A Note on Singularity Avoidance in Fourth-Order Gravity

We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective.

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.

Kinematics and Singularity Analysis of a 7-DOF Redundant Manipulator

A new method of kinematic analysis and singularity analysis is proposed for a 7-DOF redundant manipulator with three consecutive parallel axes. First, the redundancy angle is described according to the self-motion characteristics of the manipulator, the position and orientation of the end-effector are separated, and the inverse kinematics of this manipulator is analyzed by geometric methods with the redundancy angle as a constraint. Then, the Jacobian matrix is established to derive the conditions for the kinematic singularities of the robotic arm by using the primitive matrix method and the block matrix method. Then, the kinematic singularities conditions in the joint space are mapped to the Cartesian space, and the singular configuration is described using the end poses and redundancy angles of the robotic arm, and a singularity avoidance method based on the redundancy angles and end pose is proposed. Finally, the correctness and feasibility of the inverse kinematics algorithm and the singularity avoidance method are verified by simulation examples.

A Gimballed Control Moment Gyroscope Cluster Design for Spacecraft Attitude Control

This paper addresses the problem of singularity avoidance in a cluster of four Single-Gimbal Control Moment Gyroscopes (SGCMGs) in a pyramid configuration when used for the attitude control of a satellite by introducing a new gimballed control moment gyroscope (GCMG) cluster scheme. Four SGCMGs were used in a pyramid configuration, along with an additional small and simple stepper motor that was used to gimbal the full cluster around its vertical (z) axis. Contrary to the use of four variable-speed control moment gyroscopes (VSCMGs), where eight degrees of freedom are available for singularity avoidance, the proposed GCMG design uses only five degrees of freedom (DoFs), and a modified steering law was designed for the new setup. The proposed design offers the advantages of SGCMGs, such as a low weight, size, and reduced complexity, with the additional benefit of overcoming the internal elliptic singularities, which create a minor attitude error. A comparison with the four-VSCMG cluster was conducted through numerical simulations, and the results indicated that the GCMG design was considerably more efficient in terms of power while achieving a better gimbal configuration at the end of the simulation, which is essential when it is desired for different manoeuvres to be consecutively executed. Additionally, for a nano-satellite of a few kilograms, the results prove that it is feasible to manufacture the GCMG concept by using affordable and lightweight commercial off-the-shelf (COTS) stepper motors.