Adaptive model predictive control for an omnidirectional mobile robot with friction compensation and incremental input constraints

In this paper, an adaptive model predictive control (MPC) scheme with friction compensation, subject to incremental control input constraints and parameter uncertainties, is proposed for a three-wheeled omnidirectional mobile robot (OMR). The proposed control framework is in a cascaded structure, wherein the outer-loop is kinematic-based control and the inner-loop is designed based on adaptive linear MPC. First, a complex nonlinear dynamic model of the OMR in the world coordinate frame is transformed and partially linearized into a reduced nonlinear model in the moving coordinate system. The nonlinearity of the reduced model only arises from Coulomb friction. Then an estimated system is established for the reduced nonlinear system, with an adaptive update law estimating the system uncertain parameters. To facilitate the linear MPC design, part of the control efforts is derived by feedback compensation of the Coulomb friction forces, resulting in a linear estimated system. The other part is designed by a constrained linear MPC. Feasibility and stability analyses are given for the proposed adaptive MPC scheme. Finally, experimental comparisons with model-based MPC are carried out to verify the effectiveness of the proposed control scheme.