Planning Trajectories Using an Extended Sequential Linearization Algorithm

The development of autonomous driving and driver assistance systems that involve the lateral guidance of the car has the crucial challenge of trajectory calculation. Under the many possible solutions to this problem, the use of a model predictive controller (MPC) is one of the most popular. This article presents a method of calculating a trajectory using an iterative moving time horizon MPC combined with a forwardbackward velocity estimation to guess the initial solution. The discretization in the time domain provides the possibility to easily extend the method for the use with multiple vehicles while the linearization provides very high performance combined with low model complexity. The drawback of the iterative solution which usually would lead to a loss of safety due to possible errors by unfeasible problem formulation is compensated with the efficient guessing of an initial solution. To evaluate the performance of the method it is applied to the problem of global trajectory calculation for autonomous racecars. The presented approach proves to be superior to other methods that only use the geometry of the road while still being able to calculate a global trajectory for a whole circuit. The comparison with other methods like a minimum curvature optimization and the driver of the vehicle simulation program IPG Carmaker shows clear advantages both in terms of lap time and computation time while only using a very simple problem formulation. Also the results show a strong relationship between the driver, the trajectory and the driving performance which is especially relevant to emergency evasive maneuvers where the best use of the potential of the car is crucial for the driver’s safety.