This project aims to find an optimal tracking path for a vehicle to follow given waypoints. The solution uses IPOPT and CPPAD to overcome this optimization problem. The optimization considers kinematic models of a vehicle and cost functions for given boundiries and coinstraints and produces safe to drive actuation inputs as steering and throttle-braking.
N and dt together arrange that the optimizer considers how many data points in how much time. Choosing N around 10 or more and arraging dt that satisfies N*dt = 1 generally gives sufficient results. Tried combination of N & dt are 10/0.1, 25/0.04 and many others.
Latency is a real-world problem that may encounter due imperfect steering system and nonlinear effects like bushes and tires. In this project Udacity Simulator has been used to simulate latency between simulation and data acquision. 100ms latency has been used which is also good example for passenger and heavy commercial vehicles.
The waypoints are preprocessed to make them in vehicle coordinate system. This calculations are helpful to further simplify calculations by taking x = 0, y = 0, and psi = 0. Later these wayponts fitted to a 3rd degree polynomial cte and epsi are calculated accordingly.