Enumeration of Singular Configurations for Robotic Manipulators

1991 ◽  
Vol 113 (3) ◽  
pp. 272-279 ◽  
Author(s):  
H. Lipkin ◽  
E. Pohl
Keyword(s):  
Joint Angle ◽  
Robotic Manipulators ◽  
Systematic Procedure ◽  
Singular Configurations ◽  
Special Cases ◽  
Angle Space ◽  
Six Degree Of Freedom ◽  
Kinematic Singularities ◽  
And Control ◽  
Space Approach

Kinematic singularities are important considerations in the design and control of robotic manipulators. For six degree-of-freedom manipulators, the vanishing of the determinant of the Jacobian yields the conditions for the primary singularities. Examining the vanishing of the minors of the Jacobian yields further singularities which are special cases of the primary ones. A systematic procedure is presented to efficiently enumerate all possible singular configurations. Special geometries of representative manipulators are exploited by expressing the Jacobian in terms of vector elements. In contrast to using a joint-angle space approach, the resulting expressions yield direct physical interpretations.

Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

2003 ◽  
Author(s):  
Hee-Byoung Choi ◽  
Atsushi Konno ◽  
Masaru Uchiyama
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Loop Structure ◽  
Singular Configurations ◽  
Planning And Control ◽  
Kinematic Singularities ◽  
And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators

2004 ◽  
Vol 126 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Jing Wang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Special Class ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Parallel Mechanisms ◽  
Singular Configurations ◽  
Planning And Control ◽  
Robot Trajectory ◽  
Special Cases ◽  
And Control

In this paper, the singularity loci of a special class of spherical 3-DOF parallel manipulators with prismatic actuators are studied. Concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the expression of the determinant of the Jacobian matrix and the inverse kinematics of the manipulators. It is well known that there exist three different types of singularities for parallel manipulators, each having a different physical interpretation. In general, the singularity of type II is located inside the Cartesian workspace and leads to the instability of the end-effector. Therefore, it is important to be able to identify the configurations associated with this type of singularity and to find their locus in the space of all configurations. For the class of manipulators studied here, the six general cases and the five special cases of singularities are discussed. It is shown that the singularity loci in the Cartesian space (defined by the three Euler angles) are six independent planes. In the joint space (defined by the length of the three input links), the singularity loci are quadric surfaces, such as hyperboloid, sphere or a degenerated line or a degenerated circle. In addition, the three-dimensional graphical representations of the singular configurations in each of the general and special cases are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control.

scholarly journals Analysis of Singular Configuration of Robotic Manipulators

Electronics ◽  
2021 ◽  
Vol 10 (18) ◽  
pp. 2189
Author(s):  
Xinglei Zhang ◽  
Binghui Fan ◽  
Chuanjiang Wang ◽  
Xiaolin Cheng
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Joint Angle ◽  
Robotic Manipulators ◽  
Jacobian Determinant ◽  
End Effector ◽  
Serial Manipulators ◽  
Singular Configurations ◽  
Manipulability Measure ◽  
Singular Configuration

Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

Optimal Robotic Assembly Planning Using Dijkstra’s Algorithm

1994 ◽  
Author(s):  
Sam Anand ◽  
Mohamed Sabri
Keyword(s):  
Configuration Space ◽  
Material Handling ◽  
Search Algorithm ◽  
Robotic Manipulators ◽  
Robotic Assembly ◽  
Graph Search ◽  
Assembly Planning ◽  
Robotic Welding ◽  
Fast Collision ◽  
Space Approach

Abstract Robots play an important role in the modern factory and are used in a manufacturing cell for several functions such as assembly, material handling, robotic welding, etc. One of the principal problems faced by robots while performing their tasks is the presence of obstacles such as fixtures, tools, and objects in the robot workspace. Such objects could result in a collision with one of the arms of the robots. Fast collision-free motion planning algorithms are therefore necessary for robotic manipulators to operate in a wide variety of changing environments. The configuration space approach is one of the widely used methods for collision-free robotic path planning. This paper presents a novel graph-based method of searching the configuration space for a collision-free path in a robotic assembly operation. Dijkstra’s graph search algorithm is used for optimizing the joint displacements of the robot while performing the assembly task. The methodology is illustrated using a simple robotic assembly planning task.

An Analytical Method for Locating Velocity Instantaneous Centers

1992 ◽  
Author(s):  
Hong-Sen Yan ◽  
Meng-Hui Hsu
Keyword(s):  
Analytical Method ◽  
Degrees Of Freedom ◽  
Coefficient Matrix ◽  
Multiple Degrees Of Freedom ◽  
Singular Configurations ◽  
Special Cases

Abstract An analytical method is presented for locating all velocity instantaneous centers of linkage mechanisms with single or multiple degrees of freedom. The method is based on the fact that the coefficient matrix of the derived velocity equations for vector loops, independent inputs, and instantaneous centers is singular. This approach also works for special cases with kinematic indeterminacy or singular configurations.

