## Robot Arm Function

### Description:

*Dimensions: 8*

The Robot Arm function, used commonly in neural network papers, models the position of a robot arm which has four segments. While the shoulder is fixed at the origin, the four segments each have length L

_{i}, and are positioned at an angle θ

_{i}(with respect to the horizontal axis), for i = 1, …, 4.

The response is the distance from the end of the robot arm to the origin, on the (u, v)-plane.

### Input Domain:

The input variables and their usual input ranges are:θ_{1} ∈ [0, 2π] |
angle of the first arm segment |

θ_{2} ∈ [0, 2π] |
angle of the second arm segment |

θ_{3} ∈ [0, 2π] |
angle of the third arm segment |

θ_{4} ∈ [0, 2π] |
angle of the fourth arm segment |

L_{1} ∈ [0, 1] |
length of the first arm segment |

L_{2} ∈ [0, 1] |
length of the second arm segment |

L_{3} ∈ [0, 1] |
length of the third arm segment |

L_{4} ∈ [0, 1] |
length of the fourth arm segment |

### Code:

### Reference:

An, J., & Owen, A. (2001). Quasi-regression. *Journal of Complexity, 17*(4), 588-607.

For questions or comments, please email Derek Bingham at: dbingham@stat.sfu.ca.

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