Non-linear optimal control for four-wheel omnidirectional mobile robots

The article proposes a non-linear optimal control approach for four-wheel omnidirectional mobile robots. The method has been successfully tested so-far on the control problem of several types of autonomous ground vehicles and the present article shows that it can also provide the only optimal solution to the control problem of four-wheel omnidirectional robotic vehicles. To implement this control scheme, the state-space model of the robotic vehicle undergoes first approximate linearisation around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the H-infinity controller an algebraic Riccati equation is repetitively 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.