Geometric, Spatial Path Tracking Using Non-Redundant Manipulators via Speed-Ratio Control

2010 ◽  
Author(s):  
Satyajit Ambike ◽  
James P. Schmiedeler ◽  
Michael M. Stanisˇic´
Keyword(s):  
Path Tracking ◽  
Speed Ratio ◽  
Redundant Manipulators ◽  
Computationally Efficient ◽  
Third Order ◽  
Practical Advantage ◽  
First Order ◽  
Canonical Frame ◽  
Special Cases ◽  
Six Degree Of Freedom

Path tracking can be accomplished by separating the control of the desired trajectory geometry and the control of the path variable. Existing methods accomplish tracking of up to third-order geometric properties of planar paths and up to second-order properties of spatial paths using non-redundant manipulators, but only in special cases. This paper presents a novel methodology that enables the geometric tracking of a desired planar or spatial path to any order with any non-redundant regional manipulator. The governing first-order coordination equation for a spatial path-tracking problem is developed, the repeated differentiation of which generates the coordination equation of the desired order. In contrast to previous work, the equations are developed in a fixed global frame rather than a configuration-dependent canonical frame, providing a significant practical advantage. The equations are shown to be linear, and therefore, computationally efficient. As an example, the results are applied to a spatial 3-revolute mechanism that tracks a spatial path. Spatial, rigid-body guidance is achieved by applying the technique to three points on the end-effector of a six degree-of-freedom robot. A spatial 6-revolute robot is used as an illustration.

Optimization in the Design and Control of Robotic Manipulators: A Survey

1989 ◽  
Vol 42 (4) ◽  
pp. 117-128 ◽  
Author(s):  
S. S. Rao ◽  
P. K. Bhatti
Keyword(s):  
Optimal Control ◽  
Robot Manipulator ◽  
Research Effort ◽  
Industrial Robot ◽  
Load Capacity ◽  
Robotic Manipulators ◽  
Optimization Techniques ◽  
Highly Nonlinear ◽  
Manipulator Design ◽  
And Control

Robotics is a relatively new and evolving technology being applied to manufacturing automation and is fast replacing the special-purpose machines or hard automation as it is often called. Demands for higher productivity, better and uniform quality products, and better working environments are primary reasons for its development. An industrial robot is a multifunctional and computer-controlled mechanical manipulator exhibiting a complex and highly nonlinear behavior. Even though most current robots have anthropomorphic configurations, they have far inferior manipulating abilities compared to humans. A great deal of research effort is presently being directed toward improving their overall performance by using optimal mechanical structures and control strategies. The optimal design of robot manipulators can include kinematic performance characteristics such as workspace, accuracy, repeatability, and redundancy. The static load capacity as well as dynamic criteria such as generalized inertia ellipsoid, dynamic manipulability, and vibratory response have also been considered in the design stages. The optimal control problems typically involve trajectory planning, time-optimal control, energy-optimal control, and mixed-optimal control. The constraints in a robot manipulator design problem usually involve link stresses, actuator torques, elastic deformation of links, and collision avoidance. This paper presents a review of the literature on the issues of optimum design and control of robotic manipulators and also the various optimization techniques currently available for application to robotics.

Singularity analysis of a 7-DOF spatial hybrid manipulator for medical surgery

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sameer Gupta ◽  
Ekta Singla ◽  
Sanjeev Soni ◽  
Ashish Singla
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Medical Surgery ◽  
Natural Motion ◽  
Hybrid Manipulator ◽  
Contour Plots ◽  
Kinematic Singularities ◽  
And Control ◽  
Optimal Configurations

Abstract This paper presents the singularity analysis of a 7-degrees of freedom (DOF) hybrid manipulator consisting of a closed-loop within it. From the past studies, it is well-known that the kinematic singularities play a significant role in the design and control of robotic manipulators. Kinematic singularities pose two-fold effects – first, they can induce the loss of one or more DOF of the manipulator and cause infinite joint rates at that particular joint, and second, they help to determine the trajectory or zone with high mechanical advantage. In current work, a 7-DOF hybrid manipulator is considered which is being developed at Council Of Scientific And Industrial Research–Central Scientific Instruments Organisation (CSIR–CSIO) Chandigarh to assist a surgeon during a medical-surgical task. To emulate the natural motion of a surgeon, the challenging configuration with redundant DOF is utilized. Jacobian has been computed analytically and analyzed at each instantaneous configuration with the evaluation of manipulability. Effect of a closed loop in the hybrid configurations is focused at, and utilizing the contour plots, good and worst working zones are identified in the workspace of the manipulator. The verification and validation of best and worst manipulability points (singularities) are done with the help of genetic algorithms, to determine locally and globally optimal configurations. Finally, on the basis of the singularity analysis, the present work concludes with few guidelines to the surgeon about the best and worst working zones for surgical tasks.

Sign in / Sign up

Export Citation Format

Share Document