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

redundant manipulator

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

Kinematic design and motion planning of fault tolerant robots with locked joint failures

2019 Summer.Includes bibliographical references.The problem of kinematic design and motion planning of fault tolerant robots with locked joint failure is studied in this work. In kinematic design, the problem of designing optimally fault tolerant robots for equal joint failure probabilities is first explored. A measure of local fault tolerance for equal joint failure probabilities has previously been defined based on the properties of the singular values of the Jacobian matrix. Based on this measure, one can determine a Jacobian that is optimal. Because these measures are solely based on the singular values of the Jacobian, permutation of the columns does not affect the optimality. Therefore, when one generates a kinematic robot design from this optimal Jacobian, there will be 7! robot designs with the same locally optimal fault tolerant property. This work shows how to analyze and organize the kinematic structure of these 7! designs in terms of their Denavit and Hartenberg (DH) parameters. Furthermore, global fault tolerant measures are defined in order to evaluate the different designs. It is shown that robot designs that are very similar in terms of DH parameters, e.g., robots generated from Jacobians where the columns are in reverse order, can have very different global properties. Finally, a computationally efficient approach to calculate the global pre- and post-failure dexterity measures is presented and used to identify two Pareto optimal robot designs. The workspaces for these optimal designs are also shown. Then, the problem of designing optimally fault tolerant robots for different joint failure probabilities is considered. A measure of fault tolerance for different joint failure probabilities is defined based on the properties of the singular values of the Jacobian after failures. Using this measure, methods to design optimally fault tolerant robots for an arbitrary set of joint failure probabilities and multiple cases of joint failure probabilities are introduced separately. Given an arbitrary set of joint failure probabilities, the optimal null space that optimizes the fault tolerant measure is derived, and the associated isotropic Jacobians are constructed. The kinematic parameters of the optimally fault tolerant robots are then generated from these Jacobians. One special case, i.e., how to construct the optimal Jacobian of spatial 7R robots for both positioning and orienting is further discussed. For multiple cases of joint failure probabilities, the optimal robot is designed through optimizing the sum of the fault tolerant measures for all the possible joint failure probabilities. This technique is illustrated on planar 3R robots, and it is shown that there exists a family of optimal robots. After the optimally fault tolerant robots are designed, the problem of planning the optimal trajectory with minimum probability of task failure for a set of point-to-point tasks, after experiencing locked joint failures, is studied. The proposed approach first develops a method to calculate the probability of task failure for an arbitrary trajectory, where the trajectory is divided into small segments, and the probability of task failure of each segment is calculated based on its failure scenarios. Then, a motion planning algorithm is proposed to find the optimal trajectory with minimum probability of task failure. There are two cases. The trajectory in the first case is the optimal trajectory from the start configuration to the intersection of the bounding boxes of all the task points. In the other case, all the configurations along the self-motion manifold of task point 1 need to be checked, and the optimal trajectory is the trajectory with minimum probability of task failure among them. The proposed approach is demonstrated on planar 2R redundant robots, illustrating the effectiveness of the algorithm

