Real-time failure-tolerant control of kinematically redundant manipulators

Abstract

The forward kinematics of manipulators are frequently represented as to potentially catastrophic incidents in remote and/or hazardous environments. A direct approach towards increasing robot reliability is to improve the reliability of the individual components; however, achieving acceptable reliability rates is often prohibitively expensive, and sometimes technologically impossible. An alternative approach is to consider failure-tolerant robot designs. These typically incorporate a failure detection and identification scheme [:3J followed by failure recovery [4J. Designing the robot with redundant systems increases the options available for failure tolerance. Redundancy can be in the form of duplication of actuators and sensors [5, 6J, or in the form of kinematic redundancy [7, 8, 9J. Proper utilization of kinematic redundancy provides greater dexterity prior to failures, minimizes the immediate impact of a failure, and guarantees task completion by ensuring a reachable postfailure workspace.This work presents real-time implementation of schemes for utilizing kinematic redundancy to maximize the tolerance of robots to single locked-joint failures. The fault-tolerance measure used is a worst-case quantity, given by the minimum, over all single joint failures, of the minimum singular value of the post-failure Jacobians. Maximizing this measure corresponds to configuring the robot to minimize the worst-case end-effector velocity error over all single locked-joint failures. This is also equivalent to minimizing the worst-case discontinuities in the joint velocities of the healthy joints as they move to compensate for the failed joint. The main contributions of this work are computationally efficient schemes for computing the fault-tolerance measure and its gradient, which in turn enable real-time optimal configuration of robots in anticipation of failures.where x is an m-dimensional vector representing the end-effector velocity, q is an n-dimensional vector describing the joint velocities, and J is the m by n manipulator Jacobian matrix [10]. For a redundant manipulator, n > m so the equation is underconstrained and there are an infinite number of solutions which can be expressed as ABSTRACT This work considers real-time fault-tolerant control of kinematically redundant manipulators to single locked-joint failures. The fault-tolerance measure used is a worst-case quantity, given by the minimum, over all single joint failures, of the minimum singular value of the post-failure Jacobians. Given any endeffector trajectory, the goal is to continuously follow this trajectory with the manipulator in configurations that maximize the fault-tolerance measure. The computation required to track these optimal configurations with brute-force methods is prohibitive for real-time implementation. We address this issue by presenting algorithms that quickly compute estimates of the worst-case fault-tolerance measure and its gradient. Real-time implementations are presented for all these techniques, and comparisons show that the perfo...

Modifying the kinematic structure of an anthropomorphic arm to improve fault tolerance

“…1 The gradients for K and I are found using the method described in [3]. In [3] it was noted that K can be written as…”

Modifying the kinematic structure of an anthropomorphic arm to improve fault tolerance

“…1 The gradients for K and I are found using the method described in [3]. In [3] it was noted that K can be written as…”

An example of computing the failure-tolerant workspace area for a planar kinematically redundant robot

“…The goal of this work is to extend the use of robots to remote or hazardous environments, for example, in space exploration [3] and nuclear waste disposal [4], where failures are inevitable. The failure rates for components in such harsh environments are relatively high [5], [6], and maintenance is not possible. Many of these component failures will result in a robot's joint becoming immobilized, i.e., a locked joint failure mode, or be transformed into a locked joint by failure recovery mechanisms that employ fail safe brakes [7].…”

“…Assume that one is interested in operating a given robot in a locally fault tolerant manner [6] and in a manner that guarantees an optimal post-failure workspace. A planar three degree-of-freedom revolute (3R) robot is used here as an example.…”

Analyzing unidentified locked-joint failures in kinematically redundant manipulators

“…which can be obtained by combining (3), (5), and (6). Although ẋ a may not drive the end effector directly towards the desired task position, it is of interest to know whether the end effector will eventually converge to it.…”

“…where GϭW Ϫ1 J T (JW Ϫ1 J T ) Ϫ1 for some symmetric WϾ0. 5 Let S be the set of the indices of the k locked joints, and let j i and w i denote the ith columns of J and W, respectively. Then,…”

Modifying the kinematic structure of an anthropomorphic arm to improve fault tolerance

“…1 The gradients for K and I are found using the method described in [3]. In [3] it was noted that K can be written as…”

An example of computing the failure-tolerant workspace area for a planar kinematically redundant robot

“…The goal of this work is to extend the use of robots to remote or hazardous environments, for example, in space exploration [3] and nuclear waste disposal [4], where failures are inevitable. The failure rates for components in such harsh environments are relatively high [5], [6], and maintenance is not possible. Many of these component failures will result in a robot's joint becoming immobilized, i.e., a locked joint failure mode, or be transformed into a locked joint by failure recovery mechanisms that employ fail safe brakes [7].…”

“…Assume that one is interested in operating a given robot in a locally fault tolerant manner [6] and in a manner that guarantees an optimal post-failure workspace. A planar three degree-of-freedom revolute (3R) robot is used here as an example.…”

Analyzing unidentified locked-joint failures in kinematically redundant manipulators

“…which can be obtained by combining (3), (5), and (6). Although ẋ a may not drive the end effector directly towards the desired task position, it is of interest to know whether the end effector will eventually converge to it.…”

“…where GϭW Ϫ1 J T (JW Ϫ1 J T ) Ϫ1 for some symmetric WϾ0. 5 Let S be the set of the indices of the k locked joints, and let j i and w i denote the ith columns of J and W, respectively. Then,…”

Modifying the kinematic structure of an anthropomorphic arm to improve fault tolerance

“…1 The gradients for K and I are found using the method described in [3]. In [3] it was noted that K can be written as…”

An example of computing the failure-tolerant workspace area for a planar kinematically redundant robot

“…The goal of this work is to extend the use of robots to remote or hazardous environments, for example, in space exploration [3] and nuclear waste disposal [4], where failures are inevitable. The failure rates for components in such harsh environments are relatively high [5], [6], and maintenance is not possible. Many of these component failures will result in a robot's joint becoming immobilized, i.e., a locked joint failure mode, or be transformed into a locked joint by failure recovery mechanisms that employ fail safe brakes [7].…”

“…Assume that one is interested in operating a given robot in a locally fault tolerant manner [6] and in a manner that guarantees an optimal post-failure workspace. A planar three degree-of-freedom revolute (3R) robot is used here as an example.…”

Analyzing unidentified locked-joint failures in kinematically redundant manipulators

“…which can be obtained by combining (3), (5), and (6). Although ẋ a may not drive the end effector directly towards the desired task position, it is of interest to know whether the end effector will eventually converge to it.…”

“…where GϭW Ϫ1 J T (JW Ϫ1 J T ) Ϫ1 for some symmetric WϾ0. 5 Let S be the set of the indices of the k locked joints, and let j i and w i denote the ith columns of J and W, respectively. Then,…”