**Matrix: VDOL/freeFlyingRobot_7**

Description: freeFlyingRobot optimal control problem (matrix 7 of 16)

(undirected graph drawing) |

Matrix properties | |

number of rows | 3,918 |

number of columns | 3,918 |

nonzeros | 31,046 |

structural full rank? | yes |

structural rank | 3,918 |

# of blocks from dmperm | 3 |

# strongly connected comp. | 2 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | B. Senses, A. Rao |

editor | T. Davis |

date | 2015 |

kind | optimal control problem |

2D/3D problem? | no |

Additional fields | size and type |

b | full 3918-by-1 |

rowname | full 3918-by-101 |

mapping | full 3918-by-1 |

Notes:

Optimal control problem, Vehicle Dynamics & Optimization Lab, UF Anil Rao and Begum Senses, University of Florida http://vdol.mae.ufl.edu This matrix arises from an optimal control problem described below. Each optimal control problem gives rise to a sequence of matrices of different sizes when they are being solved inside GPOPS, an optimal control solver created by Anil Rao, Begum Senses, and others at in VDOL lab at the University of Florida. This is one of the matrices in one of these problems. The matrix is symmetric indefinite. Rao, Senses, and Davis have created a graph coarsening strategy that matches pairs of nodes. The mapping is given for this matrix, where map(i)=k means that node i in the original graph is mapped to node k in the smaller graph. map(i)=map(j)=k means that both nodes i and j are mapped to the same node k, and thus nodes i and j have been merged. This matrix consists of a set of nodes (rows/columns) and the names of these rows/cols are given Anil Rao, Begum Sense, and Tim Davis, 2015. VDOL/freeFlyingRobot Free flying robot optimal control problem is taken from Ref.~\cite{sakawa1999trajectory}. Free flying robot technology is expected to play an important role in unmanned space missions. Although NASA currently has free flying robots, called spheres, inside the International Space Station (ISS), these free flying robots have neither the technology nor the hardware to complete inside and outside inspection and maintanance. NASA's new plan is to send new free flying robots to ISS that are capable of completing housekeeping of ISS during off hours and working in extreme environments for the external maintanance of ISS. As a result, the crew in ISS can have more time for science experiments. The current free flying robots in ISS works are equipped with a propulsion system. The goal of the free flying robot optimal control problem is to determine the state and the control that minimize the magnitude of thrust during a mission. The state of the system is defined by the inertial coordinates of the center of gravity, the corresponding velocity, thrust direction, and the anglular velocity and the control is the thrust from two engines. The specified accuracy tolerance of $10^{-6}$ were satisfied after eight mesh iterations. As the mesh refinement proceeds, the size of the KKT matrices increases from 798 to 6078.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 38,463 |

Cholesky flop count | 5.5e+05 |

nnz(L+U), no partial pivoting, with AMD | 73,008 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 1,010,259 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 2,226,224 |

For a description of the statistics displayed above, click here.

*Maintained by Tim Davis, last updated 04-Jun-2015.Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.
*