• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.386-390
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• 1992

Algorithmic or kinematic singularities are inevitably a introduced if optimality criteria or augmented kinematic equations are used to resolve the redundancy of almost any manipulator with rotary joints. In this paper, a sufficient condition for a singularity-free optimal solution of the kinematic control of a redundant manipulator is derived and, specifically, algorithmic singularities are analyzed for optimality-based methods. A singularity-free space (SFS) to characterize the performance of a secondary task for a redundant manipulator using the sufficient condition for a redundant manipulator is defined. The SFS is a set of regions classified by the loci of configurations satisfying the inflection condition for manipulability measure in the Configuration space. Using SFS, the topological property of the Configuration space and the invertible workspace without singularities are analyzed.

• The Journal of Korea Robotics Society
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• v.12 no.2
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• pp.194-205
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• 2017

A redundantly actuated planar 3-degree-of-freedom parallel mechanism is analyzed to show its high application potential as a haptic device. Its structure along with the closed form forward position solutions is briefly discussed. Then its geometric and kinematic characteristics via singularity analysis, the kinematic isotropy index, and the input-output force transmission ratio are investigated both for the redundantly actuated cases and for the non-redundantly actuated case. In addition, comparative joint torque simulations of the mechanism with different number of redundant actuations as well as without redundant actuation are conducted to confirm the improved joint torque distribution characteristics. Through these analyses it is shown that the geometric and kinematic characteristics of the redundantly actuated mechanism are superior to the ones of the mechanism without redundant actuation. Thus, it can be concluded that the suggested planar mechanism with redundant actuation has a very high potential for haptic device applications.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.396-399
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• 1995

This paper presents a new formulation of the kinematics of closed-chain mechanisms and its applications to obtaining the kinematic solutions and analyzing the singularities. Closed-chain mechanisms under consideration may have the redundancy in the number of joints. A closed-chain mechanism can be treated as the parallel connection of two open-chains with respect to a point of interest. The kinematics of a closed-chain mechanism is then obtained by imposing the kinematic constraints of the closed-chain on the kinematics of the two open-chains. First, we formulate the kinematics of a closed-chain mechanism using the kinematic constraint between the controllable active joints and the rest of joints, instead of the kinematic constraint between the two open-chains. The kinematic formulation presented in this paper is valid for closed-chain mechanisms with and without the redundancy. Next, based on the derived kinematics of a closed-chain mechanism, we provide the kinematic solutions which are more physically meaningful and less sensitive to numerical instability, and also suggest an effective way to analyze the singularities. Finally, the computational cost associated with the kinematic formulation is analyzed.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.9
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• pp.766-773
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• 2001

Omni-directional mobile robots have been popularly employed in several application areas. However, the kinematics for these systems have not been clearly identified, specially for redundantly actuated case which is common in omni-directional mobile robot such as the Nomadic model. For such mobile robot systems, exploitation of redundant actuation as well as singularity analysis has not been extensively addressed. In light of this fact, this paper introduces two different kinematic approaches for omni-directional mobile robots. Then, a singular-free load distribution scheme for redundantly actuated three-wheeled omni-directional mobile robot is proposed. Through simulation, several advantages of redundantly actuated mobile robot in aspect of singularity avoidance, minimization of torque norm, and exploiting several subtasks are presented.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.7
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• pp.42-51
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• 1992

This paper suggests a measure constraint locus which is the loci of points satisfying the necessary constraint for optimality of a measure in the configuration space. The characterization of four measures for singularity avoidance is worked out by using the measure constraint locus. It gives a global look at the performance of an inverse kinematic algorithm whien each of measures in a kinematically redundant robot is used. The invertible workspace without singularities and the topological properties both on the configuration and operational spaces are analyzed. We discuss also some limitations, based on the topological arguments of measure constraint locus, of the inverse kinematic algorithms, and compare global properties of each of measure. Therfore, a new concept called measure constraint locus gives a methodology for obtaining a conservative joint trajectory without singularities for almost entire workspace.

