Variational Path Optimization of Linear Pentapods with a Simple Singularity Variety

Published: 22 Jan 2020 | Version 2 | DOI: 10.17632/vhf25xvmdj.2

Description of this data

This file is part of joint work between A. Rasoulzadeh and G. Nawratil at
Center for Geometry and Computational Design (GCD), Vienna University of Technology (TU Wien).
It is created on October 10th, 2019.

‎The class of linear pentapods with a simple singularity variety is obtained by imposing architectural restrictions on the design of a linear pentapod in a way that the manipulator's singularity variety is linear in orientation/position variables‎. ‎It turns out that such a simplification leads to crucial computational advantages while maintaining the machine's applications in some fundamental industrial tasks such as 5-axis milling and laser cutting‎. ‎
‎Assuming that a singularity-free path between a given start‎- ‎and end-pose of the end-effector within the manipulator's workspace‎ is known,‎ an optimization process of this path is proposed in such a way that the robot increases its distance to the singularity loci‎ while the motion is being smoothed‎.
‎In this case the computation time of the optimization is improved as one deals with the pentapods having a simple singularity variety allowing symbolic solutions for the local extrema of the singularity-distance function‎. The whole process is called variational path optimization and takes place ‎through defining a ‎novel ‎‎cost ‎function‎. ‎This optimization process takes the physical limits of prismatic joints and base spherical joints into account‎‎.

In order to use the algorithm please type "variational_path_optimization" in the MATLAB "Command Window". The code then asks the user a range of questions from "architectural aspects of your manipulator" to plot options. For most of these questions the user can simply ignore (if he/she does not wish a very specific optimization or plot) by pressing enter. However some of these questions are obligatory to answer. Therefore we ask the user to type "help variational_path_optimization" in in the MATLAB "Command Window" for a thorough description of his/her available options. Please note that a DEFAULT SETTING is made available for the code by which the user can observe how the algorithm works on a predefined simple pentapod and a predefined singularity-free initial motion (as a sample we recommend using the special curve "twisted"). Finally, if the user has access to MAPLE, then he/she can visualize the full results alongside the shape of the manipulator. In order to do so please run "variational_path_optimization.m" on a case, then execute the files "" and "" consecutively.

NOTE: 9 videos (GIF files) of motions of a sample is provided for you in the folder "Sample Videos".

WARNING: Note that the rest of the MATLAB functions in the folder are just nested functions in the file "variational_path_optimization.m". The help option is also available for all these nested functions which demonstrates their specific role within the main code.

The MATLAB files will be subject to minor updates including a GUI

Experiment data files

  • MATLAB + Maple files

    This folder contains all the MATLAB codes for the "Variational Path Optimization of Linear Pentapods with a Simple Singularity Variety ". The main code to run is "variational_path_optimization.m" and the rest of ".m" files are just the nested functions within. Additionally, to plot high resolution results in MAPLE please execute the worksheets "" and "" consecutively after running "variational_path_optimization.m".

  • Sample Videos

    This folder contains GIF files of a simple pentapod's optimized motion. The files within the folder "animation" show the final optimized motion while the files in the folder "variation" show the learning process in which the manipulator finds the optimized path.

    • Animations
    • Variations

Related links

Latest version

  • Version 2


    Published: 2020-01-22

    DOI: 10.17632/vhf25xvmdj.2

    Cite this dataset

    Rasoulzadeh, Arvin (2020), “Variational Path Optimization of Linear Pentapods with a Simple Singularity Variety”, Mendeley Data, v2


Views: 137
Downloads: 0

Previous versions

Compare to version


Technische Universitat Wien


Joint Kinematics, Kinematics of Mechanism, Geometrical Kinematics, Theoretical Kinematics


CC BY 4.0 Learn more

The files associated with this dataset are licensed under a Creative Commons Attribution 4.0 International licence.

What does this mean?
You can share, copy and modify this dataset so long as you give appropriate credit, provide a link to the CC BY license, and indicate if changes were made, but you may not do so in a way that suggests the rights holder has endorsed you or your use of the dataset. Note that further permission may be required for any content within the dataset that is identified as belonging to a third party.