Numerical filtering for the operation of robotic manipulators through kinematically singular configurations

Anthony A. Maciejewski; Charles A. Klein

doi:10.1002/rob.4620050603

A Method of Inverse Kinematics Solution for a Class of Robotic Manipulators

Volume 5: 17th Computers in Engineering Conference ◽

10.1115/detc97/cie-4283 ◽

1997 ◽

Author(s):

Tuna Balkan ◽

M. Kemal Özgören ◽

M. A. Sahir Arikan ◽

H. Murat Baykurt

Keyword(s):

Nonlinear Equation ◽

Analytical Method ◽

Multiple Solutions ◽

Inverse Kinematics ◽

Industrial Robot ◽

Robotic Manipulators ◽

Inverse Kinematic ◽

Singular Configurations ◽

Inverse Kinematics Problem ◽

Joint Variable

Abstract A semi-analytical method and a computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in wrist point equations. For this case, it becomes possible to express all the joint variables in terms of a joint variable, and this reduces the inverse kinematics problem to solving a nonlinear equation in terms of that joint variable. The solution can be obtained by iterative methods and the remaining joint variables can easily be computed by using the solved joint variable. Since the method is manipulator dependent, the equations will be different for kinematically different classes of manipulators, and should be derived analytically. A significant benefit of the method is that, the singular configurations and the multiple solutions indicated by sign ambiguities can be determined while deriving the inverse kinematic expressions. The developed method is applied to a six-revolute-joint industrial robot, FANUC Arc Mate Sr.

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Enumeration of Singular Configurations for Robotic Manipulators

Journal of Mechanical Design ◽

10.1115/1.2912779 ◽

1991 ◽

Vol 113 (3) ◽

pp. 272-279 ◽

Cited By ~ 34

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.

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A new dynamic manipulability ellipsoid for redundant manipulators

Robotica ◽

10.1017/s0263574799002106 ◽

2000 ◽

Vol 18 (4) ◽

pp. 381-387 ◽

Cited By ~ 53

Author(s):

Pasquale Chiacchio

Keyword(s):

Case Studies ◽

Robotic Manipulators ◽

Redundant Manipulators ◽

Task Space ◽

End Effector ◽

Space Analysis ◽

Singular Configurations ◽

Definition Of

Manipulability ellipsoids are effective tools to perform task space analysis of robotic manipulators in terms of velocities, accelerations and forces at the end effector. In this paper a new definition of a dynamic manipulability ellipsoid for redundant manipulators is proposed which leads to more correct results in evaluating manipulator capabilities in terms of task-space accelerations. The case of manipulators in singular configurations is also analyzed. Two case studies are presented to illustrate the correctness of the proposed approach.

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Controlling robotic manipulators through singular configurations: An overview

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)56142-x ◽

1999 ◽

Vol 32 (2) ◽

pp. 839-842

Author(s):

Sun Yu ◽

Fang Yuefa ◽

Cha Jianzhong

Keyword(s):

Robotic Manipulators ◽

Singular Configurations

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Motion Planning for Shape–Controlled Adaptable Buildings Resembling Topologically Closed–Loop Robotic Systems

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-70177 ◽

2012 ◽

Cited By ~ 5

Author(s):

Eftychios G. Christoforou ◽

Andreas Müller ◽

Marios C. Phocas

Keyword(s):

Motion Planning ◽

Shape Control ◽

Degrees Of Freedom ◽

Closed Loop ◽

Robotic Manipulators ◽

Robotic Systems ◽

Superior Performance ◽

Building Structures ◽

Singular Configurations ◽

Shape Controlled

Shape–controlled adaptable building structures have a potential of superior performance and flexibility compared to traditional fixed–shape ones. A building concept is proposed consisting of a number of interconnected planar n–bar linkages performing coordinated motions thus resembling a system of cooperating closed–loop robotic manipulators. For shape control an “effective 4–bar” linkage concept is proposed. That is, each individual n–bar mechanism is equipped with one motion actuator, and at any time of motion its degrees–of–freedom are reduced to one through the selective locking of (n – 4) joints using brakes. Shape adjustments of the overall structure can be carried out through appropriate control sequences where in each step exactly four joints of each linkage are unlocked giving rise to an effective 4–bar system. Motion planning is considered together with the relevant limitations arising from singular configurations that need to be taken into account. The concept is demonstrated through simulation examples.

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Analysis of Singular Configuration of Robotic Manipulators

Electronics ◽

10.3390/electronics10182189 ◽

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.

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