• International Journal of Precision Engineering and Manufacturing
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• v.8 no.4
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• pp.16-21
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• 2007

Robotic applications, such as automatic fish cutting, require online trajectory planning because the material properties of the object, such as the bone or flesh conditions, are not known in advance. Different trajectories are required when the material properties vary. An effective online trajectory-planning algorithm is proposed using quaternions to determine the position and orientation of a robot manipulator with a spherical wrist. Quaternions are free of representation singularities and permit computationally efficient orientation interpolations. To prevent singular configurations, the exact locations of the kinematic singularities of the PUMA 560 manipulator are derived and geometrically illustrated when a forearm offset exists and the third link length is not zero.

• The Journal of Korea Robotics Society
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• v.12 no.1
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• pp.42-54
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• 2017

Using an inverse of the geometric Jacobian matrix is one of the most popular ways to control robot manipulators, because the Jacobian matrix contains the relationship between joint space velocities and operational space velocities. However, the control algorithm based on Jacobian matrix has algorithmic singularities: The robot manipulator becomes unstable when the Jacobian matrix loses rank. To solve this problem, various methods such as damped and filtered inverse have been proposed, but comparative studies to evaluate the performance of these algorithms are insufficient. Thus, this paper deals with a comparative analysis of six representative singularity avoidance algorithms: Damped Pseudo Inverse, Error Damped Pseudo Inverse, Scaled Jacobian Transpose, Selectively Damped Inverse, Filtered Inverse, and Task Transition Method. Especially, these algorithms are verified through computer simulations with a virtual model of a humanoid robot, THORMANG, in order to evaluate tracking error, computational time, and multiple task performance. With the experimental results, this paper contains a deep discussion about the effectiveness and limitations of each algorithm.

• The Journal of Korea Robotics Society
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• v.10 no.2
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• pp.119-132
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• 2015

Two novel parallel mechanisms (PMs) employing two or three PaPaRR subchains are suggested. Each of those two PMs has translational 3-DOF motion and employs only revolute joints such that they could be adequate for haptic devices requiring minimal frictions. The position analyses of those two PMs are conducted. The mobility analysis, the kinematic modeling, and singularity analysis of each of two PMs are performed employing the screw theory. Then through optimal kinematic design, each of two PMs has excellent kinematic characteristics as well as useful workspace size adequate for haptic applications. In particular, by applying an additional redundantly actuated joint to the 2-PaPaRR type PM which has a closed-form position solution, it is shown that all of its parallel singularities within reachable workspace are completely removed and that its kinematic characteristics are improved.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.77-82
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• 1996

This paper is concerned with how to utilize kinematic redundancy to reconstruct the inverse kinematic solution which is not attainable due to hardware limitations. By analyzing the error due to hardware limitations, we are to show that the recoverability of limitation reduces to the solvability of a reconstruction equation under the feasibility condition. It will be next shown that the reconstruction equation is solvable if the configuration is not a joint-limit singularity. The reconstruction method will be proposed based on the geometrical analysis of recoverability of hardware limitations. The method has the feature that no task motion error is induced by the hardware limitations while minimizing a possible null motion error, under the recoverability assumed.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.4
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• pp.80-90
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• 1994

Basic constraint equations derived from orthogonality conditions between a pair of body-fixed vectors and a body-fixed vector or a vector between two bodies are reformulated by using relative coordinate kinematics between two adjacent reference frames. Arithmetic numbers of operations required to compute derivatives of the constraint equations are drastically reduced. A mixed formulation of relative and cartesian coordinates is developed to further simplify derivatives of the constraints. Advantages and disadvantages of the new formulation are discussed. Possible singularity problem of para llelism constraints is resolved by introducing an extra generalized coordinate. Kinematic analysis of a McPherson strut suspension system are carried out to illustrate use and efficiency of the new formulation.