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This paper proposes a tracking control method for differential-drive wheeled mobile robots with nonholonomic constraints by using a backstepping-like feedback linearization. Unlike previous backstepping controllers for wheeled mobile robots, a backstepping-like feedback control structure is proposed in the form of a cascaded kinematic and dynamic linearization to have a simpler and modular control structure. First, the pseudo commands for the forward linear velocity and the heading direction angle are designed based on kinematics. Then, the actual torque control inputs are designed to make the actual forward linear velocity and heading direction angle follow their corresponding pseudo commands. A stability analysis shows that the tracking errors of the posture (the position and heading direction angle) are globally ultimately bounded and its ultimate bound can be adjusted by the proper choice of control parameters. In addition, numerical simulations for various reference trajectories (e.g., a straight line, a circle, a sinusoidal curve, a spinning trajectory with no forward velocity and a nonzero rotational velocity, a cross-shaped trajectory changing the forward and backward directions, etc.) show the validity of the proposed scheme.
Dongkyoung Chwa (Tue,) studied this question.