Optimal Path Recovery for a Vehicle Tracking a Circular Reference Trajectory

Preprint, 2010

This paper addresses the problem of path recovery when the speed is too high to permit successful tracking of a circular reference trajectory. The optimal path recovery is formalized as an optimal control problem: to minimize the maximum off-tracking from the desired path. The essential element of the present approach is in the allocation of resultant vehicle forces derived from a simple particle representation. In this case the optimal path recovery is shown to be a classical parabolic trajectory resulting from a constant target acceleration vector. The proposed method yields significantly different outcomes when compared to the more commonly cited yaw moment allocation for understeer mitigation. A performance comparison is made between the two approaches, and the parabolic reference method results in approximately one half the off-tracking of the yaw-moment allocation algorithm. Some generalizations of the problem are also considered, namely non-isotropic friction limits and the use of a spiral reference trajectory.