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

redundant manipulator

Dexterity of underactuated six degrees of freedom three dimensional redundant manipulators

We quantify the dexterity of underactuated robot manipulators equipped with active and passive joints. We discuss the harnessing of redundant degrees of freedom in a robotic manipulator in order to keep it in service. We assume that the passive joints are locked at an arbitrary known position. There are three important dexterity measures: workspace volume, reachability, and manipulability. We discuss the workspace volume of a six degrees of freedom, three dimensional, redundant manipulator with an arbitrarily located passive joint. References X. Xin, J.-H. She, T. Yamasaki and Y. Liu, Swing-up control based on virtual composite links for n-link underactuated robot with passive first joint, Automatica, 45(9):1986–1994, 2009. doi:10.1016/j.automatica.2009.04.023 M. Bergerman and Y. Xu, Dexterity of underactuated manipulators, ICAR, 719–724, 1997. doi:10.1109/ICAR.1997.620261 S, Yahya, M. Moghavvemi and H. A. F. Mohamed, Singularity Avoidance of a Six Degrees of Freedom Three Dimensional Redundant Planar Manipulator, Comput. Math. Appl., 64(5):856–868, 2012. doi:10.1016/j.camwa.2011.12.073 S. Yahya, M. Moghavvemi and H. A. F. Almurib, Joint Torque Reduction of a Three Dimensional Redundant Planar Manipulator, Sensors, 12(6):6869–6892, 2012. doi:10.3390/s120606869 A. K. Pradeep, P. J. Yoder, R. Mukundan, R. J. Schilling, Crippled motion in robots, IEEE T. Aero. Elec. Sys., 24(1):2–13, 1988. doi:10.1109/7.1030 R. G. Roberts, Quantifying the local fault tolerance of a kinematically redundant manipulator, Amer. Contr. Conf., 3:1889–1893, 1995. doi:10.1109/ACC.1995.531215 R. G. Roberts and A. A. Maciejewski. A local measure of fault tolerance for kinematically redundant manipulators, IEEE Int. Conf. Robot., 12(4):543–552, 1996. doi:10.1109/70.508437 S. Yahya, M. Moghavvemi and H. A. F. Mohamed. Geometrical approach of planar hyper-redundant manipulators: Inverse kinematics, path planning and workspace, Simul. Model. Pract. Th., 19(1):406–422, 2011. doi:10.1016/j.simpat.2010.08.001 H. A. F. Mohamed, S. Yahya, M. Moghavvemi and S. S. Yang. A New Inverse Kinematics Method for Three Dimensional Redundant Manipulators, ICCAS-SICE, 1557–1562, 2009. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5335259&refinements%3D4274859776%26sortType%3Dasc_p_Sequence%26filter%3DAND%28p_IS_Number%3A5332438%2

Real-time failure-tolerant control of kinematically redundant manipulators

Includes bibliographical references (pages 1115-1116).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 end-effector 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. Comparisons show that the performance of the best method is indistinguishable from that of brute-force implementations. An example demonstrating the real-time performance of the algorithm on a commercially available seven degree-of-freedom manipulator is presented

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

Undetected locked-joint failures in kinematically redundant manipulators: a workspace analysis

Includes bibliographical references.Robots are frequently used for operations in hostile environments. The very nature of these environments, however, increases the likelihood of robot failures. Common failure tolerance techniques rely on effective failure detection. Since a failure may not always be successfully detected, or even if detected, may not be detected soon enough, it becomes important to consider the behavior of manipulators with undetected failures. This work focuses on developing techniques to analyze a manipulator's workspace and identify regions in which tasks, characterized by sequences of point-to-point moves, can be completed even with such failures. Measures of fault tolerance are formulated to allow for the evaluation of the workspace.This work was supported by Sandia National Labs under contract no. AL-3011 and by NSF under contract no. MIP-9708309

Real-time failure-tolerant control of kinematically redundant manipulators

Includes bibliographical references.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 end-effector 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 performance of the best is indistinguishable from that of brute-force implementations.This work was supported by Sandia National Laboratories under contract number AL-3011

Failure tolerant teleoperation of a kinematically redundant manipulator: an experimental study

Includes bibliographical references (page 765).Teleoperated robots in harsh environments have a significant likelihood of failures. It has been shown in previous work that a common type of failure such as that of a joint "locking up," when unidentified by the robot controller, can cause considerable performance degradation in the local behavior of the manipulator even for simple point-to-point motion tasks. The effects of a failure become more critical for a system with a human in the loop, where unpredictable behavior of the robotic arm can completely disorient the operator. In this experimental study involving teleoperation of a graphically simulated kinematically redundant manipulator, two control schemes, the pseudoinverse and a proposed failure-tolerant inverse, were randomly presented under both nonfailure and failure scenarios to a group of operators. Based on performance measures derived from the recorded trajectory data and operator ratings of task difficulty, it is seen that the failure-tolerant inverse kinematic control scheme improved the performance of the human/robot system

Computational feasibility study of failure-tolerant path planning, A

Includes bibliographical references (page 239).This work considers the computational costs associated with the implementation of a failure-tolerant path planning algorithm proposed in [1]. The algorithm makes the following assumptions: a manipulator is redundant relative to its task, only a single joint failure occurs at any given time, the manipulator is capable of detecting a joint failure and immediately locks the failed joint, and the environment is static and known. The algorithm is evaluated on a three degree-of-freedom planar manipulator for a total of eleven thousand different scenarios, randomly varying the robot's start and goal positions and the number and locations of obstacles in the environment. Statistical data are presented related to the computation time required by the different steps of the algorithm as a function of the complexity of the environment

Design and control of kinematically redundant robots for maximizing failure-tolerant workspaces

2021 Spring.Includes bibliographical references.Kinematically redundant robots have extra degrees of freedom so that they can tolerate a joint failure and still complete an assigned task. Previous work has defined the "failure-tolerant workspace" as the workspace that is guaranteed to be reachable both before and after an arbitrary locked-joint failure. One mechanism for maximizing this workspace is to employ optimal artificial joint limits prior to a failure. This dissertation presents two techniques for determining these optimal artificial joint limits. The first technique is based on the gradient ascent method. The proposed technique is able to deal with the discontinuities of the gradient that are due to changes in the boundaries of the failure tolerant workspace. This technique is illustrated using two examples of three degree-of-freedom planar serial robots. The first example is an equal link length robot where the optimal artificial joint limits are computed exactly. In the second example, both the link lengths and artificial joint limits are determined, resulting in a robot design that has more than twice the failure-tolerant area of previously published locally optimal designs. The second technique presented in this dissertation is a novel hybrid technique for estimating the failure-tolerant workspace size for robots of arbitrary kinematic structure and any number of degrees of freedom performing tasks in a 6D workspace. The method presented combines an algorithm for computing self-motion manifold ranges to estimate workspace envelopes and Monte-Carlo integration to estimate orientation volumes to create a computationally efficient algorithm. This algorithm is then combined with the coordinate ascent optimization technique to determine optimal artificial joint limits that maximize the size of the failure-tolerant workspace of a given robot. This approach is illustrated on multiple examples of robots that perform tasks in 3D planar and 6D spatial workspaces