I've just noticed that you changed your original post adding some extra information. The difference between Edison and Arduino, and the projects that involve BT devices such as PS3/PS4 controllers to control something else are the libraries used. On Internet there are some guides and projects to use a PS3 controller with Arduino but they use libraries designed for the Arduino (AVR architecture) so they hardly work directly with the Edison module because it has a different architecture.
If you want to use a PS3 controller or another kind of BT controller you have to write your own code and libraries, and search for the proper drivers for the device as well. Here are some threads where the users discuss about similar topics, you might find them interesting: