I. Introduction
Convergent navigation of a mobile robot refers to a control algorithm that moves the robot from an initial state to a given goal state in an environment, while avoiding obstacles, and guaranteeing finite-time convergence of the closed-loop system to the goal state. The computation time is the main concern in many real-world applications, where a robot needs to avoid slow-moving obstacles, such as people or other mobile robots. Some examples are delivery tasks in offices, hospitals, supermarkets, shop floors, warehouses, and so on. In general, to find the optimal control sequence, one has to optimize over the whole feasible state-input space, which is defined by the geometry of the environment and by the robot dynamics and state-input constraints. In practice, applying the computed optimal control sequence in an open-loop manner would be unwise (or even infeasible), since such a control system could not cope with disturbances (e.g., sudden changes in the environment) or discrepancies between the behavior of the model and the real system. One solution that introduces feedback in the control system and allows for quick reaction to the new conditions is to recompute the optimal control input at each time step over a shifted horizon, i.e., to use the receding horizon control (RHC).