I feel there should be a difference where a moving surface facilitates your walking and when the surface is moved under the feet (non-motorised treadmill) and ground. Is there any research in this area.
There is a difference although it is hard to talk directly about energy expenditure without proper literature done on the subject. Muscle activation is somewhat different so enery expenditure must also be different. This is an example of muscle activation patterns in comparison of overground and treadmill walking ( http://jap.physiology.org/highwire/markup/46645/expansion?width=1000&height=500&iframe=true&postprocessors=highwire_figures%2Chighwire_math). You can see that some interesting activation patterns emerge (e.g. hamstrings show higher level of activity during the first part of the swing in overground walking but lower activity in the final part ). There is some data on kinematic parameters and muscle activation that might help you with your work.
I did expect a difference between on ground walking and motorised treadmill walking. From your answer I understand that the evidence on energy expenditure is not established.
Yes, there is a difference. About 5 years ago a colleague in our lab did some work with a NMT and compared it to a MT. The EE was higher on the NMT but the RPE was the same at matched speeds. They did not look at overground walking. I will see if it was published, I know that was the intent. Are you looking to do research on this topic?
Your question is really interesting and the answers are too! I just want to suggest you some publications from Su-Kyoung Lee and collegues that report some changes in muscles activity changing also variables like inclination or speed of the treadmill and weight loading.
Hoping it is usefull to you i wish you a great day!
Giacomo
Article The Effect of a Vertical Load on Gluteus Medius Activity and...
Article Muscle Activity of the Gluteus Medius at Different Gait Speeds
My common sense says that motorized treadmill will be least followed by level ground walking and non motorized treadmill will be the most energy consuming activity. this can be checked by HR instead of RPE in same walking speed in all three condition.