This repository is related with my master thesis titled "Redundancy control through Lexicographic SDP".

Based on Peter Corke Robotics Toolbox for Matlab, it contains a framework to generate trajectories for a redundant robot. Each task has its own priority, which will be taken into account when solving the trajectory.

Some tasks are already implemented in a 4-link planar manipulator: pose tracking task (position and orientation), joint limits task as well as an obstacle avoidance task.

A nice exercise to do is to play with the task priorities to check their effect on the trajectory resolution.

You can do this procedure inside a folder of your choice. In order to ease the procedure, we start from the ${HOME} folder.

• Create main folder: cd ${HOME} && mkdir sdpa

• OpenBLAS

  • Download: cd sdpa && git clone https://github.com/xianyi/OpenBLAS.git && cd OpenBLAS
  • Before compiling OpenBLAS, disable the multithread options in Makefile.rule (inside of OpenBLAS folder): Uncomment USE_THREAD = 0
  • Compile and install depending on your system architecture:
    • x32: make BINARY=32 CC=gcc FC=gfortran USE_OPENMP=0 NO_CBLAS=1 NO_WARMUP=1 libs netlib
    • x64: make BINARY=64 CC=gcc FC=gfortran USE_OPENMP=0 NO_CBLAS=1 NO_WARMUP=1 libs netlib
  • Installing gfortran compiler might be necessary: sudo apt-get install gfortran

• SDPA

  • Download: cd sdpa && wget https://sourceforge.net/projects/sdpa/files/sdpa/sdpa_7.3.8.tar.gz --no-check-certificate && tar -xvzf sdpa_7.3.8.tar.gz && rm sdpa_7.3.8.tar.gz

  • Compile:

    cd sdpa_7.3.8 && export CC=gcc && export CXX=g++ && export FC=gfortran && export CFLAGS="-funroll-all-loops" && export CXXFLAGS="-funroll-all-loops" && export FFLAGS="-funroll-all-loops"

    ./configure --prefix=$PWD/../ --with-blas="$PWD/../OpenBLAS/libopenblas.a" --with-lapack="$PWD/../OpenBLAS/libopenblas.a"

    make && sudo make install

• SDPA-Matlab

  • Navigate to the mex folder: cd ${HOME}/sdpa/share/spda/mex

  • Add the following lines to the "Makefile", just before the definition of the variable ALL_INCLUDE:

    MUMPS_INCLUDE = -I${HOME}/sdpa/sdpa-7.3.8/mumps/build/include/

    MUMPS_LIBS = ${HOME}/sdpa/sdpa-7.3.8/mumps/build/lib/libdmumps.a ${HOME}/sdpa/sdpa-7.3.8/mumps/build/lib/libmumps_common.a ${HOME}/sdpa/sdpa-7.3.8/mumps/build/lib/libpord.a

    MPISEQ_LIBS = ${HOME}/sdpa/sdpa-7.3.8/mumps/build/libseq/libmpiseq.a

  • Add the variable ${MPISEQ_LIBS} to the variable ALL_LIBS, so that:

    ALL_LIBS = ${SDPA_LIB} ${MUMPS_LIBS} ${LAPACK_LIBS} ${BLAS_LIBS} ${PTHREAD_LIBS} ${FCLIBS} ${MPISEQ_LIBS}

  • Compile: make

• Download toolbox from here
• Inside Matlab, navigate to the folder where the toolbox file has been downloaded and double-click on the file. It will install automatically.

• Clone the repository in the desired folder: https://github.com/PepMS/SDP_HierarchicalTaskStability.git
• Inside matlab, you can run any of the examples contained inside the folder "examples".