Nonlinear optimal control for autonomous navigation of a truck and trailer system

Abstract

A solution to the problem of autonomous navigation of a truck and trailer system is developed using a nonlinear optimal control method. The kinematic model of the autonomous vehicle undergoes linearization through Taylor series expansion. The linearization is performed at a temporary operating point (equilibrium) that is re-computed at each time instant using the present value of the state vector and the last value of the control inputs vector. The linearization is based on the Jacobian matrices of the model. For the linearized equivalent model of the truck and trailer system an H-infinity feedback controller is designed. The feedback control gain is obtained from the solution of an algebraic Riccati equation at each iteration of the control algorithm. The stability of the control loop is proven with Lyapunov analysis. It is demonstrated that the control loop exhibits the H-infinity tracking performance which signifies elevated robustness against modelling errors and external disturbances. Moreover, under moderate conditions the global asymptotic stability of the control loop is assured. Finally, to implement state estimation-based control for the autonomous vehicle, through the processing of a small number of sensor measurements, the H-infinity Kalman Filter is proposed.