The talaria is the name of the winged sandals or shoes famously worn by Hermes in Greek Mythology. If someone were to make a high tech gadget which the attached beating wings to a pair of boots, how exactly would they need to design it to make it fly properly if it could fly at all?
Note: I'm no aerodynamics expert, so the following may be fatally wrong (I believe each fact is correct, just not sure how they interact with each other...)
Looks like all the ingredients are already available in real life:
Take a look at the following real life, working contraptions:
This TED Talk shows how a quad-rotor drone can balance a poll on top of it.
And this TED Talk shows how someone have already built a working jet suite capable of lifting a human - one of the prototypes involved leg jets in addition to arm jets (Ironman style)
Finally, this article about heavy lifting drones includes a crop duster capable of carrying 10kg of payload (can't link to relevant point in article - look for the "DJI Agras MG-1" model).
So, let's say you want to lift a 70kgs human using "winged sandals", you'd basically need something like a couple of stacked crop-dusters shoes, each with around 35kgs of lift (so 3-4 drones in each stack - those are some large boots, but possible). Add the software to balance the "pilot" and accept control commands from his leg movements, and maybe use some jet power instead of / in addition to the wings - and you've got something that may actually work (I think).
Some of the issues you'll need to deal with is power supply, and how close you want these hover-boots to look similar to winged sandals.
In order to fly with some special shoes you don't need very much, except for an high density "fuel" and the strenght and equilibrium of a good gymnast.
As per fuel, high grade fossil fuel is quite mandatory. Jet engines are powerful and small enough to match the requirements. The ironman suit isn't the Stark's masterpiece, the miniaturized arc reactor is. "Endless" amount of energy in a small case: perfect.
The main issue is to control the thrust, you have to be trained and in good shape to sustain your body in whatever position in required to manouvre. It's not mandatory to have also arm-thruster or control surfaces as long as you know what you are doing, as someone do with the flyboard.
They also produce an airborne version, which is more scarying and less funny to see, but it's not limited to a certain height respect to the water.
Lets say you already have really really small wings that flap really really fast. I think your next step is control.
Pushing something longish from one and is inherently unstable. Luckily humans are used to being pushed from their feet up (by the ground). However the ground is always pushes in one and the same direction (opposite the center of the the earth to where gravity is pulling). You cant make those magic flip-flops only produce thrust only upwards because you’ll end up with a rather weird elevator rather than a flying machine kind of thing. You want to be able to angle the thrust. This is significantly easier if you can vary the amount of thrust. Perhaps something like system that detects if there is resistance and only produces thrust when you push actively against it.
Oh, and one more thing. You may want to make those sandals boots for your more “acrobatic” flights. If youtube has told me anything, its that footwear is the first thing that comes of when something goes spectacularly wrong.
Now that i think of it, there are some other items of clothing that one can attach wings to, that perhaps make the task easier.
Stability would be your biggest problem. The pole in the video above is nice and all but it's not a body.
How does your gadget cope if the wearer leans too much and topples? What stops the wearer ending up upside down? It's well saying you have programmed stabilisers which can support you weight, but are they able to stop you moving completely? If they can, what happens if you fall backwards? Your feet can't move so what stops you breaking your ankles or knees? Either you'd need a harness to protect your legs from such a thing or a safety features that allows the device to tip when it senses a fall, or better yet, moves to stop you falling. Then you might be looking at sensors which can be placed on your body so that the device can keep you upright.