A DYNAMIC PROGRAMMING BASED PATH-FOLLOWING CONTROLLER FOR AUTONOMOUS VEHICLES

The problem of path following for autonomous vehicles under adversarial behaviour is considered. The objective is to keep the cross-track error to the reference path inside a given tolerance interval. The adversarial behaviour models system uncertainty and unknown or poorly estimated bounded disturbances to ensure that the concept of weakly invariant set is used, i.e., the set of states that the vehicle may enter while ensuring that the cross-track error will never exceed the tolerance interval. 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, there is one different control law for each mode. The control laws are synthesized using a dynamic programming approach. Simulation results with a full nonlinear dynamical model illustrate the performance and robustness of the control strategy.