When to move the camera, how to stabilize your video.
There are many reasons not to move the camera much in a 360 video, mostly because you have to remember that the viewer is inside your scene and if the action is unmotivated, it can confuse their vestibular system (and you don't want to make your viewers puke!). What I've learned can be boiled down to:
1) It's safest to keep the camera locked off, on a weighted monopod. This is "vestibular-safe" but without using the parallax from camera movement, can make scenes look less "dimensional" than would be possible otherwise.
2) If you are going to move the camera, the best way to keep your viewer nausea-free is to make sure the movement is motivated. If you're in a moving vehicle, for example, the viewer will expect to be moving. And a great way to keep viewers from being disoriented is to start a shot with the camera unmoving and then slowly begin to move it during the shot. You can then cut to another shot with the camera moving at the same speed, and during that second shot you can slow the movement down to a standstill. From what I've seen on the net, it's best to not jump cut from still to moving, and from moving to still.
3) If you move the camera in an un-motivated way, it's best to keep the movement _very_ slow and steady. The slower the better... you want just enough movement to be able to see parallax changes in the scene.
In general 360 camera movement is so complex because the camera can now see everything around it. In 2D filmmaking you can put the camera on a slider and either stand behind it to move the camera or use a motion-control system to move it for you, but if you did this with 360, you'd see the slider (or jib, or crane or whatever platform you're using) in the shot, which is unacceptable.
One way to move a 360 camera in a similar way with nobody being in the shot is to use a robotic rover, like this one. Of course these are expensive, and not super flexible as you need a fairly level and relatively smooth surface to shoot from. That said, this method can be very effective. Cost for one of these is between $2,000-6,000 (and you can find a list of options here on the 360HIPPO website.) Of course in addition to the moving platform you'll need a gimbal or gyro to support the camera in a stable way. The image below (showing the now-discontinued Nokia OZO camera) illustrates how a Kenyon Labs gyro can be used, but a more general-purpose method would be to use a gimbal made specifically for 360 cameras, like the Tarzan or Moza Air 360 gimbal. These can be either used handheld or mounted on a robotic platform. More information about gimbal options is available here on the 360HIPPO website.
The least expensive way to move the camera smoothly is with a hand-held gimbal, such as the Moza Guru 360 Air ($699, for larger cameras weighing up to 3.3lbs) and the Mozo 360 Air ($299, for small consumer cameras weighing up to 250gms). Of course when you're carrying a 360 camera on a gimbal you'll be in the shot (compared to mounting the gimbal on a rover directly beneath the camera). That will work in some cases (tours, for example), but in narrative films it's unlikely that you'll want to be in the "frame". This issue of how to move a 360 camera smoothly, essentially mimicking a traditional 2D slider shot, is an expensive and complex challenge with immersive filmmaking, since building out a full RC rig can cost as much as $8-$10,000. That said, there are people using less-expensive RC platforms with inexpensive but capable consumer cameras (such as the GoPro Fusion) for much less, and getting very effective footage. This blog post from 360 Labs has quite a bit of detail regarding their efforts at a DIY solution.
I've just purchased a GoPro Fusion 5.2k 360 camera, which provides for very smooth stabilization using the gyro/accelerometer data in the camera and then decoding that (and reversing out the movements) with their GoPro Fusion Studio software. I'll be writing more about that, and about my efforts to mount the Fusion on my Mavic Pro drone, in future posts.
Here's an example of ways to subtly move the camera with a rover vehicle as shown above, starting at about 1:20 into the piece. The camera is moving very slowly, eliminating any chance that the viewer's vestibular system would be overloaded by the movement but still providing lots of 3D depth to the scene through the use of moving parallax.
Here's an extreme example of a 360 video that moves the (virtual) camera in ways that would cause nausea in many viewers. That said, this computer-generated piece by the Dalí museum is an awesome foray into the art of Salvador Dalí.