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This paper establishes the three-wheel mobile robot kinematics model based on the research on its structure and working principle. A novel algorithm is developed for the trajectory tracking and posture stabilization of three-wheel mobile robot using contractive model, which address stability by adding terminal state penalties in the performance index and imposing constraints on the terminal state, it can predict future system behavior and penalize the system tracking error and the control effort. Intensive experiments studies have been made to check validity of the proposed algorithm. The results show that the control algorithm has the capability of simultaneous trajectory tracking and stabilization.