An Exact Solver for Geometric Constraints with Inequalities

[Mark Szlazak]

An Exact Solver for Geometric Constraints with Inequalities (2017)

Abstract
—CAD/CAM approaches have been used in the manufacturing industry for a long time, and their use in robotic systems is becoming more popular. One common element in these approaches is the use of geometric constraints to define relative object poses. Hence, approaches for solving these geometric constraints are critical to their performance. In this work, we present an exact solver for geometric constraints. Our approach is based on mathematical models of constraints and geometric properties of constraint nullspaces. Our constraint solver supports non-linear constraints with inequalities, and also mixed transformation manifolds, i.e., cases where the rotation and translation components of the constraints are not independent. Through several applications, we show how inequality constraints and mixed transformation manifolds increase the expressive power of constraint-based task definitions. The exact solver provides repeatable solutions with deterministic runtimes and our experiments show that it is also much faster than comparable iterative solvers.

http://www.i6.in.tum.de/Main/Publicatio ... i2017a.pdf

[Mark Szlazak]

There are several limitations to our approach that can form directions for future work. Firstly, we have studied constraint definitions only between a small set of primitive shapes. Extending this to generalized and more complex descriptors such as B-Splines or Bezier curves, in order to support the full B-REP standard is not trivial.

Secondly, the number of constraint combination rules required to cover all corner cases can be relatively large and cumbersome to implement. This is especially relevant for our approach since the addition of inequalities to the combination rules presented in [1] already significantly increased the number of combination cases.

So we wait to see what future research brings!

[chrisb]

Are you one of the authors?

[Mark Szlazak]

Are you one of the authors?

Intriguing idea !

[fosselius]

Are you one of the authors?

Authors are:
Nikhil Somani, Markus Rickert, Alois Knoll

Google authors and github and found this:
https://github.com/nsomani/constraint-c ... er-library

[chrisb]

Are you one of the authors?

Authors are:
Nikhil Somani, Markus Rickert, Alois Knoll

I had seen the authors, but it said nowhere: "Markus Rickert is not Mark Szlazak" nor did it for the other authors.

[Mark Szlazak]

Are you one of the authors?

Authors are:
Nikhil Somani, Markus Rickert, Alois Knoll

I had seen the authors, but it said nowhere: "Markus Rickert is not Mark Szlazak" nor did it for the other authors.

Glad to see you figured that out. If you also mean future publications on the unfinished business mentioned previously then looking to solve that is an interesting idea.

In the mean time. An appendix with a table of positioning relations. This is earlier work referenced by the authors that I initially posted about.
https://www.researchgate.net/profile/En ... ion_detail

[nsomani]

Hi,

I'm an author of this paper. Good to see that you find it interesting! For now, the approach focuses only on some "primitive" shapes. It is not clear to me how this could be done as a closed form solution for generic shape descriptors such as NURBS or B-Rep. This work is an extension of the approach by Rodriguez et al.

Are you interested to integrate this into FreeCAD?

Nikhil

[Mark Szlazak]

Hi,

I'm an author of this paper. Good to see that you find it interesting! For now, the approach focuses only on some "primitive" shapes. It is not clear to me how this could be done as a closed form solution for generic shape descriptors such as NURBS or B-Rep. This work is an extension of the approach by Rodriguez et al.

Are you interested to integrate this into FreeCAD?

Nikhil

Hello. FreeCAD currently has no good assembly workbench that comes with it. There are some interesting preliminary projects going on like the assembly 3 workbench and others more behind the scenes. Apparently there is the topological naming issue to be adequately solved. The new Part Design workbench released with FreeCAD 0.17 has raised concerns about its design that worry some. Maybe these are misplaced concerns. Anyway, I wanted to get my head around solvers used in CAD and post things I find to share with others. Right now I have no time to help any more than that. However, if you are interested then someone called Realthunder and another called ChrisB are working on all this.

[abdullah]

Hi,

I'm an author of this paper. Good to see that you find it interesting! For now, the approach focuses only on some "primitive" shapes. It is not clear to me how this could be done as a closed form solution for generic shape descriptors such as NURBS or B-Rep. This work is an extension of the approach by Rodriguez et al.

Are you interested to integrate this into FreeCAD?

Nikhil

I think it is rather obvious that FreeCAD is interested in having whatever algorithm works well to serve its purpose.

I think the question might be the other way around: Are you interested in using the well established FreeCAD infrastructure to develop your new algorithms and getting the advantage of having such a huge amount of users testing and giving you feedback?

My rationale goes in this direction: If you have a genuine interest and enough funding to make such a solver that starts working well in FreeCAD, the paper you are going to write about it is not going to be your last one. You are going to have so much feedback, relating to corner cases, relating to performance, that you could basically be writing research papers on improvements and further developments for the rest of your life. FreeCAD could be your interface between pure research and actual development. It could be your marketing platform. It could be those big neon lights with your name in for your next job interview...