A closed-form solution to the direct kinematics of nearly general parallel manipulators with optimally located three linear extra sensors

Bonev, Ilian A.; Ryu, Jeha; Kim, Sung-Gaun; Lee, Sun-Kyu

doi:10.1109/70.928560

Cited by 58 publications

(36 citation statements)

References 14 publications

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“…In [6] it is shown that the forward kinematic problem of a general 3-DOF RRR SPM leads to a polynomial with at most eight solutions, corresponding to different poses of the manipulator top mobile platform, for a given set of control inputs. However, only one, i.e., unique, kinematic solution, corresponding to the actual physical pose of a parallel manipulator, has to be used for designing a robot control system [21], [22]. A unique kinematic solution of a parallel manipulator can be directly identified using numerical procedures.…”

Section: Introductionmentioning

confidence: 99%

Numerical Optimal Control of a Spherical Parallel Manipulator Based on Unique Kinematic Solutions

Shintemirov

Niyetkaliyev

Rubagotti

2015

IEEE/ASME Trans. Mechatron.

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Abstract-This paper presents a framework for generating optimal motor trajectories for a spherical parallel manipulator (SPM) with revolute joints, actuated by servomotors with default internal position control settings. The proposed framework consists of three phases. First, an approach to obtain unique forward kinematics is introduced, in order to relate the angular positions of the servomotors to the orientation of the SPM top mobile platform. Then, a configuration space for the SPM is defined by using numerical procedures, in order to guarantee the absence of singularities and of collisions between links during the motion of the manipulator. Finally, reference trajectories of the servomotors are defined via convex optimization. These trajectories determine an optimal evolution of the SPM motion, based on configuration space and original servomotor dynamics. The proposed strategy is experimentally demonstrated on a prototype of Agile Wrist SPM with three servomotors.

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Section: Introductionmentioning

confidence: 99%

Numerical Optimal Control of a Spherical Parallel Manipulator Based on Unique Kinematic Solutions

Shintemirov

Niyetkaliyev

Rubagotti

2015

IEEE/ASME Trans. Mechatron.

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“…As compared to other methods (Shi & Fenton, 1991;Stoughton & Arai, 1991;Cheok et al, 1992) using the set {3-RRP}, the method proposed by Baron and Angeles is the most accurate and only slightly more expensive in terms of computational cost. A method based on the set {9-RRP} is proposed in (Bonev et al, 2001) to reduce the DPA of the UPS-PM with planar base and platform to the solution of a system of six linear 6-variate equations in the same 6 unknowns usually admitting a unique solution, corresponding to the actual manipulator cofiguration, which can be computed in real time. Note that the proposed method does not guarantee that the actual manipulator configuration can always be found.…”

Section: Robust Fast and Accurate Solution Of The Direct Position Anmentioning

confidence: 99%

Robust, Fast and Accurate Solution of the Direct Position Analysis of Parallel Manipulators by Using Extra-Sensors

Vertechy¹,

Parenti‐Castelli²

2008

Parallel Manipulators, Towards New Applications

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“…Different approaches are provided in literature to solve this problem either in general or in special cases. There are also several cases in which the solution to this problem is obtained for a special or novel architecture (Baron et al, 2000, Merlet, 96, Song et al, 2001, Bonev et al, 2001). Two such special 3 DOF constrained mechanisms have been studied in (Siciliano, 99, Fattah et al, 2000), where kinematics, Jacobian and dynamics have been considered for such manipulators.…”

Section: Introductionmentioning

confidence: 99%

KINEMATIC AND SINGULARITY ANALYSIS OF THE HYDRAULIC SHOULDER - A 3-DOF Redundant Parallel Manipulator

Sadjadian

Taghirad

2005

Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics

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Abstract:In this paper, kinematic modeling and singularity analysis of a three DOF redundant parallel manipulator has been elaborated in detail. It is known, that on the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed loop position control of parallel manipulators. Using the novel idea of kinematic chains recently developed for parallel manipulators, both inverse and forward kinematics of our parallel manipulator are fully developed, and a closed-form solution for the forward kinematic map of the parallel manipulator is derived. The closed form solution is also obtained in detail for the Jacobian of the mechanism and singularity analysis of the manipulator is performed based on the computed Jacobian.

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A closed-form solution to the direct kinematics of nearly general parallel manipulators with optimally located three linear extra sensors

Cited by 58 publications

References 14 publications

Numerical Optimal Control of a Spherical Parallel Manipulator Based on Unique Kinematic Solutions

Numerical Optimal Control of a Spherical Parallel Manipulator Based on Unique Kinematic Solutions

Robust, Fast and Accurate Solution of the Direct Position Analysis of Parallel Manipulators by Using Extra-Sensors

KINEMATIC AND SINGULARITY ANALYSIS OF THE HYDRAULIC SHOULDER - A 3-DOF Redundant Parallel Manipulator

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