There are plenty of fancy action cams on the market. Not all of them have great video stabilization. The GimbalCam is a 4K camera with a 3-axis gimbal built-in that lets you capture smooth video. It has a 170-degree wide angle view, IP68 waterproof construction, and iOS/Android apps.
The camera records for 2 hours each time. It weighs only 170g. Its anti-shake algorithm can get eliminate every tiny tremble. Sets you back as low as $299.