Trajectory tracking control of autonomous trolley collection robots (ATCR) is an ambitious work due to the complex environment, serious noise and external disturbances. This work investigates a control scheme for ATCR subjecting to severe environmental interference. A kinematics model based adaptive sliding mode disturbance observer with fast convergence is first proposed to estimate the lumped disturbances. On this basis, a robust controller with prescribed performance is proposed using a backstepping technique, which improves the transient performance and guarantees fast convergence. Simulation outcomes have been provided to illustrate the effectiveness of the proposed control scheme.