A Nonlinear Optimal Control Approach for Tracked Mobile Robots

Abstract

The article proposes a nonlinear optimal (H-infinity) control approach for the model of a tracked robotic vehicle. The kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of the tracks with the ground. To solve the related control problem, the dynamic model of the vehicle undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the vehicle. For the approximately linearized description of the tracked vehicle a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control, that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs.