Hello All, I only have a vary basic understanding of physical concepts so please bear with me. I'm an object with mass greater than 0, a maximum speed, a maximum rate of acceleration and deceleration. Suppose I want to travel from point A to point B. The path is chosen for me and it leads through point C (the red path in the image below). I need to stay on the chosen path (primary goal) And also, I wish to maintain a target constant speed k for as much of my travel time as possible and try not go too much below k unless I am at point A or point B (primary goal). I also wish to avoid rapid changes in acceleration because it takes a large amount of energy for me to accelerate and decelerate to my target speed and just makes me nauseous in general (secondary goal). The red path is safe for me to travel on (it is clear of debris and patrol cars) I don't necessarily like it because when I get to point C, I will need to decrease my speed to 0, turn, then work my way up to the desired speed k again (that conflicts with one of my goals). Otherwise I would overshoot my path and get a couple of bruises (that also conflicts with the other one of my goals). I have an opportunity to modify my path of travel a little bit so that I have a better chance of reaching my goals (maximize my chances of staying on the path, maximize the time I spend traveling at my target speed k, avoid jerking - I want to have as smooth of a ride as possible) but I don't want to stray away from the red path too much (think of a Hausdorff distance restriction). Given a max distance D by which I can stray from the red path, is it possible to alter the red path so that I have a better chance of achieving my goals? What physical properties do I desire my new path (curve) to have? Is there anything that makes the green or blue paths more suitable for me to travel on? My intuition tells me yes but I can't quite put my finger on it (they may not be the most optimal paths for achieving my goals). (if D is large enough, I will probably get away with traveling from A to B in straight line but that would be very rare) Your thoughts appreciated! I apologize if this is all a little to vague. Thanks!