A dynamic programming approach for the control of autonomous vehicles on planar motion

The problem of path following for autonomous vehicles 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 that the vehicle may enter while ensuring that the cross-track error will never exceed the tolerance interval. This is done through dynamic programming. Two modes of operation are then considered: 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, each mode has a corresponding control law. We discuss efficient ways of computing and implementing those control laws on currently available computational systems. For the purpose of the dynamic programming approach, the autonomous vehicles are modeled as an unicycle. Simulations with a six degree of freedom nonlinear model of an autonomous submarine are performed in order to illustrate the robustness of the control strategy.