Two robust model predictive control (MPC) schemes are proposed for tracking unicycle robots with input constraint and bounded disturbances: tube-MPC and nominal robust MPC (NRMPC). In tube-MPC, the control signal consists of a control action and a nonlinear feedback law based on the deviation of the actual states from the states of a nominal system. It renders the actual trajectory within a tube centered along the optimal trajectory of the nominal system. Recursive feasibility and input-to-state stability are established and the constraints are ensured by tightening the input domain and the terminal region. In NRMPC, an optimal control sequence is obtained by solving an optimization problem based on the current state, and then the first portion of this sequence is applied to the real system in an open-loop manner during each sampling period. The state of the nominal system model is updated by the actual state at each step, which provides additional feedback. By introducing a robust state constraint and tightening the terminal region, recursive feasibility and input-to-state stability are guaranteed. Simulation results demonstrate the effectiveness of both strategies proposed.