Minimum reconfiguration for fault tolerant manipulators

When a robotic manipulator is fault tolerant it is beneficial to study the configurations which tolerate non-catastrophic locked joint failures with a minimum relative change for the joint velocities. This problem is addressed using the properties of the condition number of the Jacobian matrix. The relationship between the faults within the joints of the manipulators and the condition number of the Jacobean matrix is used to introduce the optimal configurations for fault recovery. These optimum configurations require a minimum reconfiguration for fault tolerance of robotics manipulators. Then these configurations are studied for a 4-DOF planar manipulator to validate the proposed framework.

Optimal actuator fault tolerance for static nonlinear systems based on minimum output velocity jump

Fault tolerance for a class of non linear systems is addressed based on the velocity of their output variables. This paper presents a mapping to minimize the possible jump of the velocity of the output, due to the actuator failure. The failure of the actuator is assumed as actuator lock. The mapping is derived and it provides the proper input commands for the healthy actuators of the system to tolerate the effect of the faulty actuator on the output of the system. The introduced mapping works as an optimal input reconfiguration for fault recovery, which provides a minimum velocity jump suitable for static nonlinear systems. The proposed mapping is validated through different case studies and a complementary simulation. In the case studies and the simulation, the mapping provides the commands to compensate the effect of different faults within the joints of a robotic manipulator. The new commands and the compare between the velocity of the output variables for the health and faulty system are presented.

Fault tolerance operation of cooperative manipulators

Autonomous or teleoperation of critical tasks in space applications require fault tolerant robotic manipulators. These manipulators are able to maintain their tasks even if a joint fails. If it is presumed that the manipulator is fault tolerant on its trajectory, then the next step is to provide a fault tolerant force at the end-effector of the manipulator. The problem of cooperative fault tolerant force is addressed in this paper within the operation of two manipulators. The cooperative manipulators are used to compensate the force jump which occurs on the force of the end-effector of one manipulator due to a joint failure. To achieve fault tolerant operation, the contribution of the faulty joint for the force of the end-effector of the faulty manipulator is required to be optimally mapped into the torque of the faulty and healthy manipulators. The optimal joint torque reconfigurations of both manipulators for compensating this force jump are illustrated. The proposed frameworks are deployed for two cooperative PUMA560 manipulators. The results of the case studies validate the fault tolerant cooperation strategies.

Joint velocity redistribution for fault tolerant manipulators

If the end-effector of a robotic manipulator moves on a specified trajectory, then for the fault tolerant operation, it is required that the end-effector continues the trajectory with a minimum velocity jump when a fault occurs within a joint. This problem is addressed in the paper. A way to tolerate the fault is to find new joint velocities for the faulty manipulator in which results into the same end-effector velocity provided by the healthy manipulator. The aim of this study is to find a strategy which optimally redistributes the joint velocities for the remained healthy joints of the manipulators. The optimality is defined by the minimum end-effector velocity jump. A solution of the problem is presented and it is applied to a robotics manipulator. Then through a case study and a simulation study it is validated. The paper shows that if would be possible the joint velocity redistribution results into a zero velocity jump.

Fault-tolerant scheduling with dynamic number of replicas in heterogeneous systems

In the existing studies on fault-tolerant scheduling, the active replication schema makes use of ε + 1 replicas for each task to tolerate ε failures. However, in this paper, we show that it does not always lead to a higher reliability with more replicas. Besides, the more replicas implies more resource consumption and higher economic cost. To address this problem, with the target to satisfy the user’s reliability requirement with minimum resources, this paper proposes a new fault tolerant scheduling algorithm: MaxRe. In the algorithm, we incorporate the reliability analysis into the active replication schema and the theoretical analysis and experiments prove that the MaxRe algorithm’s schedule can certainly satisfy user’s reliability requirements. And the MaxRe scheduling algorithm can achieve the corresponding reliability with at most 70% fewer resources than the FTSA algorithm.

Navigation of four-wheel-steering mobile robots using robust fault-tolerant sliding mode control

This paper addresses the leader-follower tracking problem of a four-wheel-steering robot subjected to nonlinear uncertainties. Two control laws have been developed, based on the adaptive sliding mode method and the adaptive input-output feedback linearization method. The proposed control schemes have been tested by means of simulations.

A class of optimal fault tolerant Jacobian for minimal redundant manipulators based on symmetric geometries

Design of locally optimal fault tolerant manipulators has been recently addressed via using the constraints of the desired null space for the Jacobian matrix of the manipulators. In the present paper the Jacobian matrices for optimal fault tolerance are presented based on geometric properties of column vectors instead of the null space. They are equally fault tolerant to a single joint failure from the worst-case relative manipulability and worst-case dexterity points of view. The optimality is achieved through a symmetric distribution of points on spheres.

A hybrid approach for fault tolerance in robotics

This paper studies the difference between the human behaviours for fault tolerance with a pseudo inverse reconfiguration approach for fault tolerance of robotic arms. If this difference is well understood then it can be used to introduce a hybrid approach for fault tolerant motion of robotic arms. The proposed approach is expected to combine human fault-tolerance dexterity and advantages of a model based fault tolerance. The main aim is to add human dexterity for fault tolerance of robotic arms.

Multiple actuator fault tolerance for static nonlinear systems based on minimum velocity jump

Static nonlinear systems are common when the model of the kinematics of mechanical or civil structures is analyzed for instance kinematics of robotic manipulators. This paper addresses the maximum effort toward fault tolerance for any number of the locked actuators failures in static nonlinear systems. It optimally reconfigures the inputs via a mapping that maximally accommodates the failures. The mapping maps the failures to an extra action of healthy actuators that results to a minimum jump for the velocity of the output variables. Then from this mapping, the minimum jump of the velocity of the output is calculated. The conditions for a zero velocity jump of the output variables are discussed. This shows that, when the conditions of fault tolerance are maintained, the proposed framework is capable of fault recovery not only at fault instances but also at the whole output trajectory. The proposed mapping is validated by three case studies.

Optimal fault tolerant Jacobian matrix generators for redundant manipulators

The design of locally optimal fault-tolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian matrix is obtained. In this study, an optimal fault-tolerant Jacobian matrix generator is introduced from geometric properties instead of the null space properties. The proposed generator provides equally fault-tolerant Jacobian matrices in R3 that are optimally fault tolerant for one or two locked joint failures. It is shown that the proposed optimal Jacobian matrices are directly obtained via regular pyramids. The geometric approach and zonotopes are used as a novel tool for determining relative manipulability in the context of fault-tolerant robotics and for bringing geometric insight into the design of optimal fault-tolerant manipulators.

Optimal fault-tolerant robotic manipulators

This thesis addresses “Optimal Fault-Tolerant Robotic Manipulators” for locked-joint failures and consists of three components. It begins by investigating the regions of workspace where the manipulator can operate with high reliability. It then continues with an efficient deployment of kinematic redundancies for fault-tolerant operation. Finally, it presents a novel method for design of optimal fault-tolerant manipulators.

Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For fault-tolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump, because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of the condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator's locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. Then, it is observed that the condition number provides an upper bound of the required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. A solution is for selected optimization problem is presented. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.