On a conventional receding horizon regulator for a nonholonomic mobile robot

A car-like mobile robot has nonholonomic constraints, and according to Brockett´s theorem, this robot is not asymptotically stabilized by a smooth and time-invariant feedback control law. Receding horizon (RH) control methods for the problem have been proposed by several researchers. They defined several terminal constraints and switched a controller to reach each terminal condition in series. In contrast, we have shown that a conventional RH control method can solve a kind of back-into-garage problem without defining terminal constraints. In the simulations, an obtained trajectory consists of two processes. In the first process a vehicle first moves forward and then turns to the right. In the second process, the vehicle again approaches a target through rearward movement. Although an obtained trajectory consists of two processes and there is discontinuance between the two processes, they need not switching controllers. It is intriguing. The present paper attempts to clarify why the conventional RH control method can solve such a problem. The time history of the cost function indicates that the RH control method finds tentative control inputs around the switching time and then allows the system to move into the second process. An inaccuracy in the obtained optimal solution helps the conventional RH control to solve the problem while it does not degrade the performance of the closed-loop trajectory. The result suggests the possibility that a slightly-inaccurate algorithm for solving an optimal problem solves another similar control problem that requires switching controllers.