This paper proposes a V-shape Lyapunov function method with application to the design of a control scheme for a mobile robot navigating through multiple obstacles. The proposed design method solves the serious problem of input saturation due to big position errors in the beginning of the control associated with the conventional parabolic Lyapunov function method. The resulting control consists of a trajectory generation scheme and a motion control scheme. The trajectory generation scheme computes the translational and rotational reference velocities in real time that drive the robot to a given goal position while avoiding multiple obstacles. The motion control scheme computes the driving force and rotational torque to track the reference velocities. The nonholonomic constraints of the mobile robot are used in the design of the kinematic trajectory generation scheme, where a repulsive potential function is used for obstacle avoidance. The dynamic model of the robot is used in the design of the motion control scheme. Under certain conditions, the proposed control guarantees asymptotic stability while keeping all internal signals bounded. The effectiveness of the proposed control method has been shown with realistic computer simulations.

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