This approach is familiar with the people in CNC machining: the CNC bit is carving a path on a metal surface. Characteristic to this process are some terms: feedrate - this is actually the speed at which the metal is "plowed" by the rotating head of the tool and direction of advance - this is your vector indicating the direction the bit will advance from its current position.
There are some common-sense limitations: the faster the metal is eaten away, the less the change in the advance direction. Again, imagine a car through a curve. If it's going slowly, it can negotiate quite tight corners, while when it's going fast, it cannot without straying from that curve and leaving the road which spells disaster.
Your problem is 100% depicting these scenarios. The mathematical skills you need involve the cross product (rotate the current advance direction to allow the object to home in on a target), axis-angle rotation and a transfer function (which is nothing more than a function that decreases with the speed of the object and tells how big your cone's angle is - just like a tolerance).
Some fast details:
- the discrete case involves a currentPosition, a targetPosition, a speed and a maxTurnAngle plus the currentDir (current direction of advance)
- at each step you compute the angle between crrentDir and targetPosition - currentPosition. This angle tells you by how much you should rotate currentDir to make the object go toward the target. Now you know your maxTurnAngle and you would like an estimate for how much you can turn. The idea is to safely divide the maxTurnAngle by an amount proportional to your speed. Then rotate currentDir against the cross product of currentDir and tgt - pos by that scaled angle. That should give you an idea.