Abstract
In this paper, a model predictive path following control (MPFC) for holonomic mobile robots is considered. The MPFC is aimed to control a mobile robot to follow a geometric path, where the time evolution of the path parameterization is not fixed a priori. Instead, the time evolution is considered as an extra degree of freedom of the controller. Contrary to previous works, in this study, the closed-loop asymptotic stability of holonomic mobile robots under MPFC without terminal constraints or costs is rigorously proven and a stabilizing-horizon length is calculated. The analysis is based on verifying the cost-controllability assumption by deriving an upper bound of the MPFC value function with a finite prediction horizon. Then, using this bound, the length of a stabilizing prediction horizon is calculated. The analysis is performed in the discrete time settings and theoretical results are verified with numerical simulations as well as implementations on an actual mobile robot.
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