Informed Sampling-based Collision Avoidance with Least Deviation from the Nominal Path

This paper addresses local path re-planning for $n$-dimensional systems by introducing an informed sampling scheme and cost function to achieve collision avoidance with minimum deviation from an (optimal) nominal path. The proposed informed subset consists of the union of ellipsoids along the specified nominal path, such that the subset efficiently encapsulates all points along the nominal path. The cost function penalizes large deviations from the nominal path, thereby ensuring current safety in the face of potential collisions while retaining most of the overall efficiency of the nominal path. The proposed method is demonstrated on scenarios related to the navigation of autonomous marine crafts.