How can I check if a commit has been updated to my Gazebo?

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You can find the instructions to install Gazebo from source here. In your case, since you want to use a custom branch, the advanced tutorial series should be useful to help you figure out how to pull the specific branch you want.

You may end up doing something like this:

cd <path to osrf/gazebo clone>
hg pull https://bitbucket.org/mingfeisun/gazebo -b default
hg up default
cd build
<usual build instructions>