Natural frequency modulation of a kinematically redundant planar parallel robot

When a parallel robot is equipped with kinematic redundancy, it has sufficient capabilities of natural frequency modulation through adjusting geometric configuration. To reduce resonance of a mechanism, this paper investigates the natural frequency modulation of a kinematically redundant planar parallel robot. A double-threshold searching method is proposed for controlling the inverse kinematics solution and keeping the natural frequencies away from the excitation frequency. The effectiveness of modulating the natural frequencies is demonstrated by comparing it with a non-modulation method. The simulation results indicate that, in all directions, the responses are coupled, and every order should be taken into consideration during natural frequency modulation. Compared to the non-modulation method, the proposed method can reduce the resonance amplitude to a certain extent, and the effect of vibration suppression is remarkable.

Closeness to singularity based on kinematics and dynamics and singularity avoidance of a planar parallel robot with kinematic redundancy

Planar parallel robots are appealing due to their structural simplicity, high stiffness, and large payload capacity. One major problem is that workspace and singularity of non-redundant parallel robots are unchangeable. Hence, when the desired path crossed with singularity or exceeded the workspace’s boundary, the robot is incapable of finishing the task. Another one is closeness to singularity. If one can know the distance between the end manipulator and singularity or workspace’s boundary, the robot will avoid lose control or breakdown. Compared with the traditional planar parallel robot, the planar parallel robot with kinematic redundancy possesses the advantages of avoiding singularity, expanding workspace by adjusting kinematic redundancy parameter. Therefore, the objective of this article is to present an offline action-strategy of a planar robot with kinematic redundancy to measure the closeness to singularity and avoid singularity. It includes two main parts: First, before the robot moves along the desired paths, the closeness to singularity was measured based on the performance of the kinematics and dynamics so that one can know where to pause the robot. Second, an algorithm is designed to previously find the proper kinematic redundancy parameters for changing singularity and workspace. Hence, the robot can smoothly move far from the singularity to finish all paths. The results indicate that the robot can adjust its configuration to well realize the goal by the offline action-strategy.

Passive Decoupled Multi-Task Controller for Redundant Robots

Kinematic redundancy in robots makes it possible to execute several control tasks simultaneously. As some tasks are usually more important than others, it is reasonable to dynamically decouple them in order to ensure their execution in a hierarchical way or even without any interference at all. The most widely used technique is to decouple the system by feedback linearization. However, that requires to actively shape the inertia and consequently modify the natural dynamics of the robot. Here we propose a passivity-based multi-task tracking controller that preserves these inertial properties but fully compensates for task-space cross-couplings using external force feedback. Additionally, three formal proofs are provided: uniform exponential stability for trajectory tracking, passivity during physical interaction, and input-to-state-stability. The controller is validated in simulations and experiments and directly compared with the hierarchical PD+ approach and the feedback linearization. The proposed approach is well suited for safe physical human-robot interaction and dynamic trajectory tracking if measurements or estimations of the external forces are available.

Passive Decoupled Multi-Task Controller for Redundant Robots

Kinematic redundancy in robots makes it possible to execute several control tasks simultaneously. As some tasks are usually more important than others, it is reasonable to dynamically decouple them in order to ensure their execution in a hierarchical way or even without any interference at all. The most widely used technique is to decouple the system by feedback linearization. However, that requires to actively shape the inertia and consequently modify the natural dynamics of the robot. Here we propose a passivity-based multi-task tracking controller that preserves these inertial properties but fully compensates for task-space cross-couplings using external force feedback. Additionally, three formal proofs are provided: uniform exponential stability for trajectory tracking, passivity during physical interaction, and input-to-state-stability. The controller is validated in simulations and experiments and directly compared with the hierarchical PD+ approach and the feedback linearization. The proposed approach is well suited for safe physical human-robot interaction and dynamic trajectory tracking if measurements or estimations of the external forces are available.

Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with kinematic redundancy

The kinematic redundancy is considered as a way to improve the performance of parallel mechanism. In this paper, the kinematics performance of a three degree-of-freedom parallel mechanism with kinematic redundancy (3-DOF PM-KR) and the influence of redundant part on the PM-KR are analyzed. Firstly, the kinematics model of the PM-KR is established. The inverse solutions, the Jacobian matrix and the workspace of the PM-KR are solved. Secondly, the influence of the redundant redundancy on the PM-KR has been analyzed. Since there exists kinematic redundancy, the PM-KR possesses the fault-tolerant performance. By locking one actuated joint or two actuated joints simultaneously, the fault-tolerant workspace are obtained. When the position of the redundant part is changed, the workspace and singularity will be changed. The results show that the kinematic redundancy can be used to avoid the singularity. Finally, the simulations are performed to prove the theoretical analysis.

Model-based joint and task space control strategies for a kinematically redundant parallel manipulator

One alternative to overcome the presence of singularities within Parallel Manipulators’ workspace is kinematic redundancy. This design alternative can be realized by adding an extra active joint to a kinematic chain. Due to this addition, the IKM presents an infinite number of solutions requiring a redundancy resolution scheme. Moreover, Parallel Manipulators’ control may require complex strategies due to their coupled and complex dynamic and kinematic relations. In this work, a model-free, a joint space computed torque, and a hybrid joint-task-space computed torque control strategies are experimentally compared for a kinematically redundant parallel manipulator. The latter is a novel strategy that requires the measurement of the end-effector’s pose, which is performed by an eye-to-hand limited frame rate camera. The impact of up to three kinematic redundancy levels is also experimentally evaluated using prepositioning and ongoing positioning redundancy resolution schemes. The data are assessed by evaluating a prescribed trajectory executed using a planar kinematically redundant parallel manipulator. These results indicate that kinematic redundancy can not only be used as an alternative design for reducing the presence of singular regions, as claimed in the literature, but also be used along with model-based control strategies for improving dynamic performance and accuracy of parallel manipulators.

On the Modelling of Tethered Mobile Robots as Redundant Manipulators

Controlling a chain of tethered mobile robots (TMRs) can be a challenging task. This kind of system can be considered kinematically as an open-chain robotic arm where the mobile robots are considered as a revolute joint and the tether is considered as a variable length link, using a prismatic joint. Thus, the TMRs problem is decoupled into two parallel problems: the equivalent robotic manipulator control and the tether shape computation. Kinematic redundancy is exploited in order to coordinate the motion of all mobile robots forming the chain, expressing the constraints acting on the mobile robots as secondary tasks for the equivalent robotic arm. Implementation in the Gazebo simulation environment shows that the methodology is capable of controlling the chain of TMRs in cluttered environments.

Singularity analysis and avoidance of a planar parallel mechanism with kinematic redundancy under a fixed orientation

In this paper, the singularity of a planar mechanism with kinematic redundancy is studied. First, the architecture of the mechanism and the concept schematic diagram for singularity avoidance are stated. Next, inverse kinematics model of the planar parallel mechanism with kinematic redundancy is established. For determining the unique inverse solution of the mechanism under certain initial installation configuration, a comparison analysis based on the strategy tree and the virtual prototype is performed. Then, based on the obtained Jacobian matrices and the singular condition, the workspace-singularity map and two singular configurations of the mechanism are drawn. Finally, with the obtained workspace-singularity map, a singularity-free transition layer and an aisle can be found to perform to singularity avoidance, even if the initial designed trajectory passing through the second kind of singularity. Three tasks are carried out to illustrate that the workspace boundary and singular configuration can be changed by adjusting the kinematic redundant actuated parameter.