Trajectory optimization and optimal control of vehicle dynamics under critically stable driving conditions

A method will be presented which not only optimizes the trajectory of a road vehicle but also develops a gain-scheduled feedback controller. A major difficulty when applying this method (known as differential dynamic programming-DDP) to complex systems is the calculation of the first and second derivatives of the system equations. This calculation is here carried out by automatic differentiation, thereby increasing the flexibility and area of application of the DDP algorithm. The control policy was then successfully tested on a multi-body simulation of a road vehicle.