Inverse Kinematic Solutions With Singularity Robustness for Robot Manipulator Control

1986 ◽  
Vol 108 (3) ◽  
pp. 163-171 ◽  
Author(s):  
Yoshihiko Nakamura ◽  
Hideo Hanafusa
Keyword(s):  
Feasible Solution ◽  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Singular Points ◽  
Joint Motion ◽  
Singularity Problem ◽  
Inherent Problem ◽  
Manipulator Control ◽  
Kinematic Solution

The singularity problem is an inherent problem in controlling robot manipulators with articulated configuration. In this paper, we propose to determine the joint motion for the requested motion of the endeffector by evaluating the feasibility of the joint motion. The determined joint motion is called an inverse kinematic solution with singularity robustness, because it denotes feasible solution even at or in the neighborhood of singular points. The singularity robust inverse (SR-inverse) is introduced as an alternative to the pseudoinverse of the Jacobian matrix. The SR-inverse of the Jacobian matrix provides us with an approximating motion close to the desired Cartesian trajectory of the endeffector, even when the inverse kinematic solution by the inverse or the pseudoinverse of the Jacobian matrix is not feasible at or in the neighborhood of singular points. The properties of the SR-inverse are clarified by comparing it with the inverse and the pseudoinverse. The computational complexity of the SR-inverse is considered to discuss its implementability. Several simulation results are also shown to illustrate the singularity problem and the effectiveness of the inverse kinematic solution with singularity robustness.

scholarly journals Inverse kinematic solution of 6R robot manipulators based on screw theory and the Paden–Kahan subproblem

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881829 ◽  
Author(s):  
Rongbo Zhao ◽  
Zhiping Shi ◽  
Yong Guan ◽  
Zhenzhou Shao ◽  
Qianying Zhang ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Matrix Theory ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Kinematics Modeling ◽  
High Level ◽  
Kinematic Solution

The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.

Inverse kinematic solutions of 6-D.O.F. biopolymer segments

Robotica ◽  
2016 ◽  
Vol 34 (8) ◽  
pp. 1734-1753 ◽  
Author(s):  
Jin Seob Kim ◽  
Gregory S. Chirikjian
Keyword(s):  
Jacobian Matrix ◽  
Heuristic Method ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Robot Kinematics ◽  
Joint Angles ◽  
Elimination Method ◽  
Six Degree Of Freedom ◽  
Theoretic Description ◽  
Kinematic Solution

SUMMARYWe present two methods to find all the possible conformations of short six degree-of-freedom segments of biopolymers which satisfy end constraints in position and orientation. One of our methods is motivated by inverse kinematic solution techniques which have been developed for “general” 6R serial robotic manipulators. However, conventional robot kinematics methods are not directly applicable to the geometry of polymers, which can be treated as a degenerate case where all the “link lengths” are zero. Here, we propose a method which extends the elimination method of Kohli and Osvatic. This method can be applied directly to the geometry of biopolymers. We also propose a heuristic method based on a Lie-group-theoretic description. In this method, we utilize inverse iterations of the Jacobian matrix to obtain all conformations which satisfy end constraints. This can be easily implemented for both the general 6R manipulator and polymers. Although the extended elimination method is computationally faster than the Jacobian method, in cases where some of the joint angles are 180° (i.e., where the elimination method fails), we combine these two methods effectively to obtain the full set of inverse kinematic solutions. We demonstrate our approach with several numerical examples.

Optimal conditions for inverse kinematics of a robot manipulator with redundancy

Robotica ◽  
1995 ◽  
Vol 13 (1) ◽  
pp. 95-101 ◽  
Author(s):  
Dong Kwon Cho ◽  
Byoung Wook Choi ◽  
Myung Jin Chung
Keyword(s):  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Inverse Kinematic ◽  
Performance Measure ◽  
Configuration Change ◽  
Necessary Conditions For Optimality ◽  
Kinematic Solution

SummaryThe algorithms of inverse kinematics based on optimality constraints have some problems because those are based only on necessary conditions for optimality. One of the problems is a switching problem, i.e., an undesirable configuration change from a maximum value of a performance measure to a minimum value may occur and cause an inverse kinematic solution to be unstable. In this paper, we derive sufficient conditions for the optimal solution of the kinematic control of a redundant manipulator. In particular, we obtain the explicit forms of the switching condition for the optimality constraintsbased methods. We also show that the configuration at which switching occurs is equivalent to an algorithmic singularity in the extended Jacobian method. Through a numerical example of a cyclic task, we show the problems of the optimality constraints-based methods. To obtain good configurations without switching and kinematical singularities, we propose a simple algorithm of inverse kinematics.

scholarly journals Suboptimal approximations in repeatable inverse kinematics for robot manipulators

2017 ◽  
Vol 65 (2) ◽  
pp. 209-217
Author(s):  
I. Duleba ◽  
I. Karcz-Duleba
Keyword(s):  
Configuration Space ◽  
Simulation Study ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Forward Kinematics ◽  
Definition Of ◽  
Pseudo Inverse ◽  
Selection Of

Abstract In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

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