Walter Scott, Jr. College of Engineering

Graduate Exam Abstract

Ahmad Almarkhi
Ph.D. Final
Nov 18, 2020, 10:00 am - 12:00 pm
ONLINE (Zoom Meeting)
Characterizing the Self-Motion Manifolds of Redundant Robots of Arbitrary Kinematic Structures
Abstract: Robot fault tolerance measures can be classified into two categories: 1) Local measures that are based on the singular value decomposition (SVD) of the robot Jacobian, and 2) Global measures that are suitable to quantify the fault tolerance more effectively in pick-and-place applications. One
can use the size of the self-motion manifold of a robot as a global fault-tolerance measure. The size of the self-motion manifold at a certain end-effector location can be simply the sum of the range of the joint angles of a robot at that location. This work employs the fact that the largest self-motion manifolds occur due to merging two (or more) previously disjoint manifolds. The connection of previously disjoint manifolds occur in special configurations in the joint space called singularities.
Singularities (singular configurations) occur when two or more of the robot joint axes become aligned and are linearly dependent. A significant amount of research has been performed on identifying the robot singularities but was all based on symbolically solving for when the robot Jacobian is not of full rank. In this work, an algorithm was proposed that is based on the gradient of the singular values of the robot Jacobian. This algorithm is not limited to any Degree of Freedom (DoF) nor any specific robot kinematic structure and any rank of singularity.
Based on the robot singularities, one can search for the largest self-motion manifold near robot singularities. The measure of the size of the self-motion manifold was chosen to eliminate the
effect of the self-motion manifold’s topology and dimension. Because the SVD at singularities is indistinct, one can employ Givens rotations to define the physically meaningful singular directions, i.e., the directions where the robot is not able to move. This approach has been extensively
implemented on a 4-DoF robot, different 7-DoF robot, and an 8-DoF robot.
The global fault-tolerance measure might be further optimized by changing the kinematic structure of a robot. This may allow one to determine a globally fault-tolerant robot, i.e., a robot with 2\pi range for all of its joint angles at certain end-effector location, i.e., a location that is the most suitable for pick-and-place tasks.
Co-Adviser: N/A
Non-ECE Member: JIANGUO ZHAO, Mechanical Engineering
Member 3: EDWIN CHONG, Electrical and Computer Engineering
Addional Members: IULIANA OPREA, Math Department
1-Maximizing the Size of Self-Motion Manifolds to Improve Robot Fault Tolerance.
A. A. Almarkhi and A. A. Maciejewski, “Maximizing the size of self-motion manifolds to improve robot fault tolerance,” IEEE Robotics and Automation Letters, vol. 4, no. 3, pp. 2653–2660, 2019.

2- Singularity Analysis for Redundant Manipulators of Arbitrary Kinematic Structures
A. A. Almarkhi and A. A. Maciejewski, “Singularity analysis for redundant manipulators of arbitrary kinematic structure,” International Conference on Informatics in Control, Automation and Robotics (ICINCO 2019), pp. 42–49, 2019.

3- An Algorithm to Design Redundant Manipulators of Optimally Fault-Tolerant Kinematic Structure
Almarkhi, A. A. Maciejewski, and E. K. P. Chong, "An Algorithm to Design Redundant Manipulators of Optimally Fault-Tolerant Kinematic Structure," IEEE Robotics and Automation Letters, Vol. 5, No. 3, pp. 4727-4734, July 2020. (Will be presented in IROS2020:
Program of Study: