What are the formulas for proper first person movement that doesn't cause jarring movement?

It seems that every single built-in movement behavior causes unwanted jarring effects in first person 3D mode, ranging from backwards sliding against walls to jittering to clipping through walls to speed issues.

What are all the proper formulas for safely moving the player relative to the current direction, without these issues occurring?

You probably can improve the situation by disabling the rotation setting with the 8direction behavior. Likely there are other tweaks to be had.

Alternatively here is an event based 8dir like motion using the angle of the sprite. It has turning and strafe with settings for max speed, acceleration and deceleration. For the collision response it considers the player as a perfect circle and uses signed distance fields to allow smooth wall collisions. Basically it gives better collision handling than what usually is done.

dropbox.com/s/3days6yqvdj1t9w/custom_fps_controler.c3p