A dynamic programming approach for the motion control of autonomous vehicles

The problem of 2-dimensional vehicle path following under adversarial behavior is considered. The objective is to keep the cross-track error to the reference path inside a given tolerance interval. The adversarial behavior models system uncertainty and unknown or poorly estimated bounded disturbances. The first step to that objective is the computation of an invariant set, namely the maximal set of states where the following property holds: if the vehicle starts inside the set there exists a control law such that the cross-track will never exceed the tolerance interval. This is done through dynamic programming. Two modes of operation are then considered for the control system: when the vehicle is inside the invariant set, the objective is to stay inside it while minimizing a combination of the actuation effort and cross-track error; otherwise, the objective becomes to reach the invariant set in minimum time. Each mode corresponds to a different optimal control problem which is dealt independently thus leading to a specific control law.