Matrix: VDOL/freeFlyingRobot_10

Description: freeFlyingRobot optimal control problem (matrix 10 of 16)

VDOL/freeFlyingRobot_10 graph
(undirected graph drawing)

VDOL/freeFlyingRobot_10 dmperm of VDOL/freeFlyingRobot_10
scc of VDOL/freeFlyingRobot_10

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  • download as a MATLAB mat-file, file size: 227 KB. Use UFget(2682) or UFget('VDOL/freeFlyingRobot_10') in MATLAB.
  • download in Matrix Market format, file size: 255 KB.
  • download in Rutherford/Boeing format, file size: 217 KB.

    Matrix properties
    number of rows5,218
    number of columns5,218
    structural full rank?yes
    structural rank5,218
    # of blocks from dmperm3
    # strongly connected comp.2
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorB. Senses, A. Rao
    editorT. Davis
    kindoptimal control problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 5218-by-1
    rownamefull 5218-by-101
    mappingfull 5218-by-1


    Optimal control problem, Vehicle Dynamics & Optimization Lab, UF       
    Anil Rao and Begum Senses, University of Florida                                                                  
    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.                            
    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 AMD48,686
    Cholesky flop count6.5e+05
    nnz(L+U), no partial pivoting, with AMD92,154
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD1,782,960
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD3,875,699

    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.