Dynamic output feedback control of single-link flexible manipulators

This paper presents an efficient technique to design dynamic feedback control scheme for single-link flexible manipulators.  A linear model can be derived for the robotic system using the assumed-mode method.  Conventional techniques such as pole-placement or LQR require physical measurements of all systme states,  posing a stringent requirement for its implementation.  To overcome this problem, a low-order state functional observer is proposed here for reconstruction of the state feedback control action.  The observer design involves solving an optimisation problem with the objective to generate a feedback gain that is as close as possible to that of the required feedback controller.  A condition for robust stability of the closed-loop system under the observer-based control scheme is given.  The attractive features of the propsed technique are the resulted functional state observer is of a very low order and it requires only sensor measurements of only the output- the tip position of the arm.

Designing optimal fault tolerant Jacobian for robotic manipulators

Fault tolerance of robotic manipulators is determined based on the fault tolerance measures. In this study a Jacobian of a 7DOF optimal fault tolerant manipulator is designed based on optimality of worse case relative manipulability and worse case dexterity from geometric perspective instead of numerical solution of constrained optimisation problem or construction of optimal Jacobean through a desired null space. The proposed Jacobean matrix is optimal and equally fault tolerant for a single joint failure within any joint of the manipulators.

Fault tolerance force for redundant manipulators

Fault tolerant manipulators maintain their trajectory even if their joint/s fails. Assuming that the manipulator is fault tolerant on its trajectory, fault tolerant compliance manipulators provide required force at their end-effector even when a joint fails. To achieve this, the contributions of the faulty joints for the force of the end-effector are required to be mapped into the proper compensating joint torques of the healthy joints to maintain the force. This paper addresses the optimal mapping to minimize the force jump due to a fault, which is the maximum effort to maintain the force when a fault occurs. The paper studies the locked joint fault/s of the redundant manipulators and it relates the force jump at the end-effector to the faults within the joints. Adding on a previous study to maintain the trajectory, in here the objective is to providing fault tolerant force at the end-effector of the redundant manipulators. This optimal mapping with minimum force jump is presented using matrix perturbation model. And the force jump is calculated through this model for single and multiple joints fault. The proposed optimal mapping is used in different fault scenarios for a 5-DOF manipulator; also it is deployed to compensate the force at the end-effector for the 5-DOF manipulator through simulation study and the results are presented.

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.

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.

Task completion with partially-failed manipulators

An effort to maintain the availability of partially failed manipulator is addressed based on redundant trajectories obtained by primitive constraints. The objective is to facilitate the existing manipulators to continue their point to point motion tasks when a non catastrophic fault occurs into a joint. The fault is assumed as a joint locked failure. This is achieved through fault to primitive constraints mapping which gives the primitive constraints due to the faults. Then they are applied to update the manipulator constraints for the trajectory planning. Then it purposes a new trajectory in the case of availability. Finally the method is applied for a 6DOF manipulator and validated under a fault scenario within a simulation study and the results are presented.

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.

On the effort of task completion for partially-failed manipulators

Adding to a previous work of the authors for task completion for partially failed manipulator, other aspects of the effort are discussed. The paper aims to investigate on the strategies of maximum effort for maintaining the availability of partially failed manipulators. The failures are assumed as the joint lock failures of the manipulators. The main objective is to facilitate the existing manipulators to continue their tasks even if a non catastrophic fault occurs into their joints. The tasks includes motion tasks and force tasks. For each group of tasks a constrained optimality problem is introduced. Then in a case study a required force profile on a desired trajectory using a 3DOF planar manipulator is indicated. Through this study the joint angles and joint torques for a healthy manipulator and a faulty manipulator are shown. It is illustrated that a failure in the second joint is tolerated on the trajectory of end-effector.

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 family of planar parallel manipulators

A family of planar parallel manipulators is investigated and some novel members are proposed. The common feature of the studied manipulators is that the rotation axes of the actuated arms coincide. This feature makes it possible to rotate the whole arm system an infinite number of revolutions around the center of the manipulator. The result is a large workspace in relation to the footprint. Both 2- and 3-DOF variants are presented and the suitability of this family of manipulators for kinematic analysis is demonstrated. Thus, different methods to find optimal manipulability with respect to platform positioning and rotation have been analyzed.

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.

Parallel manipulators with a rotation-symmetric arm system

Parallel manipulators with a rotation-symmetric arm system possess all the typical advantages of parallel robots, such as high acceleration and high-accuracy positioning. Contrary to the majority of proposed parallel manipulators, the rotation-symmetric arm system leads to a large workspace in relation to the footprint of the manipulator. This paper focuses on a subclass of these manipulators with additional favorable qualities, including low inertia and high eigenfrequencies. These qualities are achieved using only 5-DOF lower arm links and by mounting all actuators on the nonmoving base column of the manipulator. The common feature of all previously proposed manipulators in this subclass is identified and several novel 3-DOF and 4-DOF members are introduced.