Gazebo: Q&A Forum - RSS feedhttp://answers.gazebosim.org/questions/Open source question and answer forum for GazeboenCopyright Askbot, 2010-2011.Fri, 06 Oct 2017 05:42:41 -0500Integrator type in order to solve the differential equationshttp://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/ Hi,
Does anyone know which integrator type (e.g. implicit Euler) is used in Gazebo, respectively ODE, in order to solve the differential equations?
Best
NilsThu, 28 Sep 2017 07:26:28 -0500http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/Answer by Ying Lu for <p>Hi,</p>
<p>Does anyone know which integrator type (e.g. implicit Euler) is used in Gazebo, respectively ODE, in order to solve the differential equations?</p>
<p>Best
Nils</p>
http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?answer=17354#post-id-17354Gazebo uses ODE as physics engine by default and ODE uses [semi-implicit Euler integration](https://en.wikipedia.org/wiki/Semi-implicit_Euler_method).
Bullet uses semi-implicit Euler integration as well. Thu, 28 Sep 2017 18:39:20 -0500http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?answer=17354#post-id-17354Comment by Ying Lu for <p>Gazebo uses ODE as physics engine by default and ODE uses <a href="https://en.wikipedia.org/wiki/Semi-implicit_Euler_method">semi-implicit Euler integration</a>.
Bullet uses semi-implicit Euler integration as well. </p>
http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?comment=17412#post-id-17412You can probably refer to this webpage: http://wiki.ros.org/physics_ode/ODE although the latex display is bad, but you might get an idea.
If you are looking for how the time stepper is working, refer to my thesis here https://foswiki.cs.rpi.edu/foswiki/pub/RoboticsWeb/LabPublications/YLu_thesis.pdf
In chapter 3, From basic equation of motion (3.1), you can jump to equation (3.27) Hopefully section 3.3 in this thesis will give you some reference as wellWed, 04 Oct 2017 11:11:46 -0500http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?comment=17412#post-id-17412Comment by NRottmann for <p>Gazebo uses ODE as physics engine by default and ODE uses <a href="https://en.wikipedia.org/wiki/Semi-implicit_Euler_method">semi-implicit Euler integration</a>.
Bullet uses semi-implicit Euler integration as well. </p>
http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?comment=17366#post-id-17366Hi, thanks for your answer. Do you know where I can find some paper or something else where the integrator type of the ODE is described?Mon, 02 Oct 2017 03:19:38 -0500http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?comment=17366#post-id-17366Answer by josephcoombe for <p>Hi,</p>
<p>Does anyone know which integrator type (e.g. implicit Euler) is used in Gazebo, respectively ODE, in order to solve the differential equations?</p>
<p>Best
Nils</p>
http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?answer=17376#post-id-17376From the ODE manual (https://www.ode-wiki.org/wiki/index.php?title=Manual:_All&printable=yes):
"**ODE uses a first order semi-implicit integrator.** The "semi implicit" means that some forces are calculated as though an implicit integrator is being used, and other forces are calculated as though the integrator is explicit. The constraint forces (applied to bodies to keep the constraints together) are implicit, and the "external" forces (applied by the user, and due to rotational effects) are explicit. Now, inaccuracy in implicit integrators is manifested as a reduction in energy - in other words the integrator damps the system for you. Inaccuracy in explicit integrators has the opposite effect - it increases the system energy. This is why systems simulated with explicit first order integrators can explode."
Searching for *integrator* in the manual turns up other tidbits regarding ODE's integration behavior.Mon, 02 Oct 2017 14:43:45 -0500http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?answer=17376#post-id-17376Answer by NRottmann for <p>Hi,</p>
<p>Does anyone know which integrator type (e.g. implicit Euler) is used in Gazebo, respectively ODE, in order to solve the differential equations?</p>
<p>Best
Nils</p>
http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?answer=17434#post-id-17434Thanks a lot for your answers :)Fri, 06 Oct 2017 05:42:41 -0500http://answers.gazebosim.org/question/17349/integrator-type-in-order-to-solve-the-differential-equations/?answer=17434#post-id-17434