I think what you are looking for is running docker engine as non-root but without using root access. For this you will have to add it to docker group:
But before that you will have to create a docker group if it already does not there :
$ sudo groupadd docker
Then add the user you are using to this docker group.
$ sudo usermod -aG docker $USER
then Logout and then login again and then run docker
$ newgrp docker
You will now be able to use docker commands without typing sudo.
Hope that helps :)
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