Safe navigation using NMPC based on a K-invariant set and its exploration features
Résumé
This paper presents a framework for safe navigation in cluttered, unknown environments. The control layer employs a new Nonlinear Model Predictive Control (NMPC) framework based on K-invariant sets, which guarantees that the trajectories of nonlinear systems satisfy safety constraints despite the unknown environment. The recursive feasibility is guaranteed by ensuring the existence of a backup trajectory at each sampling instance. The backup trajectories return to Kinvariant sets, which are designed offline but can be parameterized online by leveraging the system's translation and rotation invariance. The planning layer uses an improved convex lifting method, employing the limited information provided by the sensors to find a path. This method is both efficient and exhibits versatile exploration features. It generates an interconnected graph at each computation step, based on which the shortest path to a goal can be extracted, or alternatively, a shortest path to an unexplored region can be identified.
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