe we have contributed significant improvements to the potential overall reliability of the system. Additionally, we have expanded the applicability of the AR method to nonlinear systems in the course of our work, making this valuable fault detection method more broadly applicable.National Science FoundationSandia National Laborator

Derivation and Application of Nonlinear Analytical Redundancy Techniques with Applications to Robotics

PhD ThesisDerivation and Application of Nonlinear Analytical Redundancy Techniques with Applications to Robotics Fault detection is important in many robotic applications. Failures of powerful robots, high velocity robots, or robots in hazardous environments are quite capable of causing significant and possibly irreparable havoc if they are not detected promptly and appropriate action taken. As robots are commonly used because power, speed, or resistances to environmental factors need to exceed human capabilities, fault detection is a common and serious concern in the robotics arena. Analytical redundancy (AR) is a fault-detection method that allows us to explicitly derive the maximum possible number of linearly independent control model-based consistency tests for a system. Using a linear model of the system of interest, analytical redundancy exploits the null-space of the state space control observability matrix to allow the creation of a set of test residuals. These tests use sensor data histories and known control inputs to detect any deviation from the static or dynamic behaviors of the model in real time. The standard analytical redundancy fault detection technique is limited mathematically to linear systems. Since analytical redundancy is a model-based technique, it is extremely sensitive to differences between the nominal model behavior and the actual system behavior. A system model with strong nonlinear characteristics, such as a multi-joint robot manipulator, changes significantly in behavior when linearized. Often a linearized model is no longer an accurate description of the system behavior. This makes effective implementation of the analytical redundancy technique difficult, as modeling errors will generate significant false error signals when linear analytical redundancy is applied. To solve this problem we have used nonlinear control theory to extend the analytical redundancy principle into the nonlinear realm. Our nonlinear analytical redundancy (NLAR) technique is applicable to systems described by nonlinear ordinary differential equations and preserves the important formal guarantees of linear analytical redundancy. Nonlinear analytical redundancy generates considerable improvement in performance over linear analytical redundancy when performing fault detection on nonlinear systems, as it removes all of the extraneous residual signal generated by the modeling inaccuracies introduced by linearization, allowing for lower threshold

Derivation and application of nonlinear analytical redundancy techniques with applications to robotics

Fault detection is important in many robotic applications. Failures of powerful robots, high velocity robots, or robots in hazardous environments are quite capable of causing significant and possibly irreparable havoc if they are not detected promptly and appropriate action taken. As robots are commonly used because power, speed, or resistances to environmental factors need to exceed human capabilities, fault detection is a common and serious concern in the robotics arena. Analytical redundancy (AR) is a fault-detection method that allows us to explicitly derive the maximum possible number of linearly independent control model-based consistency tests for a system. Using a linear model of the system of interest, analytical redundancy exploits the null-space of the state space control observability matrix to allow the creation of a set of test residuals. These tests use sensor data histories and known control inputs to detect any deviation from the static or dynamic behaviors of the model in real time. The standard analytical redundancy fault detection technique is limited mathematically to linear systems. Since analytical redundancy is a model-based technique, it is extremely sensitive to differences between the nominal model behavior and the actual system behavior. A system model with strong nonlinear characteristics, such as a multi-joint robot manipulator, changes significantly in behavior when linearized. Often a linearized model is no longer an accurate description of the system behavior. This makes effective implementation of the analytical redundancy technique difficult, as modeling errors will generate significant false error signals when linear analytical redundancy is applied. To solve this problem we have used nonlinear control theory to extend the analytical redundancy principle into the nonlinear realm. Our nonlinear analytical redundancy (NLAR) technique is applicable to systems described by nonlinear ordinary differential equations and preserves the important formal guarantees of linear analytical redundancy. Nonlinear analytical redundancy generates considerable improvement in performance over linear analytical redundancy when performing fault detection on nonlinear systems, as it removes all of the extraneous residual signal generated by the modeling inaccuracies introduced by linearization, allowing for lower threshold

Robotic fault detection using nonlinear analytical redundancy

In this paper we discuss the application of our recently developed nonlinear analytical redundancy (NLAR) fault detection technique to a two-degree of freedom robot manipulator. NLAR extends the traditional linear AR technique to derive the maximum possible number of fault detection tests into the continuous nonlinear domain. The ability to handle nonlinear systems vastly expands the accuracy and viable applications of the AR technique. The effectiveness of the approach is demonstrated through an example. 1