The “Follow Path” action clip, has a setting called “Look Ahead Distance” in it’s inspector. The smaller the number is, the closer the object will look ahead of the path, while the higher the number the further away. Please try and set this slider to something quite small like 0.01 and let me know if it works for you.
Of course, if you have any more question, don’t hesitate to ask ahead and I will be glad to help!
Thanks!
Gavalakis
