Derivation and application of nonlinear analytical redundancy techniques with applications to robotics
type: CreativeWork
description: 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 im…
abstract: 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 im…
author: Leuschen, Martin L.
language: eng
keywords: Electronics, Electrical engineering
date published: 2002
date modified: 2026-07-24T04:10:34Z
provider: Rice University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Rice University

PropertyValue
property ID: Handle
value: https://hdl.handle.net/1911/18106