Google map, not updating based on current location / position
First of all make sure you have turned your GPS (if available) and data connection turned on. This helps the device to get your precise location easily.

When using the app, make sure that you don't touch your devices screen by mistake. This often happens even without you knowing it and causes the map to tilt, losing the automatic center alignment of your current position.

Now open the app and press . Then the map will center to your current location. Then tap the location icon again. Now the location icon should move with you. Tap the location icon again and then it will look like .

Now you should get a more driver friendly view with your location icon moving smoothly. Happy driving!