### Abstract

Although many algorithms of optimum trajectory planning for manipulators have been proposed, the efficient ones which treat the general cost problem have not necessarily been obtained yet. This paper treats this general trajectory planning problem which includes the optimization of a spatial path. The proposed method is divided into two stages. One is the optimization of time trajectory with a given spatial path. For this part some efficient algorithms have already been proposed. Therefore, we use one of these algorithms in our method. The other is the optimization of the spatial path itself. To consider this problem, we represent the manipulator dynamics using a path parameter ‘s’, and we solve this differential equation as a two-point boundary value problem. In this procedure, the gradient method is used to calculate the improved input torques. The advantages of the proposed method are the following. (1) It is easy to satisfy the given boundary condition because the dynamics is represented by the path parameter ‘s’ which is not directly related to time. (2) The algorithm takes the form of a feasible method, thus we may stop the calculation when we get the desired accuracy of a solution. Finally the proposed method is applied to a manipulator with two links. Numerical results of the example show the effectiveness of this method.

Original language | English |
---|---|

Pages (from-to) | 1881-1886 |

Number of pages | 6 |

Journal | Transactions of the Japan Society of Mechanical Engineers Series C |

Volume | 56 |

Issue number | 527 |

DOIs | |

Publication status | Published - Jan 1 1990 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering
- Industrial and Manufacturing Engineering

### Cite this

*Transactions of the Japan Society of Mechanical Engineers Series C*,

*56*(527), 1881-1886. https://doi.org/10.1299/kikaic.56.1881

**An Algorithm of Near-Optimum Trajectory Planning for Manipulators.** / Yamamoto, Motoji; Marushima, Shinya; Mohri, Akira.

Research output: Contribution to journal › Article

*Transactions of the Japan Society of Mechanical Engineers Series C*, vol. 56, no. 527, pp. 1881-1886. https://doi.org/10.1299/kikaic.56.1881

}

TY - JOUR

T1 - An Algorithm of Near-Optimum Trajectory Planning for Manipulators

AU - Yamamoto, Motoji

AU - Marushima, Shinya

AU - Mohri, Akira

PY - 1990/1/1

Y1 - 1990/1/1

N2 - Although many algorithms of optimum trajectory planning for manipulators have been proposed, the efficient ones which treat the general cost problem have not necessarily been obtained yet. This paper treats this general trajectory planning problem which includes the optimization of a spatial path. The proposed method is divided into two stages. One is the optimization of time trajectory with a given spatial path. For this part some efficient algorithms have already been proposed. Therefore, we use one of these algorithms in our method. The other is the optimization of the spatial path itself. To consider this problem, we represent the manipulator dynamics using a path parameter ‘s’, and we solve this differential equation as a two-point boundary value problem. In this procedure, the gradient method is used to calculate the improved input torques. The advantages of the proposed method are the following. (1) It is easy to satisfy the given boundary condition because the dynamics is represented by the path parameter ‘s’ which is not directly related to time. (2) The algorithm takes the form of a feasible method, thus we may stop the calculation when we get the desired accuracy of a solution. Finally the proposed method is applied to a manipulator with two links. Numerical results of the example show the effectiveness of this method.

AB - Although many algorithms of optimum trajectory planning for manipulators have been proposed, the efficient ones which treat the general cost problem have not necessarily been obtained yet. This paper treats this general trajectory planning problem which includes the optimization of a spatial path. The proposed method is divided into two stages. One is the optimization of time trajectory with a given spatial path. For this part some efficient algorithms have already been proposed. Therefore, we use one of these algorithms in our method. The other is the optimization of the spatial path itself. To consider this problem, we represent the manipulator dynamics using a path parameter ‘s’, and we solve this differential equation as a two-point boundary value problem. In this procedure, the gradient method is used to calculate the improved input torques. The advantages of the proposed method are the following. (1) It is easy to satisfy the given boundary condition because the dynamics is represented by the path parameter ‘s’ which is not directly related to time. (2) The algorithm takes the form of a feasible method, thus we may stop the calculation when we get the desired accuracy of a solution. Finally the proposed method is applied to a manipulator with two links. Numerical results of the example show the effectiveness of this method.

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U2 - 10.1299/kikaic.56.1881

DO - 10.1299/kikaic.56.1881

M3 - Article

VL - 56

SP - 1881

EP - 1886

JO - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

JF - Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C

SN - 0387-5024

IS - 527

ER -