Stutters might indicate some network lag, either between the trainer and computer, or with the WiFi signal and possibly the internet service to your building.
I took the liberty of looking at what our server logged from today’s (Dec 23) session, and noticed some odd behavior.
There are 9 separate login/ logouts starting at 10:59am UTC to 18:20pm. Most of them last only a couple of minutes (as though you were just testing something out), but two of them are long enough that you were actually riding. These short login/logouts that lasted a few minutes - was that intentional? If not, you may have network connectivity issues: either with the WiFi inside your home, or possibly with the internet connection to your ISP.
Of those two sessions that lasted long enough to be actual rides
A. During the morning session: your ANT USB stick was connected, and also the Kickr’s power, cadence, controllable and heart rate sensors
B. During the evening session, your ANT USB stick was connected, also your Kickr’s power and controllable. But no heart rate or cadence sensor was connected. Was that an intentional choice? If no, it might indicate a problem with your ANT+ signal between your trainer and your PC.
Tell us which ANT USB stick you have?
We have a couple of articles on support.zwift.com that cover some troubleshooting steps with ANT+.
Issues with Zwift Finding your USB ANT dongle
BLE vs ANT+ Interference Troubleshooting Steps