# Quadrotor helicopter control problem

Quadrotor helicopter control problem | |
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State dimension: | 1 |

Differential states: | 6 |

Continuous control functions: | 1 |

Discrete control functions: | 3 |

Interior point equalities: | 6 |

The mixed-integer optimal control problem of a quadrotor helicopter in two dimensions is taken from (Link: Gillula et al.) and from (Link: Vasudevan et al.). The evolution of the quadrotor can be defined with respect to a fixed two dimensional reference frame using six dimensions, where the first three dimensions represent the position along a horizontal axis, the position along the vertical axis, and the roll angle of the helicopter, respectively, and the last three dimensions represent the time derivative of the first three dimensions.

## Mathematical formulation

The mixed-integer optimal control problem is given by

## Parameters

These fixed values are used within the model.

## Reference Solutions

A reference solution can be found in Vasudevan et al. based on the embedding transformation technique for switched systems.

## Variants

There are several alternative formulations and variants of the above problem, in particular

- Quadrotor (binary variant): The quadrotor helicoptor problem, where the continuous control is replaced via partial outer convexification by binary controls.