A nonlinear optimal control approach for the truck and N-trailer robotic system

Truck and N-trailer mobile robots find use in freight transportation, urban transportation, mining as well as in agriculture. The article proposes a nonlinear optimal (H-infinity) control approach for the truck and N-trailer robotic system. The method has been successfully tested so far on the control problem of several types of robotic vehicles and here it is shown that it can also provide an optimal solution to the control problem of the underactuated truck and N-trailer mobile robot. To implement this control scheme, the state-space description of the kinematic model of the truck and N-trailer robotic system undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is designed. To select the feedback gains of the optimal (H-infinity) controller an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. Finally, to implement state estimation-based feedback control, the H-infinity Kalman Filter is used as a robust state estimator.