Does anyone else find it irritating/interesting that the racetrack in problem 5-4 is impossible to follow in real life? The driver would have to instantaneously adjust the steering wheel at the join points between the arcs and the edges.
Edit: This is a point that civil engineers are very conscious of. The transition between an arc and a straight segment of road must follow a spiral.
You're right, it's an impossible implementation: in real life, you would find that your errors would be larger (CTE) so your response would be amplified (steer more to correct the error). So really, the way we modeled the robot's reaction is not right. To make it more accurate, we would have to model the maximum delta steering / delta time. And we should model a much smaller delta t. :)
For the purposes of what we're doing here, it gets the theory introduced. Perhaps you might post the question to the office hours thread - how can we more accurately model the robot's response to the CTE?
answered 22 Mar '12, 12:33