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

Modeling, Control and Estimation of Reconfigurable Cable Driven Parallel Robots

The motivation for this thesis was to develop a cable-driven parallel robot (CDPR) as part of a two-part robotic device for concrete 3D printing. This research addresses specific research questions in this domain, chiefly, to present advantages offered by the addition of kinematic redundancies to CDPRs. Due to the natural actuation redundancy present in a fully constrained CDPR, the addition of internal mobility offers complex challenges in modeling and control that are not often encountered in literature. This work presents a systematic analysis of modeling such kinematic redundancies through the application of reciprocal screw theory (RST) and Lie algebra while further introducing specific challenges and drawbacks presented by cable driven actuators. It further re-contextualizes well-known performance indices such as manipulability, wrench closure quality, and the available wrench set for application with reconfigurable CDPRs. The existence of both internal redundancy and static redundancy in the joint space offers a large subspace of valid solutions that can be condensed through the selection of appropriate objective priorities, constraints or cost functions. Traditional approaches to such redundancy resolution necessitate computationally expensive numerical optimization. The control of both kinematic and actuation redundancies requires cascaded control frameworks that cannot easily be applied towards real-time control. The selected cost functions for numerical optimization of rCDPRs can be globally (and sometimes locally) non-convex. In this work we present two applied examples of redundancy resolution control that are unique to rCDPRs. In the first example, we maximize the directional wrench ability at the end-effector while minimizing the joint torque requirement by utilizing the fitness of the available wrench set as a constraint over wrench feasibility. The second example focuses on directional stiffness maximization at the end-effector through a variable stiffness module (VSM) that partially decouples the tension and stiffness. The VSM introduces an additional degrees of freedom to the system in order to manipulate both reconfigurability and cable stiffness independently. The controllers in the above examples were designed with kinematic models, but most CDPRs are highly dynamic systems which can require challenging feedback control frameworks. An approach to real-time dynamic control was implemented in this thesis by incorporating a learning-based frameworks through deep reinforcement learning. Three approaches to rCDPR training were attempted utilizing model-free TD3 networks. Robustness and safety are critical features for robot development. One of the main causes of robot failure in CDPRs is due to cable breakage. This not only causes dangerous dynamic oscillations in the workspace, but also leads to total robot failure if the controllability (due to lack of cables) is lost. Fortunately, rCDPRs can be utilized towards failure tolerant control for task recovery. The kinematically redundant joints can be utilized to help recover the lost degrees of freedom due to cable failure. This work applies a Multi-Model Adaptive Estimation (MMAE) framework to enable online and automatic objective reprioritization and actuator retasking. The likelihood of cable failure(s) from the estimator informs the mixing of the control inputs from a bank of feedforward controllers. In traditional rigid body robots, safety procedures generally involve a standard emergency stop procedure such as actuator locking. Due to the flexibility of cable links, the dynamic oscillations of the end-effector due to cable failure must be actively dampened. This work incorporates a Linear Quadratic Regulator (LQR) based feedback stabilizer into the failure tolerant control framework that works to stabilize the non-linear system and dampen out these oscillations. This research contributes to a growing, but hitherto niche body of work in reconfigurable cable driven parallel manipulators. Some outcomes of the multiple engineering design, control and estimation challenges addressed in this research warrant further exploration and study that are beyond the scope of this thesis. This thesis concludes with a thorough discussion of the advantages and limitations of the presented work and avenues for further research that may be of interest to continuing scholars in the community

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

Analysis of the post-fault behavior of robotic manipulators, An

Includes bibliographical references.Operations in hazardous or remote environments are invariably performed by robots. The hostile nature of the environments, however, increase the likelihood of failures for robots used in such applications. The difficulty and delay in the detection and consequent correction of these faults makes the post-fault performance of the robots particularly important. This work investigates the behavior of robots experiencing undetected locked-joint failures in a general class of tasks characterized by point-to-point motion. The robot is considered to have "converged" to a task position and orientation if all its joints come to rest when the end-effector is at that position. It is seen that the post-fault behavior may be classified into three categories: 1) The robot converges to the task position; 2) the robot converges to a position other than the task position; or 3) the robot does not converge, but keeps moving forever. The specific conditions for convergence are identified, and the different behaviors illustrated with examples of simple planar manipulators.This work was supported by Sandia National Laboratories under contract number AL-3011

Modifying the Kinematic Structure of an Anthropomorphic Arm to Improve Fault Tolerance

Abstract-It is well known that anthropomorphic manipulators, such as the PA-10, are intolerant to a single locked joint failure of the elbow. This is because the elbow is the only joint that can change the distance between the spherical shoulder joint and the spherical wrist. In this work, it is shown how such arms can be made significantly more fault tolerant by a minor modification to the kinematic structure of the arm. We quantify the degree of fault tolerance to locked joint failures as the minimum of the smallest singular value of the resulting seven Jacobians over all possible single failures. The DH parameters for the modified arm are designed so that the corresponding fault tolerant properties are close to those of a robot with an optimally failure tolerant Jacobian. The fault tolerance of the designed robot is evaluated for two different classes of applications, i.e., point-to-point motions and specified end-effector trajectories