This paper develops a unified framework for point stabilization and tracking control of differential drive robots under hard input constraints. The proposed control strategy is based on the recently introduced Pointwise Angle Minimization method and addresses the steering problem by studying a robot's achievable directions of motion considering the constraints imposed on it. To illustrate the strength of the proposed framework, a new control problem which combines the posture stabilization and tracking control is studied. The problem of interest is steering a constrained-input mobile robot from an initial point towards a final point on a desired trajectory while regulating the robot's heading such that the control convergence is guaranteed within the admissible input space. Inspired by the geometry of sliding mode control, this paper proposes a new control strategy for this problem. The stability of the closed loop system under the proposed steering scheme is proved by Lyapunov analysis for the shortest path trajectory and generalization to the case of arbitrarily chosen desired trajectory has been proposed. Finally, effectiveness of the discussed control strategies are illustrated by several simulation results.
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