Workspace generation and planning singularity-free path for parallel manipulators

Dash, Anjan Kumar; Chen, I‐Ming; Yeo, Song Huat; Yang, Guilin

doi:10.1016/j.mechmachtheory.2005.01.001

Cited by 108 publications

(83 citation statements)

References 17 publications

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“…They include an algorithm based on deforming a parametrized path between the query configurations [15], a variational approach that reduces the problem to a boundary value problem [16], and a numerical technique based on treating the singularity locus as a collection of obstacles [17]. All of these methods work well in favorable situations, but [15] and [16] mention limitations relative to proving path existence in some cases, and the one in [17] is computationally intensive, as it requires constructing polytope approximations of the entire singularity set before searching for a feasible path. In some way or another, also, the methods in [15]- [17] exploit the fact that the considered C-spaces have closed-form parameterizations, so that it is difficult to extend them to tackle manipulators with a more complex architecture.…”

Section: E Henderson Is With the Numerical Analysis Group In The mentioning

confidence: 99%

“…All of these methods work well in favorable situations, but [15] and [16] mention limitations relative to proving path existence in some cases, and the one in [17] is computationally intensive, as it requires constructing polytope approximations of the entire singularity set before searching for a feasible path. In some way or another, also, the methods in [15]- [17] exploit the fact that the considered C-spaces have closed-form parameterizations, so that it is difficult to extend them to tackle manipulators with a more complex architecture. The method provided in this paper, in contrast, makes no recourse to closed-form parameterizations, and can be applied to any non-redundant closed-chain manipulator, with the sole limitations imposed by the curse of dimensionality.…”

Section: E Henderson Is With the Numerical Analysis Group In The mentioning

confidence: 99%

“…The method provided in this paper, in contrast, makes no recourse to closed-form parameterizations, and can be applied to any non-redundant closed-chain manipulator, with the sole limitations imposed by the curse of dimensionality. As opposed to [17], it treats singularities implicitly, not explicitly as obstacles, resulting in a computationally less intensive approach.…”

Section: E Henderson Is With the Numerical Analysis Group In The mentioning

confidence: 99%

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Planning Singularity-Free Paths on Closed-Chain Manipulators

et al. 2013

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Abstract-This paper provides an algorithm for computing singularity-free paths on closed-chain manipulators. Given two non-singular configurations of the manipulator, the method attempts to connect them through a path that maintains a minimum clearance with respect to the singularity locus at all points, which guarantees the controllability of the manipulator everywhere along the path. The method can be applied to non-redundant manipulators of general architecture, and it is resolution-complete. It always returns a path whenever one exists at a given resolution, or determines path non-existence otherwise. The strategy relies on defining a smooth manifold that maintains a one-to-one correspondence with the singularity-free C-space of the manipulator, and on using a higher-dimensional continuation technique to explore this manifold systematically from one configuration, until the second configuration is found. If desired, the method can also be used to compute an exhaustive atlas of the whole singularity-free component reachable from a given configuration, which is useful to rapidly resolve subsequent planning queries within such component, or to visualize the singularity-free workspace of any of the manipulator coordinates.Examples are included that demonstrate the performance of the method on illustrative situations.

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Section: E Henderson Is With the Numerical Analysis Group In The mentioning

confidence: 99%

Section: E Henderson Is With the Numerical Analysis Group In The mentioning

confidence: 99%

Section: E Henderson Is With the Numerical Analysis Group In The mentioning

confidence: 99%

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Planning Singularity-Free Paths on Closed-Chain Manipulators

et al. 2013

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“…Many scholars have developed different approaches and algorithms to investigate the features of workspace, especially its volume [15][16][17][18][19][20][21][22][23][24][25][26][27]. In [15], the joint workspace of a parallel kinematic machine (PKM) was calculated using the forward kinematic model.…”

Section: Introductionmentioning

confidence: 99%

“…In [19], the reachable workspace was mapped without considering the joints limits and interferences between links. In [20], the path planning for singularity free route in a reachable workspace which was generated with a generic numerical algorithm was developed. In [21], the configuration optimization of a Delta-type parallel kinematic mechanism called Orthoglide was conducted based on a Cartesian workspace with prescribed kinetostatic performances.…”

Section: Introductionmentioning

confidence: 99%

Workspace Representation and Optimization of a Novel Parallel Mechanism with Three-Degrees-of-Freedom

Gao

Zhang

2011

Sustainability

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Abstract:The development of a new parallel mechanism based on simulation driven design is a rapid approach to discover the unique features or advantages of a conceptual model. In this research, one novel parallel mechanism which can generate three degrees-of-freedom translations is proposed. The kinematic model and Jacobian matrix is derived. The workspace generation and mapping is investigated based on simplified boundary searching method. The particle swarm algorithm is applied to search for the optimal volume of workspace.

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Implementation of BFA (Backtrack‐Free path planning Algorithm) for three‐dimensional workspaces and its application to path planning of multi manipulators

Murata

Tamura

Kawai

2011

Elect Comm in Japan

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SUMMARYTogether with a newly developed method for avoiding collisions between links themselves, the BFA (Backtrack-Free path planning Algorithm) has been implemented for calculating the paths of manipulators that are operated in three-dimensional workspaces. An approach to extending the BFA to an algorithm for calculating the paths of multiple manipulators cooperating to accomplish complicated tasks, in which multiple manipulators are considered as a single composite one with many links, is also discussed. The algorithm is backtrack-free and resolution-complete. Its computational volume is proportional to the total number of links and does not change drastically with the environments in which the manipulators are operated. Simulation results have demonstrated that the BFA allows efficient generation of paths for both single and multiple manipulators.

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Workspace generation and planning singularity-free path for parallel manipulators

Cited by 108 publications

References 17 publications

Planning Singularity-Free Paths on Closed-Chain Manipulators

Planning Singularity-Free Paths on Closed-Chain Manipulators

Workspace Representation and Optimization of a Novel Parallel Mechanism with Three-Degrees-of-Freedom

Implementation of BFA (Backtrack‐Free path planning Algorithm) for three‐dimensional workspaces and its application to path planning of multi manipulators

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